types of problem solving in education

Center for Teaching

Teaching problem solving.

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Tips and Techniques

Expert vs. novice problem solvers, communicate.

Have students identify specific problems, difficulties, or confusions . Don’t waste time working through problems that students already understand.
If students are unable to articulate their concerns, determine where they are having trouble by asking them to identify the specific concepts or principles associated with the problem.
In a one-on-one tutoring session, ask the student to work his/her problem out loud . This slows down the thinking process, making it more accurate and allowing you to access understanding.
When working with larger groups you can ask students to provide a written “two-column solution.” Have students write up their solution to a problem by putting all their calculations in one column and all of their reasoning (in complete sentences) in the other column. This helps them to think critically about their own problem solving and helps you to more easily identify where they may be having problems. Two-Column Solution (Math) Two-Column Solution (Physics)

Encourage Independence

Model the problem solving process rather than just giving students the answer. As you work through the problem, consider how a novice might struggle with the concepts and make your thinking clear
Have students work through problems on their own. Ask directing questions or give helpful suggestions, but provide only minimal assistance and only when needed to overcome obstacles.
Don’t fear group work ! Students can frequently help each other, and talking about a problem helps them think more critically about the steps needed to solve the problem. Additionally, group work helps students realize that problems often have multiple solution strategies, some that might be more effective than others

Be sensitive

Frequently, when working problems, students are unsure of themselves. This lack of confidence may hamper their learning. It is important to recognize this when students come to us for help, and to give each student some feeling of mastery. Do this by providing positive reinforcement to let students know when they have mastered a new concept or skill.

Encourage Thoroughness and Patience

Try to communicate that the process is more important than the answer so that the student learns that it is OK to not have an instant solution. This is learned through your acceptance of his/her pace of doing things, through your refusal to let anxiety pressure you into giving the right answer, and through your example of problem solving through a step-by step process.

Experts (teachers) in a particular field are often so fluent in solving problems from that field that they can find it difficult to articulate the problem solving principles and strategies they use to novices (students) in their field because these principles and strategies are second nature to the expert. To teach students problem solving skills, a teacher should be aware of principles and strategies of good problem solving in his or her discipline .

The mathematician George Polya captured the problem solving principles and strategies he used in his discipline in the book How to Solve It: A New Aspect of Mathematical Method (Princeton University Press, 1957). The book includes a summary of Polya’s problem solving heuristic as well as advice on the teaching of problem solving.

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Don’t Just Tell Students to Solve Problems. Teach Them How.

The positive impact of an innovative UC San Diego problem-solving educational curriculum continues to grow

Daniel Kane - [email protected]

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Not getting stuck

One of the overarching goals of this project is to teach both problem-identification and problem-solving skills that help students avoid getting stuck during the learning process. Stuck feelings lead to frustration – and when it’s a Science, Technology, Engineering and Math (STEM) project, that frustration can lead students to feel they don’t belong in a STEM major or a STEM career. Instead, the UC San Diego curriculum is designed to give students the tools that lead to reactions like “this class is hard, but I know I can do this!” – as Ogo, a celebrated high school biomedical sciences and technology teacher, put it.

Three years into the curriculum development effort, the light-hearted energy of the students combined with their intense focus points to success. On the last day of the class, Mourad Mjahed PhD, Director of the MESA Program at Southwestern College’s School of Mathematics, Science and Engineering came to UC San Diego to see the final project presentations made by his 22 MESA students.

“Industry is looking for students who have learned from their failures and who have worked outside of their comfort zones,” said Mjahed. The UC San Diego problem-solving curriculum, Mjahed noted, is an opportunity for students to build the skills and the confidence to learn from their failures and to work outside their comfort zone. “And from there, they see pathways to real careers,” he said.

What does it mean to explicitly teach problem solving?

This approach to teaching problem solving includes a significant focus on learning to identify the problem that actually needs to be solved, in order to avoid solving the wrong problem. The curriculum is organized so that each day is a complete experience. It begins with the teacher introducing the problem-identification or problem-solving strategy of the day. The teacher then presents case studies of that particular strategy in action. Next, the students get introduced to the day’s challenge project. Working in teams, the students compete to win the challenge while integrating the day’s technique. Finally, the class reconvenes to reflect. They discuss what worked and didn't work with their designs as well as how they could have used the day’s problem-identification or problem-solving technique more effectively.

The challenges are designed to be engaging – and over three years, they have been refined to be even more engaging. But the student engagement is about much more than being entertained. Many of the students recognize early on that the problem-identification and problem-solving skills they are learning can be applied not just in the classroom, but in other classes and in life in general.

Gabriel from Southwestern College is one of the students who saw benefits outside the classroom almost immediately. In addition to taking the UC San Diego problem-solving course, Gabriel was concurrently enrolled in an online computer science programming class. He said he immediately started applying the UC San Diego problem-identification and troubleshooting strategies to his coding assignments.

Gabriel noted that he was given a coding-specific troubleshooting strategy in the computer science course, but the more general problem-identification strategies from the UC San Diego class had been extremely helpful. It’s critical to “find the right problem so you can get the right solution. The strategies here,” he said, “they work everywhere.”

Phan echoed this sentiment. “We believe this curriculum can prepare students for the technical workforce. It can prepare students to be impactful for any career path.”

The goal is to be able to offer the course in community colleges for course credit that transfers to the UC, and to possibly offer a version of the course to incoming students at UC San Diego.

As the team continues to work towards integrating the curriculum in both standardized high school courses such as physics, and incorporating the content as a part of the general education curriculum at UC San Diego, the project is expected to impact thousands more students across San Diego annually.

Portrait of the Problem-Solving Curriculum

On a sunny Wednesday in July 2023, an experiential-learning classroom was full of San Diego community college students. They were about half-way through the three-week problem-solving course at UC San Diego, held in the campus’ EnVision Arts and Engineering Maker Studio. On this day, the students were challenged to build a contraption that would propel at least six ping pong balls along a kite string spanning the laboratory. The only propulsive force they could rely on was the air shooting out of a party balloon.

A team of three students from Southwestern College – Valeria, Melissa and Alondra – took an early lead in the classroom competition. They were the first to use a plastic bag instead of disposable cups to hold the ping pong balls. Using a bag, their design got more than half-way to the finish line – better than any other team at the time – but there was more work to do.

As the trio considered what design changes to make next, they returned to the problem-solving theme of the day: unintended consequences. Earlier in the day, all the students had been challenged to consider unintended consequences and ask questions like: When you design to reduce friction, what happens? Do new problems emerge? Did other things improve that you hadn’t anticipated?

Other groups soon followed Valeria, Melissa and Alondra’s lead and began iterating on their own plastic-bag solutions to the day’s challenge. New unintended consequences popped up everywhere. Switching from cups to a bag, for example, reduced friction but sometimes increased wind drag.

Over the course of several iterations, Valeria, Melissa and Alondra made their bag smaller, blew their balloon up bigger, and switched to a different kind of tape to get a better connection with the plastic straw that slid along the kite string, carrying the ping pong balls.

One of the groups on the other side of the room watched the emergence of the plastic-bag solution with great interest.

“We tried everything, then we saw a team using a bag,” said Alexander, a student from City College. His team adopted the plastic-bag strategy as well, and iterated on it like everyone else. They also chose to blow up their balloon with a hand pump after the balloon was already attached to the bag filled with ping pong balls – which was unique.

“I don’t want to be trying to put the balloon in place when it's about to explode,” Alexander explained.

Asked about whether the structured problem solving approaches were useful, Alexander’s teammate Brianna, who is a Southwestern College student, talked about how the problem-solving tools have helped her get over mental blocks. “Sometimes we make the most ridiculous things work,” she said. “It’s a pretty fun class for sure.”

Yoshadara, a City College student who is the third member of this team, described some of the problem solving techniques this way: “It’s about letting yourself be a little absurd.”

Alexander jumped back into the conversation. “The value is in the abstraction. As students, we learn to look at the problem solving that worked and then abstract out the problem solving strategy that can then be applied to other challenges. That’s what mathematicians do all the time,” he said, adding that he is already thinking about how he can apply the process of looking at unintended consequences to improve both how he plays chess and how he goes about solving math problems.

Looking ahead, the goal is to empower as many students as possible in the San Diego area and beyond to learn to problem solve more enjoyably. It’s a concrete way to give students tools that could encourage them to thrive in the growing number of technical careers that require sharp problem-solving skills, whether or not they require a four-year degree.

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Why Every Educator Needs to Teach Problem-Solving Skills

Strong problem-solving skills will help students be more resilient and will increase their academic and career success .

Want to learn more about how to measure and teach students’ higher-order skills, including problem solving, critical thinking, and written communication?

Problem-solving skills are essential in school, careers, and life.

Problem-solving skills are important for every student to master. They help individuals navigate everyday life and find solutions to complex issues and challenges. These skills are especially valuable in the workplace, where employees are often required to solve problems and make decisions quickly and effectively.

Problem-solving skills are also needed for students’ personal growth and development because they help individuals overcome obstacles and achieve their goals. By developing strong problem-solving skills, students can improve their overall quality of life and become more successful in their personal and professional endeavors.

Problem-Solving Skills Help Students…

develop resilience.

Problem-solving skills are an integral part of resilience and the ability to persevere through challenges and adversity. To effectively work through and solve a problem, students must be able to think critically and creatively. Critical and creative thinking help students approach a problem objectively, analyze its components, and determine different ways to go about finding a solution.

This process in turn helps students build self-efficacy . When students are able to analyze and solve a problem, this increases their confidence, and they begin to realize the power they have to advocate for themselves and make meaningful change.

When students gain confidence in their ability to work through problems and attain their goals, they also begin to build a growth mindset . According to leading resilience researcher, Carol Dweck, “in a growth mindset, people believe that their most basic abilities can be developed through dedication and hard work—brains and talent are just the starting point. This view creates a love of learning and a resilience that is essential for great accomplishment.”

Set and Achieve Goals

Students who possess strong problem-solving skills are better equipped to set and achieve their goals. By learning how to identify problems, think critically, and develop solutions, students can become more self-sufficient and confident in their ability to achieve their goals. Additionally, problem-solving skills are used in virtually all fields, disciplines, and career paths, which makes them important for everyone. Building strong problem-solving skills will help students enhance their academic and career performance and become more competitive as they begin to seek full-time employment after graduation or pursue additional education and training.

Resolve Conflicts

In addition to increased social and emotional skills like self-efficacy and goal-setting, problem-solving skills teach students how to cooperate with others and work through disagreements and conflicts. Problem-solving promotes “thinking outside the box” and approaching a conflict by searching for different solutions. This is a very different (and more effective!) method than a more stagnant approach that focuses on placing blame or getting stuck on elements of a situation that can’t be changed.

While it’s natural to get frustrated or feel stuck when working through a conflict, students with strong problem-solving skills will be able to work through these obstacles, think more rationally, and address the situation with a more solution-oriented approach. These skills will be valuable for students in school, their careers, and throughout their lives.

Achieve Success

We are all faced with problems every day. Problems arise in our personal lives, in school and in our jobs, and in our interactions with others. Employers especially are looking for candidates with strong problem-solving skills. In today’s job market, most jobs require the ability to analyze and effectively resolve complex issues. Students with strong problem-solving skills will stand out from other applicants and will have a more desirable skill set.

In a recent opinion piece published by The Hechinger Report , Virgel Hammonds, Chief Learning Officer at KnowledgeWorks, stated “Our world presents increasingly complex challenges. Education must adapt so that it nurtures problem solvers and critical thinkers.” Yet, the “traditional K–12 education system leaves little room for students to engage in real-world problem-solving scenarios.” This is the reason that a growing number of K–12 school districts and higher education institutions are transforming their instructional approach to personalized and competency-based learning, which encourage students to make decisions, problem solve and think critically as they take ownership of and direct their educational journey.

Problem-Solving Skills Can Be Measured and Taught

Research shows that problem-solving skills can be measured and taught. One effective method is through performance-based assessments which require students to demonstrate or apply their knowledge and higher-order skills to create a response or product or do a task.

What Are Performance-Based Assessments?

With the No Child Left Behind Act (2002), the use of standardized testing became the primary way to measure student learning in the U.S. The legislative requirements of this act shifted the emphasis to standardized testing, and this led to a decline in nontraditional testing methods .

But many educators, policy makers, and parents have concerns with standardized tests. Some of the top issues include that they don’t provide feedback on how students can perform better, they don’t value creativity, they are not representative of diverse populations, and they can be disadvantageous to lower-income students.

While standardized tests are still the norm, U.S. Secretary of Education Miguel Cardona is encouraging states and districts to move away from traditional multiple choice and short response tests and instead use performance-based assessment, competency-based assessments, and other more authentic methods of measuring students abilities and skills rather than rote learning.

Performance-based assessments measure whether students can apply the skills and knowledge learned from a unit of study. Typically, a performance task challenges students to use their higher-order skills to complete a project or process. Tasks can range from an essay to a complex proposal or design.

Preview a Performance-Based Assessment

Want a closer look at how performance-based assessments work? Preview CAE’s K–12 and Higher Education assessments and see how CAE’s tools help students develop critical thinking, problem-solving, and written communication skills.

Performance-Based Assessments Help Students Build and Practice Problem-Solving Skills

In addition to effectively measuring students’ higher-order skills, including their problem-solving skills, performance-based assessments can help students practice and build these skills. Through the assessment process, students are given opportunities to practically apply their knowledge in real-world situations. By demonstrating their understanding of a topic, students are required to put what they’ve learned into practice through activities such as presentations, experiments, and simulations.

This type of problem-solving assessment tool requires students to analyze information and choose how to approach the presented problems. This process enhances their critical thinking skills and creativity, as well as their problem-solving skills. Unlike traditional assessments based on memorization or reciting facts, performance-based assessments focus on the students’ decisions and solutions, and through these tasks students learn to bridge the gap between theory and practice.

Performance-based assessments like CAE’s College and Career Readiness Assessment (CRA+) and Collegiate Learning Assessment (CLA+) provide students with in-depth reports that show them which higher-order skills they are strongest in and which they should continue to develop. This feedback helps students and their teachers plan instruction and supports to deepen their learning and improve their mastery of critical skills.

Explore CAE’s Problem-Solving Assessments

CAE offers performance-based assessments that measure student proficiency in higher-order skills including problem solving, critical thinking, and written communication.

College and Career Readiness Assessment (CCRA+) for secondary education and
Collegiate Learning Assessment (CLA+) for higher education.

Our solution also includes instructional materials, practice models, and professional development.

We can help you create a program to build students’ problem-solving skills that includes:

Measuring students’ problem-solving skills through a performance-based assessment
Using the problem-solving assessment data to inform instruction and tailor interventions
Teaching students problem-solving skills and providing practice opportunities in real-life scenarios
Supporting educators with quality professional development

Get started with our problem-solving assessment tools to measure and build students’ problem-solving skills today! These skills will be invaluable to students now and in the future.

Ready to Get Started?

Learn more about cae’s suite of products and let’s get started measuring and teaching students important higher-order skills like problem solving..

Teaching Problem-Solving Skills

Many instructors design opportunities for students to solve “problems”. But are their students solving true problems or merely participating in practice exercises? The former stresses critical thinking and decision making skills whereas the latter requires only the application of previously learned procedures.

Problem solving is often broadly defined as "the ability to understand the environment, identify complex problems, review related information to develop, evaluate strategies and implement solutions to build the desired outcome" (Fissore, C. et al, 2021). True problem solving is the process of applying a method – not known in advance – to a problem that is subject to a specific set of conditions and that the problem solver has not seen before, in order to obtain a satisfactory solution.

Below you will find some basic principles for teaching problem solving and one model to implement in your classroom teaching.

Principles for teaching problem solving

Model a useful problem-solving method . Problem solving can be difficult and sometimes tedious. Show students how to be patient and persistent, and how to follow a structured method, such as Woods’ model described below. Articulate your method as you use it so students see the connections.
Teach within a specific context . Teach problem-solving skills in the context in which they will be used by students (e.g., mole fraction calculations in a chemistry course). Use real-life problems in explanations, examples, and exams. Do not teach problem solving as an independent, abstract skill.
Help students understand the problem . In order to solve problems, students need to define the end goal. This step is crucial to successful learning of problem-solving skills. If you succeed at helping students answer the questions “what?” and “why?”, finding the answer to “how?” will be easier.
Take enough time . When planning a lecture/tutorial, budget enough time for: understanding the problem and defining the goal (both individually and as a class); dealing with questions from you and your students; making, finding, and fixing mistakes; and solving entire problems in a single session.
Ask questions and make suggestions . Ask students to predict “what would happen if …” or explain why something happened. This will help them to develop analytical and deductive thinking skills. Also, ask questions and make suggestions about strategies to encourage students to reflect on the problem-solving strategies that they use.
Link errors to misconceptions . Use errors as evidence of misconceptions, not carelessness or random guessing. Make an effort to isolate the misconception and correct it, then teach students to do this by themselves. We can all learn from mistakes.

Woods’ problem-solving model

Define the problem.

The system . Have students identify the system under study (e.g., a metal bridge subject to certain forces) by interpreting the information provided in the problem statement. Drawing a diagram is a great way to do this.
Known(s) and concepts . List what is known about the problem, and identify the knowledge needed to understand (and eventually) solve it.
Unknown(s) . Once you have a list of knowns, identifying the unknown(s) becomes simpler. One unknown is generally the answer to the problem, but there may be other unknowns. Be sure that students understand what they are expected to find.
Units and symbols . One key aspect in problem solving is teaching students how to select, interpret, and use units and symbols. Emphasize the use of units whenever applicable. Develop a habit of using appropriate units and symbols yourself at all times.
Constraints . All problems have some stated or implied constraints. Teach students to look for the words "only", "must", "neglect", or "assume" to help identify the constraints.
Criteria for success . Help students consider, from the beginning, what a logical type of answer would be. What characteristics will it possess? For example, a quantitative problem will require an answer in some form of numerical units (e.g., $/kg product, square cm, etc.) while an optimization problem requires an answer in the form of either a numerical maximum or minimum.

Think about it

“Let it simmer”. Use this stage to ponder the problem. Ideally, students will develop a mental image of the problem at hand during this stage.
Identify specific pieces of knowledge . Students need to determine by themselves the required background knowledge from illustrations, examples and problems covered in the course.
Collect information . Encourage students to collect pertinent information such as conversion factors, constants, and tables needed to solve the problem.

Plan a solution

Consider possible strategies . Often, the type of solution will be determined by the type of problem. Some common problem-solving strategies are: compute; simplify; use an equation; make a model, diagram, table, or chart; or work backwards.
Choose the best strategy . Help students to choose the best strategy by reminding them again what they are required to find or calculate.

Carry out the plan

Be patient . Most problems are not solved quickly or on the first attempt. In other cases, executing the solution may be the easiest step.
Be persistent . If a plan does not work immediately, do not let students get discouraged. Encourage them to try a different strategy and keep trying.

Encourage students to reflect. Once a solution has been reached, students should ask themselves the following questions:

Does the answer make sense?
Does it fit with the criteria established in step 1?
Did I answer the question(s)?
What did I learn by doing this?
Could I have done the problem another way?

If you would like support applying these tips to your own teaching, CTE staff members are here to help. View the CTE Support page to find the most relevant staff member to contact.

Fissore, C., Marchisio, M., Roman, F., & Sacchet, M. (2021). Development of problem solving skills with Maple in higher education. In: Corless, R.M., Gerhard, J., Kotsireas, I.S. (eds) Maple in Mathematics Education and Research. MC 2020. Communications in Computer and Information Science, vol 1414. Springer, Cham. https://doi.org/10.1007/978-3-030-81698-8_15
Foshay, R., & Kirkley, J. (1998). Principles for Teaching Problem Solving. TRO Learning Inc., Edina MN. (PDF) Principles for Teaching Problem Solving (researchgate.net)
Hayes, J.R. (1989). The Complete Problem Solver. 2nd Edition. Hillsdale, NJ: Lawrence Erlbaum Associates.
Woods, D.R., Wright, J.D., Hoffman, T.W., Swartman, R.K., Doig, I.D. (1975). Teaching Problem solving Skills.
Engineering Education. Vol 1, No. 1. p. 238. Washington, DC: The American Society for Engineering Education.

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Teaching problem solving

Strategies for teaching problem solving apply across disciplines and instructional contexts. First, introduce the problem and explain how people in your discipline generally make sense of the given information. Then, explain how to apply these approaches to solve the problem.

Introducing the problem

Explaining how people in your discipline understand and interpret these types of problems can help students develop the skills they need to understand the problem (and find a solution). After introducing how you would go about solving a problem, you could then ask students to:

frame the problem in their own words
define key terms and concepts
determine statements that accurately represent the givens of a problem
identify analogous problems
determine what information is needed to solve the problem

Working on solutions

In the solution phase, one develops and then implements a coherent plan for solving the problem. As you help students with this phase, you might ask them to:

identify the general model or procedure they have in mind for solving the problem
set sub-goals for solving the problem
identify necessary operations and steps
draw conclusions
carry out necessary operations

You can help students tackle a problem effectively by asking them to:

systematically explain each step and its rationale
explain how they would approach solving the problem
help you solve the problem by posing questions at key points in the process
work together in small groups (3 to 5 students) to solve the problem and then have the solution presented to the rest of the class (either by you or by a student in the group)

In all cases, the more you get the students to articulate their own understandings of the problem and potential solutions, the more you can help them develop their expertise in approaching problems in your discipline.

Chapter 9: Facilitating Complex Thinking

Problem-solving.

Somewhat less open-ended than creative thinking is problem solving , the analysis and solution of tasks or situations that are complex or ambiguous and that pose difficulties or obstacles of some kind (Mayer & Wittrock, 2006). Problem solving is needed, for example, when a physician analyzes a chest X-ray: a photograph of the chest is far from clear and requires skill, experience, and resourcefulness to decide which foggy-looking blobs to ignore, and which to interpret as real physical structures (and therefore real medical concerns). Problem solving is also needed when a grocery store manager has to decide how to improve the sales of a product: should she put it on sale at a lower price, or increase publicity for it, or both? Will these actions actually increase sales enough to pay for their costs?

Example 1: Problem Solving in the Classroom

Problem solving happens in classrooms when teachers present tasks or challenges that are deliberately complex and for which finding a solution is not straightforward or obvious. The responses of students to such problems, as well as the strategies for assisting them, show the key features of problem solving. Consider this example, and students’ responses to it. We have numbered and named the paragraphs to make it easier to comment about them individually:

Scene #1: A problem to be solved

A teacher gave these instructions: “Can you connect all of the dots below using only four straight lines?” She drew the following display on the chalkboard:

The problem itself and the procedure for solving it seemed very clear: simply experiment with different arrangements of four lines. But two volunteers tried doing it at the board, but were unsuccessful. Several others worked at it at their seats, but also without success.

Scene #2: Coaxing students to re-frame the problem

When no one seemed to be getting it, the teacher asked, “Think about how you’ve set up the problem in your mind—about what you believe the problem is about. For instance, have you made any assumptions about how long the lines ought to be? Don’t stay stuck on one approach if it’s not working!”

Scene #3: Alicia abandons a fixed response

After the teacher said this, Alicia indeed continued to think about how she saw the problem. “The lines need to be no longer than the distance across the square,” she said to herself. So she tried several more solutions, but none of them worked either.

The teacher walked by Alicia’s desk and saw what Alicia was doing. She repeated her earlier comment: “Have you assumed anything about how long the lines ought to be?”

Alicia stared at the teacher blankly, but then smiled and said, “Hmm! You didn’t actually say that the lines could be no longer than the matrix! Why not make them longer?” So she experimented again using oversized lines and soon discovered a solution:

Nine dots in a three-by-three grid, all dots are connected using just four lines. The first line travels through the top-right dot, the center dot, and the bottom-left dot. The second line travels from the the bottom-left dot, through the middle-left dot, and through the top-right dot, then extends past the top-right dot. The third line starts where the second line extended, forming an angle as it passes through the top-middle dot and the middle-right dot. The third line then extends past the right-middle dot until it is even with the bottom of the grid. The fourth line starts where the third line extended, then passes through the bottom-right, bottom-middle, and bottom-left dots. The end result are four lines, three of which form a right triangle with corners extending beyond the three-by-three grid, with the remaining line bisecting the right angle of the triangle so that it passes through the middle and top-right dots.

Scene #4: Willem’s and Rachel’s alternative strategies

Meanwhile, Willem worked on the problem. As it happened, Willem loved puzzles of all kinds, and had ample experience with them. He had not, however, seen this particular problem. “It must be a trick,” he said to himself, because he knew from experience that problems posed in this way often were not what they first appeared to be. He mused to himself: “Think outside the box, they always tell you. . .” And that was just the hint he needed: he drew lines outside the box by making them longer than the matrix and soon came up with this solution:

When Rachel went to work, she took one look at the problem and knew the answer immediately: she had seen this problem before, though she could not remember where. She had also seen other drawing-related puzzles, and knew that their solution always depended on making the lines longer, shorter, or differently angled than first expected. After staring at the dots briefly, she drew a solution faster than Alicia or even Willem. Her solution looked exactly like Willem’s.

This story illustrates two common features of problem solving: the effect of degree of structure or constraint on problem solving, and the effect of mental obstacles to solving problems. The next sections discuss each of these features, and then looks at common techniques for solving problems.

The effect of constraints: well-structured versus ill-structured problems

Problems vary in how much information they provide for solving a problem, as well as in how many rules or procedures are needed for a solution. A well-structured problem provides much of the information needed and can in principle be solved using relatively few clearly understood rules. Classic examples are the word problems often taught in math lessons or classes: everything you need to know is contained within the stated problem and the solution procedures are relatively clear and precise. An ill-structured problem has the converse qualities: the information is not necessarily within the problem, solution procedures are potentially quite numerous, and a multiple solutions are likely (Voss, 2006). Extreme examples are problems like “How can the world achieve lasting peace?” or “How can teachers insure that students learn?”

By these definitions, the nine-dot problem is relatively well-structured—though not completely. Most of the information needed for a solution is provided in Scene #1: there are nine dots shown and instructions given to draw four lines. But not all necessary information was given: students needed to consider lines that were longer than implied in the original statement of the problem. Students had to “think outside the box,” as Willem said—in this case, literally.

When a problem is well-structured, so are its solution procedures likely to be as well. A well-defined procedure for solving a particular kind of problem is often called an algorithm ; examples are the procedures for multiplying or dividing two numbers or the instructions for using a computer (Leiserson, et al., 2001). Algorithms are only effective when a problem is very well-structured and there is no question about whether the algorithm is an appropriate choice for the problem. In that situation it pretty much guarantees a correct solution. They do not work well, however, with ill-structured problems, where they are ambiguities and questions about how to proceed or even about precisely what the problem is about. In those cases it is more effective to use heuristics , which are general strategies—“rules of thumb,” so to speak—that do not always work, but often do, or that provide at least partial solutions. When beginning research for a term paper, for example, a useful heuristic is to scan the library catalogue for titles that look relevant. There is no guarantee that this strategy will yield the books most needed for the paper, but the strategy works enough of the time to make it worth trying.

In the nine-dot problem, most students began in Scene #1 with a simple algorithm that can be stated like this: “Draw one line, then draw another, and another, and another.” Unfortunately this simple procedure did not produce a solution, so they had to find other strategies for a solution. Three alternatives are described in Scenes #3 (for Alicia) and 4 (for Willem and Rachel). Of these, Willem’s response resembled a heuristic the most: he knew from experience that a good general strategy that often worked for such problems was to suspect a deception or trick in how the problem was originally stated. So he set out to question what the teacher had meant by the word line , and came up with an acceptable solution as a result.

Common obstacles to solving problems

The example also illustrates two common problems that sometimes happen during problem solving. One of these is functional fixedness : a tendency to regard the functions of objects and ideas as fixed (German & Barrett, 2005). Over time, we get so used to one particular purpose for an object that we overlook other uses. We may think of a dictionary, for example, as necessarily something to verify spellings and definitions, but it also can function as a gift, a doorstop, or a footstool. For students working on the nine-dot matrix described in the last section, the notion of “drawing” a line was also initially fixed; they assumed it to be connecting dots but not extending lines beyond the dots. Functional fixedness sometimes is also called response set , the tendency for a person to frame or think about each problem in a series in the same way as the previous problem, even when doing so is not appropriate to later problems. In the example of the nine-dot matrix described above, students often tried one solution after another, but each solution was constrained by a set response not to extend any line beyond the matrix.

Functional fixedness and the response set are obstacles in problem representation , the way that a person understands and organizes information provided in a problem. If information is misunderstood or used inappropriately, then mistakes are likely—if indeed the problem can be solved at all. With the nine-dot matrix problem, for example, construing the instruction to draw four lines as meaning “draw four lines entirely within the matrix” means that the problem simply could not be solved. For another, consider this problem: “The number of water lilies on a lake doubles each day. Each water lily covers exactly one square foot. If it takes 100 days for the lilies to cover the lake exactly, how many days does it take for the lilies to cover exactly half of the lake?” If you think that the size of the lilies affects the solution to this problem, you have not represented the problem correctly. Information about lily size is not relevant to the solution, and only serves to distract from the truly crucial information, the fact that the lilies double their coverage each day. (The answer, incidentally, is that the lake is half covered in 99 days; can you think why?)

Strategies to assist problem solving

Just as there are cognitive obstacles to problem solving, there are also general strategies that help the process be successful, regardless of the specific content of a problem (Thagard, 2005). One helpful strategy is problem analysis —identifying the parts of the problem and working on each part separately. Analysis is especially useful when a problem is ill-structured. Consider this problem, for example: “Devise a plan to improve bicycle transportation in the city.” Solving this problem is easier if you identify its parts or component subproblems, such as (1) installing bicycle lanes on busy streets, (2) educating cyclists and motorists to ride safely, (3) fixing potholes on streets used by cyclists, and (4) revising traffic laws that interfere with cycling. Each separate subproblem is more manageable than the original, general problem. The solution of each subproblem contributes the solution of the whole, though of course is not equivalent to a whole solution.

Another helpful strategy is working backward from a final solution to the originally stated problem. This approach is especially helpful when a problem is well-structured but also has elements that are distracting or misleading when approached in a forward, normal direction. The water lily problem described above is a good example: starting with the day when all the lake is covered (Day 100), ask what day would it therefore be half covered (by the terms of the problem, it would have to be the day before, or Day 99). Working backward in this case encourages reframing the extra information in the problem (i. e. the size of each water lily) as merely distracting, not as crucial to a solution.

A third helpful strategy is analogical thinking —using knowledge or experiences with similar features or structures to help solve the problem at hand (Bassok, 2003). In devising a plan to improve bicycling in the city, for example, an analogy of cars with bicycles is helpful in thinking of solutions: improving conditions for both vehicles requires many of the same measures (improving the roadways, educating drivers). Even solving simpler, more basic problems is helped by considering analogies. A first grade student can partially decode unfamiliar printed words by analogy to words he or she has learned already. If the child cannot yet read the word screen , for example, he can note that part of this word looks similar to words he may already know, such as seen or green , and from this observation derive a clue about how to read the word screen . Teachers can assist this process, as you might expect, by suggesting reasonable, helpful analogies for students to consider.

Bassok, J. (2003). Analogical transfer in problem solving. In Davidson, J. & Sternberg, R. (Eds.). The psychology of problem solving. New York: Cambridge University Press.

German, T. & Barrett, H. (2005). Functional fixedness in a technologically sparse culture. Psychological Science, 16 (1), 1–5.

Leiserson, C., Rivest, R., Cormen, T., & Stein, C. (2001). Introduction to algorithms. Cambridge, MA: MIT Press.

Luchins, A. & Luchins, E. (1994). The water-jar experiment and Einstellung effects. Gestalt Theory: An International Interdisciplinary Journal, 16 (2), 101–121.

Mayer, R. & Wittrock, M. (2006). Problem-solving transfer. In D. Berliner & R. Calfee (Eds.), Handbook of Educational Psychology, pp. 47–62. Mahwah, NJ: Erlbaum.

Thagard, R. (2005). Mind: Introduction to Cognitive Science, 2nd edition. Cambridge, MA: MIT Press.

Voss, J. (2006). Toulmin’s model and the solving of ill-structured problems. Argumentation, 19 (3), 321–329.

Educational Psychology. Authored by : Kelvin Seifert and Rosemary Sutton. Located at : https://open.umn.edu/opentextbooks/BookDetail.aspx?bookId=153 . License : CC BY: Attribution

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Problem-Based Learning Clearinghouse of Activities, University of Delaware

Problem-Based Learning

Problem-based learning  (PBL) is a student-centered approach in which students learn about a subject by working in groups to solve an open-ended problem. This problem is what drives the motivation and the learning. 

Why Use Problem-Based Learning?

Nilson (2010) lists the following learning outcomes that are associated with PBL. A well-designed PBL project provides students with the opportunity to develop skills related to:

Working in teams.
Managing projects and holding leadership roles.
Oral and written communication.
Self-awareness and evaluation of group processes.
Working independently.
Critical thinking and analysis.
Explaining concepts.
Self-directed learning.
Applying course content to real-world examples.
Researching and information literacy.
Problem solving across disciplines.

Considerations for Using Problem-Based Learning

Rather than teaching relevant material and subsequently having students apply the knowledge to solve problems, the problem is presented first. PBL assignments can be short, or they can be more involved and take a whole semester. PBL is often group-oriented, so it is beneficial to set aside classroom time to prepare students to  work in groups  and to allow them to engage in their PBL project.

Students generally must:

Examine and define the problem.
Explore what they already know about underlying issues related to it.
Determine what they need to learn and where they can acquire the information and tools necessary to solve the problem.
Evaluate possible ways to solve the problem.
Solve the problem.
Report on their findings.

Getting Started with Problem-Based Learning

Articulate the learning outcomes of the project. What do you want students to know or be able to do as a result of participating in the assignment?
Create the problem. Ideally, this will be a real-world situation that resembles something students may encounter in their future careers or lives. Cases are often the basis of PBL activities. Previously developed PBL activities can be found online through the University of Delaware’s PBL Clearinghouse of Activities .
Establish ground rules at the beginning to prepare students to work effectively in groups.
Introduce students to group processes and do some warm up exercises to allow them to practice assessing both their own work and that of their peers.
Consider having students take on different roles or divide up the work up amongst themselves. Alternatively, the project might require students to assume various perspectives, such as those of government officials, local business owners, etc.
Establish how you will evaluate and assess the assignment. Consider making the self and peer assessments a part of the assignment grade.

Nilson, L. B. (2010). Teaching at its best: A research-based resource for college instructors (2nd ed.).  San Francisco, CA: Jossey-Bass. 

Educational leaders’ problem-solving for educational improvement: Belief validity testing in conversations

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Published: 01 October 2021
Volume 24 , pages 133–181, ( 2023 )

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Claire Sinnema ORCID: orcid.org/0000-0002-6707-6726 1 ,
Frauke Meyer 1 ,
Deidre Le Fevre 1 ,
Hamish Chalmers 1 &
Viviane Robinson 1

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Educational leaders’ effectiveness in solving problems is vital to school and system-level efforts to address macrosystem problems of educational inequity and social injustice. Leaders’ problem-solving conversation attempts are typically influenced by three types of beliefs—beliefs about the nature of the problem, about what causes it, and about how to solve it. Effective problem solving demands testing the validity of these beliefs—the focus of our investigation. We analyzed 43 conversations between leaders and staff about equity related problems including teaching effectiveness. We first determined the types of beliefs held and the validity testing behaviors employed drawing on fine-grained coding frameworks. The quantification of these allowed us to use cross tabs and chi-square tests of independence to explore the relationship between leaders’ use of validity testing behaviors (those identified as more routine or more robust, and those relating to both advocacy and inquiry) and belief type. Leaders tended to avoid discussion of problem causes, advocate more than inquire, bypass disagreements, and rarely explore logic between solutions and problem causes. There was a significant relationship between belief type and the likelihood that leaders will test the validity of those beliefs—beliefs about problem causes were the least likely to be tested. The patterns found here are likely to impact whether micro and mesosystem problems, and ultimately exo and macrosystem problems, are solved. Capability building in belief validity testing is vital for leadership professional learning to ensure curriculum, social justice and equity policy aspirations are realized in practice.

Addressing inequity and underachievement: Intervening to improve middle leaders’problem-solving conversations

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This study examines the extent to which leaders, in their conversations with others, test rather than assume the validity of their own and others’ beliefs about the nature, causes of, and solutions to problems of teaching and learning that arise in their sphere of responsibility. We define a problem as a gap between the current and desired state, plus the demand that the gap be reduced (Robinson, 1993 ). We position this focus within the broader context of educational change, and educational improvement in particular, since effective discussion of such problems is central to improvement and vital for addressing issues of educational equity and social justice.

Educational improvement and leaders’ role in problem solving

Educational leaders work in a discretionary problem-solving space. Ball ( 2018 ) describes discretionary spaces as the micro level practices of the teacher. It is imperative to attend to what happens in these spaces because the specific talk and actions that occur in particular moments (for example, what the teacher says or does when one student responds in a particular way to his or her question) impact all participants in the classroom and shape macro level educational issues including legacies of racism, oppression, and marginalization of particular groups of students. A parallel exists, we argue, for leaders’ problem solving—how capable leaders are at dealing with micro-level problems in the conversational moment impacts whether a school or network achieves its improvement goals. For example, how a leader deals with problems with a particular teacher or with a particular student or group of students is subtly but strongly related to the solving of equity problems at the exo and macro levels. Problem solving effectiveness is also related to challenges in the realization of curriculum reform aspirations, including curriculum reform depth, spread, reach, and pace (Sinnema & Stoll, 2020b ).

The conversations leaders have with others in their schools in their efforts to solve educational problems are situated in a broader environment which they both influence and are influenced by. We draw here on Bronfonbrenner’s ( 1992 ) ecological systems theory to construct a nested model of educational problem solving (see Fig. 1 ). Bronfenbrenner focused on the environment around children, and set out five interrelated systems that he professed influence a child’s development. We propose that these systems can also be used to understand another type of learner—educators, including leaders and teachers—in the context of educational problem solving.

Nested model of educational problem solving

Bronfenbrenner’s ( 1977 ) microsystem sets out the immediate environment, parents, siblings, teachers, and peers as influencers of and influenced by children. We propose the micro system for educators to include those they have direct contact with including their students, other teachers in their classroom and school, the school board, and the parent community. Bronfenbrenner’s meso system referred to the interactions between a child’s microsystems. In the same way, when foregrounding the ecological system around educators, we suggest attention to the problems that occur in the interactions between students, teachers, school leaders, their boards, and communities. In the exo system, Bronfenbrenner directs attention to other social structures (formal and informal), which do not themselves contain the child, but indirectly influence them as they affect one of the microsystems. In the same way, we suggest educational ministries, departments and agencies function to influence educators. The macro system as theorized by Bronfenbrenner focuses on how child development is influenced by cultural elements established in society, including prevalent beliefs, attitudes, and perceptions. In our model, we recognise how such cultural elements of Bronfenbrenner’s macro system also relate to educators in that dominant and pervasive beliefs, attitudes and perceptions create and perpetuate educational problems, including those relating to educational inequity, bias, racism, social injustice, and underachievement. The chronosystem, as Bronfenbrenner describes, shows the role of environmental changes across a lifetime, which influences development. In a similar way, educators′ professional transitions and professional milestones influence and are influenced by other system levels, and in the context of our work, their problem solving approaches.

Leaders’ effectiveness in discussions about problems related to the micro and mesosystem contributes greatly to the success of exosystem reform efforts, and those efforts, in turn, influence the beliefs, attitudes, and ideologies of the macrosystem. As Fig. 1 shows, improvement goals (indicated by the arrows moving from the current to a desired state) in the exo or macrosystem are unlikely to be achieved without associated improvement in the micro and mesosystem involving students, teachers, and groups of teachers, schools and their boards and parent communities. Similarly, the level of improvement in the macro and exosystems is limited by the extent to which more improvement goals at the micro and mesosystem are achieved through solving problems relating to students’ experience and school and classroom practices including curriculum, teaching, and assessment. As well as drawing on Bronfenbrenner’s ecological systems theory, our nested model of problem solving draws on problem solving theory to draw attention to how gaps between current and desired states at each of the system levels also influence each other (Newell & Simon, 1972 ). Efforts to solve problems in any one system (to move from current state toward a more desired state) are supported by similar moves at other interrelated systems. For example, the success of a teacher seeking to solve a curriculum problem (demand from parents to focus on core knowledge in traditional learning domains, for example)—a problem related to the microsystem and mesosystem—will be influenced by how similar problems are recognised, attended to, and solved by those in the ministries, departments and agencies in the exosystem.

In considering the role of educational leaders in this nested model of problem solving, we take a capability perspective (Mumford et al., 2000 ) rather than a leadership style perspective (Bedell-Avers et al., 2008 ). School leaders (including those with formal and informal leadership positions) require particular capabilities if they are to enact ambitious policies and solve complex problems related to enhancing equity for marginalized and disadvantaged groups of students (Mavrogordato & White, 2020 ). Too often, micro and mesosystem problems remain unsolved which is problematic not only for those directly involved, but also for the resolution of the related exo and macrosystem problems. The ill-structured nature of the problems school leaders face, and the social nature of the problem-solving process, contribute to the ineffectiveness of leaders’ problem-solving efforts and the persistence of important microsystem and mesosystem problems in schools.

Ill-structured problems

The problems that leaders need to solve are typically ill-structured rather than clearly defined, complex rather that than straight-forward, and adaptive rather than routine challenges (Bedell-Avers et al., 2008 ; Heifetz et al., 2009 ; Leithwood & Stager, 1989 ; Leithwood & Steinbach, 1992 , 1995 ; Mumford & Connelly, 1991 ; Mumford et al., 2000 ; Zaccaro et al., 2000 ). As Mumford and Connelly explain, “even if their problems are not totally unprecedented, leaders are, […] likely to be grappling with unique problems for which there is no clear-cut predefined solution” (Mumford & Connelly, 1991 , p. 294). Most such problems are difficult to solve because they can be construed in various ways and lack clear criteria for what counts as a good solution. Mumford et al. ( 2000 ) highlight the particular difficulties in solving ill-structured problems with regard to accessing, evaluating and using relevant information:

Not only is it difficult in many organizational settings for leaders to say exactly what the problem is, it may not be clear exactly what information should be brought to bear on the problem. There is a plethora of available information in complex organizational systems, only some of which is relevant to the problem. Further, it may be difficult to obtain accurate, timely information and identify key diagnostic information. As a result, leaders must actively seek and carefully evaluate information bearing on potential problems and goal attainment. (p. 14)

Problems in schools are complex. Each single problem can comprise multiple educational dimensions (learners, learning, curriculum, teaching, assessment) as well as relational, organizational, psychological, social, cultural, and political dimensions. In response to a teaching problem, for example, a single right or wrong answer is almost never at play; there are typically countless possible ‘responses’ to the problem of how to teach effectively in any given situation.

Problem solving as socially situated

Educational leaders’ problem solving is typically social because multiple people are usually involved in defining, explaining, and solving any given problem (Mumford et al., 2000 ). When there are multiple parties invested in addressing a problem, they typically hold diverse perspectives on how to describe (frame, perceive, and communicate about problems), explain (identify causes which lead to the problem), and solve the problem. Argyris and Schön ( 1974 ) argue that effective leaders must manage the complexity of integrating multiple and diverse perspectives, not only because all parties need to be internally committed to solutions, but also because quality solutions rely on a wide range of perspectives and evidence. Somewhat paradoxically, while the multiple perspectives involved in social problem solving add to their inherent complexity, these perspectives are a resource for educational change, and for the development of more effective solutions (Argyris & Schön, 1974 ). The social nature of problem solving requires high trust so participants can provide relevant, accurate, and timely information (rather than distort or withhold it), recognize their interdependence, and avoid controlling others. In high trust relationships, as Zand’s early work in this field established, “there is less socially generated uncertainty and problems are solved more effectively” (Zand, 1972 , p. 238).

Leaders’ capabilities in problem solving

Leadership research has established the centrality of capability in problem solving to leadership effectiveness generally (Marcy & Mumford, 2010 ; Mumford et al., 2000 , 2007 ) and to educational leadership in particular. Leithwood and Stager ( 1989 ), for example, consider “administrator’s problem-solving processes as crucial to an understanding of why principals act as they do and why some principals are more effective than others” (p. 127). Similarly, Robinson ( 1995 , 2001 , 2010 ) positions the ability to solve complex problems as central to all other dimensions of effective educational leadership. Unsurprisingly, problem solving is often prominent in standards for school leaders/leadership and is included in tools for the assessment of school leadership (Goldring et al., 2009 ). Furthermore, its importance is heightened given the increasing demand and complexity in standards for teaching (Sinnema, Meyer & Aitken, 2016) and the trend toward leadership across networks of schools (Sinnema, Daly, Liou, & Rodway, 2020a ) and the added complexity of such problem solving where a system perspective is necessary.

Empirical research on leaders’ practice has revealed that there is a need for capability building in problem solving (Le Fevre et al., 2015 ; Robinson et al., 2020 ; Sinnema et al., 2013 ; Sinnema et al., 2016 ; Smith, 1997 ; Spillane et al., 2009 ; Timperley & Robinson, 1998 ; Zaccaro et al., 2000 ). Some studies have compared the capability of leaders with varying experience. For example, Leithwood and Stager ( 1989 ) noted differences in problem solving approaches between novice and expert principals when responding to problem scenarios, particularly when the scenarios described ill-structured problems. Principals classified as ‘experts’ were more likely to collect information rather than make assumptions, and perceived unstructured problems to be manageable, whereas typical principals found these problems stressful. Expert principals also consulted extensively to get relevant information and find ways to deal with constraints. In contrast, novice principals consulted less frequently and tended to see constraints as obstacles (Leithwood & Stager, 1989 ). Allison and Allison ( 1993 ) reported that while experienced principals were better than novices at developing abstract problem-solving goals, they were less interested in the detail of how they would pursue these goals. Similar differences were found in Spillane et al.’s ( 2009 ) work that found expert principals to be better at interpreting problems and reflecting on their own actions compared with aspiring principals. More recent work (Sinnema et al., 2021 ) highlights that educators perceptions of discussion quality is positively associated with both new learning for the educator (learning that influences their practice) and improved practice (practices that reach students)—the more robust and helpful educators report their professional discussion to be, the more likely they are to report improvement in their practice. This supports the demand for quality conversation in educational teams.

Solving problems related to teaching and learning that occur in the micro or mesosystem usually requires conversations that demand high levels of interpersonal skill. Skill development is important because leaders tend to have difficulty inquiring deeply into the viewpoints of others (Le Fevre & Robinson, 2015 ; Le Fevre et al., 2015 ; Robinson & Le Fevre, 2011 ). In a close analysis of 43 conversation transcripts, Le Fevre et al. ( 2015 ) showed that when leaders anticipated or encountered diverse views, they tended to ask leading or loaded rather than genuine questions. This pattern was explained by their judgmental thinking, and their desire to avoid negative emotion and stay in control of the conversation. In a related study of leaders’ conversations, a considerable difference was found between the way educational leaders described their problem before and during the conversation with those involved (Sinnema et al., 2013 ). Prior to the conversation, privately, they tended to describe their problem as more serious and more urgent than they did in the conversation they held later with the person concerned.

One of the reasons for the mismatch between their private descriptions and public disclosures was the judgmental framing of their beliefs about the other party’s intentions, attitudes, and/or motivations (Peeters & Robinson, 2015 ). If leaders are not willing or able to reframe such privately-held beliefs in a more respectful manner, they will avoid addressing problems through fear of provoking negative emotion, and neither party will be able to critique the reasoning that leads to the belief in question (Robinson et al., 2020 ). When that happens, beliefs based on faulty reasoning may prevail, problem solutions may be based only on that which is discussable, and the problem may persist.

A model of effective problem-solving conversations

We present below a normative model of effective problem-solving conversations (Fig. 2 ) in which testing the validity of relevant beliefs plays a central role. Leaders test their beliefs about a problem when they draw on a set of validity testing behaviors and enact those behaviors, through their inquiry and advocacy, in ways that are consistent with the three interpersonal values included in the model. The model proposes that these processes increase the effectiveness of social problem solving, with effectiveness understood as progressing the task of solving the problem while maintaining or improving the leader’s relationship with those involved. In formulating this model, we drew on the previously discussed research on problem solving and theories of interpersonal and organisational effectiveness.

Model of effective problem-solving conversations

The role of beliefs in problem solving

Beliefs are important in the context of problem solving because they shape decisions about what constitutes a problem and how it can be explained and resolved. Beliefs link the object of the belief (e.g., a teacher’s planning) to some attribute (e.g., copied from the internet). In the context of school problems these attributes are usually tightly linked to a negative evaluation of the object of the belief (Fishbein & Ajzen, 1975 ). Problem solving, therefore, requires explicit attention by leaders to the validity of the information on which their own and others’ beliefs are based. The model draws on the work of Mumford et al. ( 2000 ) by highlighting three types of beliefs that are central to how people solve problems—beliefs about whether and why a situation is problematic (we refer to these as problem description beliefs); beliefs about the precursors of the problem situation (we refer to these as problem explanation beliefs); and beliefs about strategies which could, would, or should improve the situation (we refer to these as problem solution beliefs). With regard to problem explanation beliefs, it is important that attention is not limited to surface level factors, but also encompasses consideration of deeper related issues in the broader social context and how they contribute to any given problem.

The role of values in problem-solving conversations

Figure 2 proposes that problem solving effectiveness is increased when leaders’ validity testing behaviors are consistent with three values—respecting the views of others, seeking to maximize validity of their own and others’ beliefs, and building internal commitment to decisions reached. The inclusion of these three values in the model means that our validity testing behaviors must be conceptualized and measured in ways that capture their interpersonal (respect and internal commitment) and epistemic (valid information) underpinnings. Without this conceptual underpinning, it is likely to be difficult to identify the validity testing behaviors that are associated with effectiveness. For example, the act of seeking agreement can be done in a coercive or a respectful manner, so it is important to define and measure this behavior in ways that distinguish between the two. How this and similar distinctions were accomplished is described in the subsequent section on the five validity testing behaviors.

The three values in Fig. 2 are based on the theories and practice of interpersonal and organizational effectiveness developed by Argyris and Schön ( 1974 , 1978 , 1996 ) and applied more recently in a range of educational leadership research contexts (Hannah et al., 2018 ; Patuawa et al., 2021 ; Sinnema et al., 2021a ). We have drawn on the work of Argyris and Schön because their theories explain the dilemma many leaders experience between the two components of problem solving effectiveness and indicate how that dilemma can be avoided or resolved.

Seeking to maximize the validity of information is important because leaders’ beliefs have powerful consequences for the lives and learning of teachers and students and can limit or support educational change efforts. Leaders who behave consistently with the validity of information value are truth seekers rather than truth claimers in that they are open-minded and thus more attentive to the information that disconfirms rather than confirms their beliefs. Rather than assuming the validity of their beliefs and trying to impose them on others, their stance is one of seeking to detect and correct errors in their own and others′ thinking (Robinson, 2017 ).

The value of respect is closely linked to the value of maximizing the validity of information. Leaders increase validity by listening carefully to the views of others, especially if those views differ from their own. Listening carefully requires the accordance of worth and respect, rather than private or public dismissal of views that diverge from or challenge one’s own. If leaders’ conversations are guided by the two values of valid information and respect, then the third value of fostering internal commitment is also likely to be present. Teachers become internally committed to courses of action when their concerns have been listened to and directly addressed as part of the problem-solving process.

The role of validity testing behaviors in problem solving

Figure 2 includes five behaviors designed to test the validity of the three types of belief involved in problem solving. They are: 1) disclosing beliefs; 2) providing grounds; 3) exploring difference; 4) examining logic; and 5) seeking agreement. These behaviors enable leaders to check the validity of their beliefs by engaging in open minded disclosure and discussion of their thinking. While these behaviors are most closely linked to the value of maximizing valid information, the values of respect and internal commitment are also involved in these behaviors. For example, it is respectful to honestly and clearly disclose one’s beliefs about a problem to the other person concerned (advocacy), and to do so in ways that make the grounds for the belief testable and open to revision. It is also respectful to combine advocacy of one’s own beliefs with inquiry into others’ reactions to those beliefs and with inquiry into their own beliefs. When leaders encounter doubts and disagreements, they build internal rather than external commitment by being open minded and genuinely interested in understanding the grounds for them (Spiegel, 2012 ). By listening to and responding directly to others’ concerns, they build internal commitment to the process and outcomes of the problem solving.

Advocacy and inquiry dimensions

Each of the five validity testing behaviors can take the form of a statement (advocacy) or a question (inquiry). A leader’s advocacy contributes to problem solving effectiveness when it communicates his or her beliefs and the grounds for them, in a manner that is consistent with the three values. Such disclosure enables others to understand and critically evaluate the leader’s thinking (Tompkins, 2013 ). Respectful inquiry is equally important, as it invites the other person into the conversation, builds the trust they need for frank disclosure of their views, and signals that diverse views are welcomed. Explicit inquiry for others’ views is particularly important when there is a power imbalance between the parties, and when silence suggests that some are reluctant to disclose their views. Across their careers, leaders tend to rely more heavily on advocating their own views than on genuinely inquiring into the views of others (Robinson & Le Fevre, 2011 ). It is the combination of advocacy and inquiry behaviors, that enables all parties to collaborate in formulating a more valid understanding of the nature of the problem and of how it may be solved.

The five validity testing behaviors

Disclosing beliefs is the first and most essential validity testing behavior because beliefs cannot be publicly tested, using the subsequent four behaviors, if they are not disclosed. This behavior includes leaders’ advocacy of their own beliefs and their inquiry into others’ beliefs, including reactions to their own beliefs (Peeters & Robinson, 2015 ; Robinson & Le Fevre, 2011 ).

Honest and respectful disclosure ensures that all the information that is believed to be relevant to the problem, including that which might trigger an emotional reaction, is shared and available for validity testing (Robinson & Le Fevre, 2011 ; Robinson et al., 2020 ; Tjosvold et al., 2005 ). Respectful disclosure has been linked with follower trust. The empirical work of Norman et al. ( 2010 ), for example, showed that leaders who disclose more, and are more transparent in their communication, instill higher levels of trust in those they work with.

Providing grounds , the second validity testing behavior, is concerned with leaders expressing their beliefs in a way that makes the reasoning that led to them testable (advocacy) and invites others to do the same (inquiry). When leaders clearly explain the grounds for their beliefs and invite the other party to critique their relevance or accuracy, the validity or otherwise of the belief becomes more apparent. Both advocacy and inquiry about the grounds for beliefs can lead to a strengthening, revision, or abandonment of the beliefs for either or both parties (Myran & Sutherland, 2016 ; Robinson & Le Fevre, 2011 ; Robinson et al., 2020 ).

Exploring difference is the third validity testing behavior. It is essential because two parties simply disclosing beliefs and the grounds for them is insufficient for arriving at a joint solution, particularly when such disclosure reveals that there are differences in beliefs about the accuracy and implications of the evidence or differences about the soundness of arguments. Exploring difference through advocacy is seen in such behaviors as identifying and signaling differing beliefs and evaluating contrary evidence that underpins those differing beliefs. An inquiry approach to exploring difference (Timperley & Parr, 2005 ) occurs when a leader inquires into the other party’s beliefs about difference, or their response to the leaders’ beliefs about difference.

Exploring differences in beliefs is key to increasing validity in problem solving efforts (Mumford et al., 2007 ; Robinson & Le Fevre, 2011 ; Tjosvold et al., 2005 ) because it can lead to more integrative solutions and enhance the commitment from both parties to work with each other in the future (Tjosvold et al., 2005 ). Leaders who are able to engage with diverse beliefs are more likely to detect and challenge any faulty reasoning and consequently improve solution development (Le Fevre & Robinson, 2015 ). In contrast, when leaders do not engage with different beliefs, either by not recognizing or by intentionally ignoring them, validity testing is more limited. Such disengagement may be the result of negative attributions about the other person, such as that they are resistant, stubborn, or lazy. Such attributions reduce opportunities for the rigorous public testing that is afforded by the exchange and critical examination of competing views.

Examining logic , the fourth validity testing behavior, highlights the importance of devising a solution that adequately addresses the nature of the problem at hand and its causes. To develop an effective solution both parties must be able to evaluate the logic that links problems to their assumed causes and solutions. This behavior is present when the leader suggests or critiques the relationship between possible causes of and solutions to the identified problem. In its inquiry form, the leader seeks such information from the other party. As Zaccaro et al. ( 2000 ) explain, good problem solvers have skills and expertise in selecting the information to attend to in their effort to “understand the parameters of problems and therefore the dimensions and characteristics of a likely solution” (p. 44–45). These characteristics may include solution timeframes, resource capacities, an emphasis on organizational versus personal goals, and navigation of the degree of risk allowed by the problem approach. Explicitly exploring beliefs is key to ensuring the logic linking problem causes and any proposed solution. Taking account of a potentially complex set of contributing factors when crafting logical solutions, and testing the validity of beliefs about them, is likely to support effective problem solving. This requires what Copland ( 2010 ) describes as a creative process with similarities to clinical reasoning in medicine, in which “the initial framing of the problem is fundamental to the development of a useful solution” (p. 587).

Seeking agreement , the fifth validity testing behavior, signals the importance of warranted agreement about problem beliefs. We use the term ‘warranted’ to make clear that the goal is not merely getting the other party to agree (either that something is a problem, that a particular cause is involved, or that particular actions should be carried out to solve it)—mere agreement is insufficient. Rather, the goal is for warranted agreement whereby both parties have explored and critiqued the beliefs (and their grounds) of the other party in ways that provide a strong basis for the agreement. Both parties must come to some form of agreement on beliefs because successful solution implementation occurs in a social context, in that it relies on the commitment of all parties to carry it out (Mumford et al., 2000 ; Robinson & Le Fevre, 2011 ; Tjosvold et al., 2005 ). Where full agreement does not occur, the parties must at least be clear about where agreement/disagreement lies and why.

Testing the validity of beliefs using these five behaviors, and underpinned by the values described earlier is, we argue, necessary if conversations are to lead to two types of improvement—progress on the task (i.e., solving the problem) and improving the relationship between those involved in the conversation (i.e., ensuring those relationship between the problem-solvers is intact and enhanced through the process). We draw attention here to those improvement purposes as distinct from those underpinning work in the educational leadership field that takes a neo-managerialist perspective. The rise of neo-managerialism is argued to redefine school management and leadership along managerial lines and hence contribute to schools that are inequitable, reductionist, and inauthentic (Thrupp & Willmott, 2003 ). School leaders, when impacted by neo-managerialism, need to be (and are seen as) “self-interested, opportunistic innovators and risk-takers who exploit information and situations to produce radical change.” In contrast, the model we propose rejects self-interest. Our model emphasizes on deep respect for the views of others and the relentless pursuit of genuine shared commitment to understanding and solving problems that impact on children and young people through collaborative engagement in joint problem solving. Rather than permitting leaders to exploit others, our model requires leaders to be adept at using both inquiry and advocacy together with listening to both progress the task (solving problems) and simultaneously enhance the relationship between those involved. We position this model of social problem solving effectiveness as a tool for addressing social justice concerns—it intentionally dismisses problem solving approaches that privilege organizational efficiency indicators and ignore the wellbeing of learners and issues of inequity, racism, bias, and social injustice within and beyond educational contexts.

Methodology

The following section outlines the purpose of the study, the participants, and the mixed methods approach to data collection and analysis.

Research purpose

Our prior qualitative research (Robinson et al., 2020 ) involving in-depth case studies of three educational leaders revealed problematic patterns in leaders’ approach to problem-solving conversations: little disclosure of causal beliefs, little public testing of beliefs that might trigger negative emotions, and agreement on solutions that were misaligned with causal beliefs. The present investigation sought to understand if a quantitative methodological approach would reveal similar patterns and examine the relationship between belief types and leaders’ use of validity testing behaviors. Thus, our overarching research question was: to what extent do leaders test the validity of their beliefs in conversations with those directly involved in the analysis and resolution of the problem? Our argument is that while new experiences might motivate change in beliefs (Bonner et al., 2020 ), new insights gained through testing the validity of beliefs is also imperative to change. The sub-questions were:

What is the relative frequency in the types of beliefs leaders hold about problems involving others?

To what extent do leaders employ validity testing behaviors in conversations about those problems?

Are there differential patterns in leaders’ validity testing of the different belief types?

Participants

The participants were 43 students in a graduate course on educational leadership in New Zealand who identified an important on the job problem that they intended to discuss with the person directly involved.

The mixed methods approach

The study took a mixed methods approach using a partially mixed sequential equal status design; (QUAL → QUAN) (Leech & Onwuegbuzie, 2009 ). The five stages of sourcing and analyzing data and making interpretations are summarised in Fig. 3 below and outlined in more detail in the following sections (with reference in brackets to the numbered phases in the figure). We describe the study as partially mixed because, as Leech & Onwuegbuzie, 2009 explain, in partially mixed methods “both the quantitative and qualitative elements are conducted either concurrently or sequentially in their entirety before being mixed at the data interpretation stage” (p. 267).

Overview of mixed methods approach

Stage 1: Qualitative data collection

Three data sources were used to reveal participants’ beliefs about the problem they were seeking to address. The first source was their response to nine open ended items in a questionnaire focused on a real problem the participant had attempted to address but that still required attention (1a). The items were about: the nature and history of the problem; its importance; their own and others’ contribution to it; the causes of the problem; and the approach to and effectiveness of prior attempts to resolve it.

The second source (1b) was the transcript of a real conversation (typically between 5 and 10 minutes duration) the leaders held with the other person involved in the problem, and the third was the leaders’ own annotations of their unspoken thoughts and feelings during the course of the conversation (1c). The transcription was placed in the right-hand column (RHC) of a split page with the annotations recorded at the appropriate place in the left-hand column (LHC). The LHC method was originally developed by Argyris and Schön ( 1974 ) as a way of examining discrepancies between people’s espoused and enacted interpersonal values. Referring to data about each leader’s behavior (as recorded in the transcript of the conversation) and their thoughts (as indicated in the LHC) was important since the model specifies validity testing behaviors that are motivated by the values of respect, valid information, and internal commitment. Since motives cannot be revealed by speech alone, we also needed access to the thoughts that drove their behavior, hence our use of the LHC data collection technique. This approach allowed us to respond to Leithwood and Stager’s ( 1989 ) criticism that much research on effective problem solving gives results that “reveal little or nothing about how actions were selected or created and treat the administrator’s mind as a ‘black box’” (p. 127).

Stage 2: Qualitative analysis

The three stages of qualitative analysis focused on identifying discrete beliefs in the three qualitative data sources, distilling those discrete beliefs into key beliefs, and identifying leaders’ use of validity testing behaviors.

Stage 2a: Analyzing types of beliefs about problems

For this stage, we developed and applied coding rules (see Table 1 ) for the identification of the three types of beliefs in the three sources described earlier—leaders’ questionnaire responses, conversation transcript (RHC), and unexpressed thoughts (LHC). We identified 903 discrete beliefs (utterances or thoughts) from the 43 transcripts, annotations, and questionnaires and recorded these on a spreadsheet (2a). While our model proposes that leaders’ inquiry will surface and test the beliefs of others, we quantify in this study only the leaders’ beliefs.

Stage 2b: Distilling discrete beliefs into key beliefs

Next, we distilled the 903 discrete beliefs into key beliefs (KBs) (2b). This was a complex process and involved multiple iterations across the research team to determine, check, and test the coding rules. The final set of rules for distilling key beliefs were:

Beliefs should be made more succinct in the key belief statement, and key words should be retained as much as possible

Judgment quality (i.e., negative or positive) of the belief needs to be retained in the key belief

Key beliefs should use overarching terms where possible

The meaning and the object of the belief need to stay constant in the key belief

When reducing overlap, the key idea of both beliefs need to be captured in the key beliefs

Distinctive beliefs need to be summarized on their own and not combined with other beliefs

The subject of the belief must be retained in the key belief—own belief versus restated belief of other

All belief statements must be accounted for in key beliefs

These rules were applied to the process of distilling multiple related beliefs into statements of key beliefs as illustrated by the example in the table below (Table 2 ).

Further examples of how the rules were applied are outlined in ' Appendix A '. The number of discrete beliefs for each leader ranged from 7 to 35, with an average of 21, and the number of key beliefs for each leader ranged between 4 and 14, with an average of eight key beliefs. Frequency counts were used to identify any patterns in the types of key beliefs which were held privately (not revealed in the conversation but signalled in the left hand column or questionnaire) or conveyed publicly (in conversation with the other party).

Stage 2c: Analyzing leaders’ use of validity testing behaviors

We then developed and applied coding rules for the five validity testing behaviors (VTB) outlined in our model (disclosing beliefs, providing grounds, exploring difference, examining logic, and seeking agreement). Separate rules were established for the inquiry and advocacy aspects of each VTB, generating ten coding rules in all (Table 3 ).

These rules, summarised in the table below, and outlined more fully in ' Appendix A ', encompassed inclusion and exclusion criteria for the advocacy and inquiry dimensions of each validity testing behavior. For example, the inclusion rule for the VTB of ‘Disclosing Beliefs’ required leaders to disclose their beliefs about the nature, and/or causes, and/or possible solutions to the problem, in ways that were consistent with the three values included in the model. The associated exclusion rule signalled that this criterion was not met if, for example, the leader asked a question in order to steer the other person toward their own views without having ever disclosed their own views, or if they distorted the urgency or seriousness of the problem related to what they had expressed privately. The exclusion rules also noted how thoughts expressed in the left hand column would exclude the verbal utterance from being treated as disclosure—for example if there were contradictions between the right hand (spoken) and left hand column (thoughts), or if the thoughts indicated that the disclosure had been distorted in order to minimise negative emotion.

The coding rules reflected the values of respect and internal commitment in addition to the valid information value that was foregrounded in the analysis. The emphasis on inquiry, for example (into others’ beliefs and/or responses to the beliefs already expressed by the leader), recognised that internal commitment would be impossible if the other party held contrary views that had not been disclosed and discussed. Similarly, the focus on leaders advocating their beliefs, grounds for those beliefs and views about the logic linking solutions to problem causes recognise that it is respectful to make those transparent to another party rather than impose a solution in the absence of such disclosure.

The coding rules were applied to all 43 transcripts and the qualitative analysis was carried out using NVivo 10. A random sample of 10% of the utterances coded to a VTB category was checked independently by two members of the research team following the initial analysis by a third member. Any discrepancies in the coding were resolved, and data were recoded if needed. Descriptive analyses then enabled us to compare the frequency of leaders’ use of the five validity testing behaviors.

Stage 3: Data transformation: From qualitative to quantitative data

We carried out transformation of our data set (Burke et al., 2004 ), from qualitative to quantitative, to allow us to carry out statistical analysis to answer our research questions. The databases that resulted from our data transformation, with text from the qualitative coding along with numeric codes, are detailed next. In database 1, key beliefs were all entered as cases with indications in adjacent columns as to the belief type category they related to, and the source/s of the belief (questionnaire, transcript or unspoken thoughts/feelings). A unique identifier was created for each key belief.

In database 2, each utterance identified as meeting the VTB coding rules were entered in column 1. The broader context of the utterance from the original transcript was then examined to establish the type of belief (description, explanation, or solution) the VTB was being applied to, with this recorded numerically alongside the VTB utterance itself. For example, the following utterance had been coded to indicate that it met the ‘providing grounds’ coding rule, and in this phase it was also coded to indicate that it was in relation to a ‘problem description’ belief type:

“I noticed on the feedback form that a number of students, if I’ve got the numbers right here, um, seven out of ten students in your class said that you don’t normally start the lesson with a ‘Do Now’ or a starter activity.” (case 21)

A third database listed all of the unique identifiers for each leader’s key beliefs (KB) in the first column. Subsequent columns were set up for each of the 10 validity testing codes (the five validity testing behaviors for both inquiry and advocacy). The NVivo coding for the VTBs was then examined, one piece of coding at a time, to identify which key belief the utterance was associated with. Each cell that intersected the appropriate key belief and VTB was increased by one as a VTB utterance was associated with a key belief. Our database included variables for both the frequency of each VTB (the number of instances the behavior was used) and a parallel version with just a dichotomous variable indicating the presence or absence or each VTB. The dichotomous variable was used for our subsequent analysis because multiple utterances indicating a certain validity testing behavior were not deemed to necessarily constitute better quality belief validity testing than one utterance.

Stage 4: Quantitative analysis

The first phase of quantitative analysis involved the calculation of frequency counts for the three belief types (4a). Next, frequencies were calculated for the five validity testing behaviors, and for those behaviors in relation to each belief type (4b).

The final and most complex stage of the quantitative analysis, stages 4c through 4f, involved looking for patterns across the two sets of data created through the prior analyses (belief type and validity testing behaviors) to investigate whether leaders might be more inclined to use certain validity testing behaviors in conjunction with a particular belief type.

Stage 4a: Analyzing for relationships between belief type and VTB

We investigated the relationship between belief type and VTB, first, for all key beliefs. Given initial findings about variability in the frequency of the VTBs, we chose not to use all five VTBs separately in our analysis, but rather the three categories of: 1) None (key beliefs that had no VTB applied to them); 2) VTB—Routine (the sum of VTBs 1 and 2; given those were much more prevalent than others in the case of both advocacy and inquiry); and 3) VTB—Robust (the sum of the VTBs 3, 4 and 5 given these were all much less prevalent than VTBs 1 and 2, again including both advocacy and/or inquiry). Cross tabs were prepared and a chi-square test of independence was performed on the data from all 331 key beliefs.

Stage 4b: Analyzing for relationships between belief type and VTB

Next, because more than half (54.7%, 181) of the 331 key beliefs were not tested by leaders using any one of the VTBs, we analyzed a sub-set of the database, selecting only those key beliefs where leaders had disclosed the belief (using advocacy and/or inquiry). The reason for this was to ensure that any relationships established statistically were not unduly influenced by the data collection procedure which limited the time for the conversation to 10 minutes, during which it would not be feasible to fully disclose and address all key beliefs held by the leader. For this subset we prepared cross tabs and carried out chi-square tests of independence for the 145 key beliefs that leaders had disclosed. We again investigated the relationship between key belief type and VTBs, this time using a VTB variable with two categories: 1) More routine only and 2) More routine and robust.

Stage 4c: Analyzing for relationships between belief type and advocacy/inquiry dimensions of validity testing

Next, we investigated the relationship between key belief type and the advocacy and inquiry dimensions of validity testing. This analysis was to provide insight into whether leaders might be more or less inclined to use certain VTBs for certain types of belief. Specifically, we compared the frequency of utterances about beliefs of all three types for the categories of 1) No advocacy or inquiry, 2) Advocacy only, 3) Inquiry only, and 4) Advocacy and inquiry (4e). Cross tabs were prepared, and a chi-square test of independence was performed on the data from all 331 key beliefs. Finally, we again worked with the subset of 145 key beliefs that had been disclosed, comparing the frequency of utterances coded to 1) Advocacy or inquiry only, or 2) Both advocacy and inquiry (4f).

Below, we highlight findings in relation to the research questions guiding our analysis about: the relative frequency in the types of beliefs leaders hold about problems involving others; the extent to which leaders employ validity testing behaviors in conversations about those problems; and differential patterns in leaders’ validity testing of the different belief types. We make our interpretations based on the statistical analysis and draw on insights from the qualitative analysis to illustrate those results.

Belief types

Leaders’ key beliefs about the problem were evenly distributed between the three belief types, suggesting that when they think about a problem, leaders think, though not necessarily in a systematic way, about the nature of, explanation for, and solutions to their problem (see Table 4 ). These numbers include beliefs that were communicated and also those recorded privately in the questionnaire or in writing on the conversation transcripts.

Patterns in validity testing

The majority of the 331 key beliefs (54.7%, 181) were not tested by leaders using any one of the VTBs, not even the behavior of disclosing the belief. Our analysis of the VTBs that leaders did use (see Table 5 ) shows the wide variation in frequency of use with some, arguably the more robust ones, hardly used at all.

The first pattern was more frequent disclosure of key beliefs than provision of the grounds for them. The lower levels of providing grounds is concerning because it has implications for the likelihood of those in the conversation subsequently reaching agreement and being able to develop solutions logically aligned to the problem (VTB4). The logical solution if it is the time that guided reading takes that is preventing a teacher doing ‘shared book reading’ (as Leader 20 believed to be the case) is quite different to the solution that is logical if in fact the reason is something different, for example uncertainty about how to go about ‘shared book reading’, lack of shared book resources, or a misunderstanding that school policy requires greater time on shared reading.

The second pattern was a tendency for leaders to advocate much more than they inquire— there was more than double the proportion of advocacy than inquiry overall and for some behaviors the difference between advocacy and inquiry was up to seven times greater. This suggests that leaders were more comfortable disclosing their own beliefs, providing the grounds for their own beliefs and expressing their own assumptions about agreement, and less comfortable in inquiring in ways that created space and invited the other person in the conversation to reveal their beliefs.

A third pattern revealed in this analysis was the difference in the ratio of inquiry to advocacy between VTB1 (disclosing beliefs)—a ratio of close to 1:2 and VTB2 (providing grounds)—a ratio of close to 1:7. Leaders are more likely to seek others’ reactions when they disclose their beliefs than when they give their grounds for those beliefs. This might suggest that leaders assume the validity of their own beliefs (and therefore do not see the need to inquire into grounds) or that they do not have the skills to share the grounds associated with the beliefs they hold.

Fourthly, there was an absence of attention to three of the VTBs outlined in our model—in only very few of the 329 validity testing utterances the 43 leaders used were they exploring difference (11 instances), examining logic (4 instances) or seeking agreement (22 instances). In Case 22, for example, the leader claimed that learning intentions should be displayed and understood by children and expressed concern that the teacher was not displaying them, and that her students thus did not understand the purpose of the activities they were doing. While the teacher signaled her disagreement with both of those claims—“I do learning intentions, it’s all in my modelling books I can show them to you if you want” and “I think the children know why they are learning what they are learning”—the fact that there were differences in their beliefs was not explicitly signaled, and the differences were not explored. The conversation went on, with each continuing to assume the accuracy of their own beliefs. They were unable to reach agreement on a solution to the problem because they had not established and explored the lack of agreement about the nature of the problem itself. We presume from these findings, and from our prior qualitative work in this field, that those VTBs are much more difficult, and therefore much less likely to be used than the behaviors of disclosing beliefs and providing grounds.

The relationship between belief type and validity testing behaviors

The relationship between belief type and category of validity testing behavior was significant ( Χ 2 (4) = 61.96, p < 0.001). It was notable that problem explanation beliefs were far less likely than problem description or problem solution beliefs to be subject to any validity testing (the validity of more than 80% of PEBs was not tested) and, when they were tested, it was typically with the more routine rather than robust VTBs (see Table 6 ).

Problem explanation beliefs were also most likely to not be tested at all; more than 80% of the problem explanation beliefs were not the focus of any validity testing. Further, problem description beliefs were less likely than problem solution beliefs to be the target of both routine and robust validity testing behaviors—12% of PDBs and 18% of PSBs were tested using both routine and robust VTBs.

Two important assumptions underpin the study reported here. The first is that problems of equity must be solved, not only in the macrosystem and exosystem, but also as they occur in the day to day practices of leaders and teachers in micro and mesosystems. The second is that conversations are the key practice in which problem solving occurs in the micro and mesosystems, and that is why we focused on conversation quality. We focused on validity testing as an indicator of quality by closely analyzing transcripts of conversations between 43 individual leaders and a teacher they were discussing problems with.

Our findings suggest a considerable gap between our normative model of effective problem solving conversations and the practices of our sample of leaders. While beliefs about what problems are, and proposed solutions to them are shared relatively often, rarely is attention given to beliefs about the causes of problems. Further, while leaders do seem to be able to disclose and provide grounds for their beliefs about problems, they do so less often for beliefs about problem cause than other belief types. In addition, the critical validity testing behaviors of exploring difference, examining logic, and seeking agreement are very rare. Learning how to test the validity of beliefs is, therefore, a relevant focus for educational leaders’ goals (Bendikson et al., 2020 ; Meyer et al., 2019 ; Sinnema & Robinson, 2012 ) as well as a means for achieving other goals.

The patterns we found are problematic from the point of view of problem solving in schools generally but are particularly problematic from the point of view of macrosystem problems relating to equity. In New Zealand, for example, the underachievement and attendance issues of Pasifika students is a macrosystem problem that has been the target of many attempts to address through a range of policies and initiatives. Those efforts include a Pasifika Education Plan (Ministry of Education, 2013 ) and a cultural competencies framework for teachers of Pasifika learners—‘Tapasa’ (Ministry of Education, 2018 ) At the level of the mesosystem, many schools have strategic plans and school-wide programmes for interactions seeking to address those issues.

Resolving such equity issues demands that macro and exosystem initiatives are also reflected in the interactions of educators—hence our investigation of leaders’ problem-solving conversations and attention to whether leaders have the skills required to solve problems in conversations that contribute to aspirations in the exo and macrosystem, include of excellence and equity in new and demanding national curricula (Sinnema et al., 2020a ; Sinnema, Stoll, 2020a ). An example of an exosystem framework—the competencies framework for teachers of Pacific students in New Zealand—is useful here. It requires that teachers “establish and maintain collaborative and respectful relationships and professional behaviors that enhance learning and wellbeing for Pasifika learners” (Ministry of Education, 2018 , p. 12). The success of this national framework is influenced by and also influences the success that leaders in school settings have at solving problems in the conversations they have about related micro and mesosystem problems.

To illustrate this point, we draw here on the example of one case from our sample that showed how problem-solving conversation capability is related to the success or otherwise of system level aspirations of this type. In the case of Leader 36, under-developed skill in problem solving talk likely stymied the success of the equity-focused system initiatives. Leader 36 had been alerted by the parents of a Pasifika student that their daughter “feels that she is being unfairly treated, picked on and being made to feel very uncomfortable in the teacher’s class.” In the conversation with Leader 36, the teacher described having established a good relationship with the student, but also having had a range of issues with her including that she was too talkative, that led the teacher to treat her in ways the teacher acknowledged could have made her feel picked on and consequently reluctant to come to school.

The teacher also told the leader that there were issues with uniform irregularities (which the teacher picked on) and general non conformity—“No, she doesn’t [conform]. She often comes with improper footwear, incorrect jacket, comes late to school, she puts make up on, there are quite a few things that aren’t going on correctly….”. The teacher suggested that the student was “drawing the wrong type of attention from me as a teacher, which has had a negative effect on her.” The teacher described to the leader a recent incident:

[The student] had come to class with her hair looking quite shabby so I quietly asked [the student] “Did you wake up late this morning?” and then she but I can’t remember, I made a comment like “it looks like you didn’t take too much interest in yourself.” To me, I thought there was nothing wrong with the comment as it did not happen publicly; it happened in class and I had walked up to her. Following that, [her] Mum sends another email about girls and image and [says] that I am picking on her again. I’m quite baffled as to what is happening here. (case 36)

This troubling example represented a critical discretionary moment. The pattern of belief validity testing identified through our analysis of this case (see Table 7 ), however, mirrors some of the patterns evident in the wider sample.

The leader, like the student’s parents, believed that the teacher had been offensive in her communication with the student and also that the relationship between the teacher and student would be negatively impacted as a result. These two problem description beliefs were disclosed by the leader during her conversation with the teacher. However, while her disclosure of her belief about the problem description involved both advocating the belief, and inquiring into the other’s perception of it, the provision of grounds for the belief involved advocacy only. She reported the basis of the concern (the email from the student’s parents about their daughter feeling unfairly treated, picked on, and uncomfortable in class) but did not explicitly inquire into the grounds. This may be explained in this case through the teacher offering her own account of the situation that matched the parent’s report. Leader 36 also disclosed in her conversation with the teacher, her problem solution key belief that they should hold a restorative meeting between the teacher, the student, and herself.

What Leader 36 did not disclose was her belief about the explanation for the problem—that the teacher did not adequately understand the student personally, or their culture. The problem explanation belief (KB4) that she did inquire into was one the teacher raised—suggesting that the student has “compliance issues” that led the teacher to respond negatively to the student’s communication style—and that the teacher agreed with. The leader did not use any of the more robust but important validity testing behaviors for any of the key beliefs they held, either about problem description, explanation or solutions. And most importantly, this conversation highlights how policies and initiatives developed by those in the macrosystem, aimed at addressing equity issues, can be thwarted through well-intentioned but ultimately unsuccessful efforts of educators as they operate in the micro and mesosystem in what we referred to earlier as a discretionary problem solving space. The teacher’s treatment of the Pasifika student in our example was in stark contrast to the respectful and strong relationships demanded by the exosystem policy, the framework for teachers of Pasifika students. Furthermore, while the leader recognized the problem, issues of culture were avoided—they were not skilled enough in disclosing and testing their beliefs in the course of the conversation to contribute to broader equity concerns. The skill gap resonates with the findings of much prior work in this field (Le Fevre et al., 2015 ; Robinson et al., 2020 ; Sinnema et al., 2013 ; Smith, 1997 ; Spillane et al., 2009 ; Timperley & Robinson, 1998 ; Zaccaro et al., 2000 ), and highlights the importance of leaders, and those working with them in leadership development efforts, to recognize the interactions between the eco-systems outlined in the nested model of problem solving detailed in Fig. 1 .

The reluctance of Leader 36 to disclose and discuss her belief that the teacher misunderstands the student and her culture is important given the wider research evidence about the nature of the beliefs teachers may hold about indigenous and minority learners. The expectations teachers hold for these groups are typically lower and more negative than for white students (Gay, 2005 ; Meissel et al., 2017 ). In evidence from the New Zealand context, Turner et al. ( 2015 ), for example, found expectations to differ according to ethnicity with higher expectations for Asian and European students than for Māori and Pasifika students, even when controlling for achievement, due to troubling teacher beliefs about students’ home backgrounds, motivations, and aspirations. These are just the kind of beliefs that leaders must be able to confront in conversations with their teachers.

We use this example to illustrate both the interrelatedness of problems across the ecosystem, and the urgency of leadership development intervention in this area. Our normative model of effective problem solving conversations (Fig. 2 ), we suggest, provides a useful framework for the design of educational leadership intervention in this area. It shows how validity testing behaviors should embody both advocacy and inquiry and be used to explore not only perceptions of problem descriptions and solutions, but also problem causes. In this way, we hope to offer insights into how the dilemma between trust and accountability (Ehren et al., 2020 ) might be solved through increased interpersonal effectiveness. The combination of inquiry with advocacy also marks this approach out from neo-liberal approaches that emphasize leaders staying in control and predominantly advocating authoritarian perspectives of educational leadership. The interpersonal effectiveness theory that we draw on (Argyris & Schön, 1974 ) positions such unilateral control as ineffective, arguing for a mutual learning alternative. The work of problem solving is, we argue, joint work, requiring shared commitment and control.

Our findings also call for more research explicitly designed to investigate linkages between the systems. Case studies are needed, of macro and exosystem inequity problems backward mapped to initiatives and interactions that occur in schools related to those problems and initiatives. Such research could capture the complex ways in which power plays out “in relation to structural inequalities (of class, disability, ethnicity, gender, nationality, race, sexuality, and so forth)” and in relation to “more shifting and fluid inequalities that play out at the symbolic and cultural levels (for example, in ways that construct who “has” potential)” (Burke & Whitty, 2018 , p. 274).

Leadership development in problem solving should be approached in ways that surface and test the validity of leaders’ beliefs, so that they similarly learn to surface and test others’ beliefs in their leadership work. That is important not only from a workforce development point of view, but also from a social justice point of view since leaders’ capabilities in this area are inextricably linked to the success of educational systems in tackling urgent equity concerns.

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Problem-Solving Strategies and Obstacles

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From deciding what to eat for dinner to considering whether it's the right time to buy a house, problem-solving is a large part of our daily lives. Learn some of the problem-solving strategies that exist and how to use them in real life, along with ways to overcome obstacles that are making it harder to resolve the issues you face.

What Is Problem-Solving?

In cognitive psychology , the term 'problem-solving' refers to the mental process that people go through to discover, analyze, and solve problems.

A problem exists when there is a goal that we want to achieve but the process by which we will achieve it is not obvious to us. Put another way, there is something that we want to occur in our life, yet we are not immediately certain how to make it happen.

Maybe you want a better relationship with your spouse or another family member but you're not sure how to improve it. Or you want to start a business but are unsure what steps to take. Problem-solving helps you figure out how to achieve these desires.

The problem-solving process involves:

Discovery of the problem
Deciding to tackle the issue
Seeking to understand the problem more fully
Researching available options or solutions
Taking action to resolve the issue

Before problem-solving can occur, it is important to first understand the exact nature of the problem itself. If your understanding of the issue is faulty, your attempts to resolve it will also be incorrect or flawed.

Problem-Solving Mental Processes

Several mental processes are at work during problem-solving. Among them are:

Perceptually recognizing the problem
Representing the problem in memory
Considering relevant information that applies to the problem
Identifying different aspects of the problem
Labeling and describing the problem

Problem-Solving Strategies

There are many ways to go about solving a problem. Some of these strategies might be used on their own, or you may decide to employ multiple approaches when working to figure out and fix a problem.

An algorithm is a step-by-step procedure that, by following certain "rules" produces a solution. Algorithms are commonly used in mathematics to solve division or multiplication problems. But they can be used in other fields as well.

In psychology, algorithms can be used to help identify individuals with a greater risk of mental health issues. For instance, research suggests that certain algorithms might help us recognize children with an elevated risk of suicide or self-harm.

One benefit of algorithms is that they guarantee an accurate answer. However, they aren't always the best approach to problem-solving, in part because detecting patterns can be incredibly time-consuming.

There are also concerns when machine learning is involved—also known as artificial intelligence (AI)—such as whether they can accurately predict human behaviors.

Heuristics are shortcut strategies that people can use to solve a problem at hand. These "rule of thumb" approaches allow you to simplify complex problems, reducing the total number of possible solutions to a more manageable set.

If you find yourself sitting in a traffic jam, for example, you may quickly consider other routes, taking one to get moving once again. When shopping for a new car, you might think back to a prior experience when negotiating got you a lower price, then employ the same tactics.

While heuristics may be helpful when facing smaller issues, major decisions shouldn't necessarily be made using a shortcut approach. Heuristics also don't guarantee an effective solution, such as when trying to drive around a traffic jam only to find yourself on an equally crowded route.

Trial and Error

A trial-and-error approach to problem-solving involves trying a number of potential solutions to a particular issue, then ruling out those that do not work. If you're not sure whether to buy a shirt in blue or green, for instance, you may try on each before deciding which one to purchase.

This can be a good strategy to use if you have a limited number of solutions available. But if there are many different choices available, narrowing down the possible options using another problem-solving technique can be helpful before attempting trial and error.

In some cases, the solution to a problem can appear as a sudden insight. You are facing an issue in a relationship or your career when, out of nowhere, the solution appears in your mind and you know exactly what to do.

Insight can occur when the problem in front of you is similar to an issue that you've dealt with in the past. Although, you may not recognize what is occurring since the underlying mental processes that lead to insight often happen outside of conscious awareness .

Research indicates that insight is most likely to occur during times when you are alone—such as when going on a walk by yourself, when you're in the shower, or when lying in bed after waking up.

How to Apply Problem-Solving Strategies in Real Life

If you're facing a problem, you can implement one or more of these strategies to find a potential solution. Here's how to use them in real life:

Create a flow chart . If you have time, you can take advantage of the algorithm approach to problem-solving by sitting down and making a flow chart of each potential solution, its consequences, and what happens next.
Recall your past experiences . When a problem needs to be solved fairly quickly, heuristics may be a better approach. Think back to when you faced a similar issue, then use your knowledge and experience to choose the best option possible.
Start trying potential solutions . If your options are limited, start trying them one by one to see which solution is best for achieving your desired goal. If a particular solution doesn't work, move on to the next.
Take some time alone . Since insight is often achieved when you're alone, carve out time to be by yourself for a while. The answer to your problem may come to you, seemingly out of the blue, if you spend some time away from others.

Obstacles to Problem-Solving

Problem-solving is not a flawless process as there are a number of obstacles that can interfere with our ability to solve a problem quickly and efficiently. These obstacles include:

Assumptions: When dealing with a problem, people can make assumptions about the constraints and obstacles that prevent certain solutions. Thus, they may not even try some potential options.
Functional fixedness : This term refers to the tendency to view problems only in their customary manner. Functional fixedness prevents people from fully seeing all of the different options that might be available to find a solution.
Irrelevant or misleading information: When trying to solve a problem, it's important to distinguish between information that is relevant to the issue and irrelevant data that can lead to faulty solutions. The more complex the problem, the easier it is to focus on misleading or irrelevant information.
Mental set: A mental set is a tendency to only use solutions that have worked in the past rather than looking for alternative ideas. A mental set can work as a heuristic, making it a useful problem-solving tool. However, mental sets can also lead to inflexibility, making it more difficult to find effective solutions.

How to Improve Your Problem-Solving Skills

In the end, if your goal is to become a better problem-solver, it's helpful to remember that this is a process. Thus, if you want to improve your problem-solving skills, following these steps can help lead you to your solution:

Recognize that a problem exists . If you are facing a problem, there are generally signs. For instance, if you have a mental illness , you may experience excessive fear or sadness, mood changes, and changes in sleeping or eating habits. Recognizing these signs can help you realize that an issue exists.
Decide to solve the problem . Make a conscious decision to solve the issue at hand. Commit to yourself that you will go through the steps necessary to find a solution.
Seek to fully understand the issue . Analyze the problem you face, looking at it from all sides. If your problem is relationship-related, for instance, ask yourself how the other person may be interpreting the issue. You might also consider how your actions might be contributing to the situation.
Research potential options . Using the problem-solving strategies mentioned, research potential solutions. Make a list of options, then consider each one individually. What are some pros and cons of taking the available routes? What would you need to do to make them happen?
Take action . Select the best solution possible and take action. Action is one of the steps required for change . So, go through the motions needed to resolve the issue.
Try another option, if needed . If the solution you chose didn't work, don't give up. Either go through the problem-solving process again or simply try another option.

You can find a way to solve your problems as long as you keep working toward this goal—even if the best solution is simply to let go because no other good solution exists.

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By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

40 problem-solving techniques and processes

All teams and organizations encounter challenges. Approaching those challenges without a structured problem solving process can end up making things worse.

Proven problem solving techniques such as those outlined below can guide your group through a process of identifying problems and challenges , ideating on possible solutions , and then evaluating and implementing the most suitable .

In this post, you'll find problem-solving tools you can use to develop effective solutions. You'll also find some tips for facilitating the problem solving process and solving complex problems.

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What is problem solving?

Problem solving is a process of finding and implementing a solution to a challenge or obstacle. In most contexts, this means going through a problem solving process that begins with identifying the issue, exploring its root causes, ideating and refining possible solutions before implementing and measuring the impact of that solution.

For simple or small problems, it can be tempting to skip straight to implementing what you believe is the right solution. The danger with this approach is that without exploring the true causes of the issue, it might just occur again or your chosen solution may cause other issues.

Particularly in the world of work, good problem solving means using data to back up each step of the process, bringing in new perspectives and effectively measuring the impact of your solution.

Effective problem solving can help ensure that your team or organization is well positioned to overcome challenges, be resilient to change and create innovation. In my experience, problem solving is a combination of skillset, mindset and process, and it’s especially vital for leaders to cultivate this skill.

A group of people looking at a poster with notes on it

What is the seven step problem solving process?

A problem solving process is a step-by-step framework from going from discovering a problem all the way through to implementing a solution.

With practice, this framework can become intuitive, and innovative companies tend to have a consistent and ongoing ability to discover and tackle challenges when they come up.

You might see everything from a four step problem solving process through to seven steps. While all these processes cover roughly the same ground, I’ve found a seven step problem solving process is helpful for making all key steps legible.

We’ll outline that process here and then follow with techniques you can use to explore and work on that step of the problem solving process with a group.

The seven-step problem solving process is:

1. Problem identification

The first stage of any problem solving process is to identify the problem(s) you need to solve. This often looks like using group discussions and activities to help a group surface and effectively articulate the challenges they’re facing and wish to resolve.

Be sure to align with your team on the exact definition and nature of the problem you’re solving. An effective process is one where everyone is pulling in the same direction – ensure clarity and alignment now to help avoid misunderstandings later.

2. Problem analysis and refinement

The process of problem analysis means ensuring that the problem you are seeking to solve is the right problem . Choosing the right problem to solve means you are on the right path to creating the right solution.

At this stage, you may look deeper at the problem you identified to try and discover the root cause at the level of people or process. You may also spend some time sourcing data, consulting relevant parties and creating and refining a problem statement.

Problem refinement means adjusting scope or focus of the problem you will be aiming to solve based on what comes up during your analysis. As you analyze data sources, you might discover that the root cause means you need to adjust your problem statement. Alternatively, you might find that your original problem statement is too big to be meaningful approached within your current project.

Remember that the goal of any problem refinement is to help set the stage for effective solution development and deployment. Set the right focus and get buy-in from your team here and you’ll be well positioned to move forward with confidence.

3. Solution generation

Once your group has nailed down the particulars of the problem you wish to solve, you want to encourage a free flow of ideas connecting to solving that problem. This can take the form of problem solving games that encourage creative thinking or techniquess designed to produce working prototypes of possible solutions.

The key to ensuring the success of this stage of the problem solving process is to encourage quick, creative thinking and create an open space where all ideas are considered. The best solutions can often come from unlikely places and by using problem solving techniques that celebrate invention, you might come up with solution gold.

4. Solution development

No solution is perfect right out of the gate. It’s important to discuss and develop the solutions your group has come up with over the course of following the previous problem solving steps in order to arrive at the best possible solution. Problem solving games used in this stage involve lots of critical thinking, measuring potential effort and impact, and looking at possible solutions analytically.

During this stage, you will often ask your team to iterate and improve upon your front-running solutions and develop them further. Remember that problem solving strategies always benefit from a multitude of voices and opinions, and not to let ego get involved when it comes to choosing which solutions to develop and take further.

Finding the best solution is the goal of all problem solving workshops and here is the place to ensure that your solution is well thought out, sufficiently robust and fit for purpose.

5. Decision making and planning

Nearly there! Once you’ve got a set of possible, you’ll need to make a decision on which to implement. This can be a consensus-based group decision or it might be for a leader or major stakeholder to decide. You’ll find a set of effective decision making methods below.

Once your group has reached consensus and selected a solution, there are some additional actions that also need to be decided upon. You’ll want to work on allocating ownership of the project, figure out who will do what, how the success of the solution will be measured and decide the next course of action.

Set clear accountabilities, actions, timeframes, and follow-ups for your chosen solution. Make these decisions and set clear next-steps in the problem solving workshop so that everyone is aligned and you can move forward effectively as a group.

Ensuring that you plan for the roll-out of a solution is one of the most important problem solving steps. Without adequate planning or oversight, it can prove impossible to measure success or iterate further if the problem was not solved.

6. Solution implementation

This is what we were waiting for! All problem solving processes have the end goal of implementing an effective and impactful solution that your group has confidence in.

Project management and communication skills are key here – your solution may need to adjust when out in the wild or you might discover new challenges along the way. For some solutions, you might also implement a test with a small group and monitor results before rolling it out to an entire company.

You should have a clear owner for your solution who will oversee the plans you made together and help ensure they’re put into place. This person will often coordinate the implementation team and set-up processes to measure the efficacy of your solution too.

7. Solution evaluation

So you and your team developed a great solution to a problem and have a gut feeling it’s been solved. Work done, right? Wrong. All problem solving strategies benefit from evaluation, consideration, and feedback.

You might find that the solution does not work for everyone, might create new problems, or is potentially so successful that you will want to roll it out to larger teams or as part of other initiatives.

None of that is possible without taking the time to evaluate the success of the solution you developed in your problem solving model and adjust if necessary.

Remember that the problem solving process is often iterative and it can be common to not solve complex issues on the first try. Even when this is the case, you and your team will have generated learning that will be important for future problem solving workshops or in other parts of the organization.

It’s also worth underlining how important record keeping is throughout the problem solving process. If a solution didn’t work, you need to have the data and records to see why that was the case. If you go back to the drawing board, notes from the previous workshop can help save time.

What does an effective problem solving process look like?

Every effective problem solving process begins with an agenda . In our experience, a well-structured problem solving workshop is one of the best methods for successfully guiding a group from exploring a problem to implementing a solution.

The format of a workshop ensures that you can get buy-in from your group, encourage free-thinking and solution exploration before making a decision on what to implement following the session.

This Design Sprint 2.0 template is an effective problem solving process from top agency AJ&Smart. It’s a great format for the entire problem solving process, with four-days of workshops designed to surface issues, explore solutions and even test a solution.

Check it for an example of how you might structure and run a problem solving process and feel free to copy and adjust it your needs!

For a shorter process you can run in a single afternoon, this remote problem solving agenda will guide you effectively in just a couple of hours.

Whatever the length of your workshop, by using SessionLab, it’s easy to go from an idea to a complete agenda . Start by dragging and dropping your core problem solving activities into place . Add timings, breaks and necessary materials before sharing your agenda with your colleagues.

The resulting agenda will be your guide to an effective and productive problem solving session that will also help you stay organized on the day!

Complete problem-solving methods

In this section, we’ll look at in-depth problem-solving methods that provide a complete end-to-end process for developing effective solutions. These will help guide your team from the discovery and definition of a problem through to delivering the right solution.

If you’re looking for an all-encompassing method or problem-solving model, these processes are a great place to start. They’ll ask your team to challenge preconceived ideas and adopt a mindset for solving problems more effectively.

Six Thinking Hats

Individual approaches to solving a problem can be very different based on what team or role an individual holds. It can be easy for existing biases or perspectives to find their way into the mix, or for internal politics to direct a conversation.

Six Thinking Hats is a classic method for identifying the problems that need to be solved and enables your team to consider them from different angles, whether that is by focusing on facts and data, creative solutions, or by considering why a particular solution might not work.

Like all problem-solving frameworks, Six Thinking Hats is effective at helping teams remove roadblocks from a conversation or discussion and come to terms with all the aspects necessary to solve complex problems.

The Six Thinking Hats #creative thinking #meeting facilitation #problem solving #issue resolution #idea generation #conflict resolution The Six Thinking Hats are used by individuals and groups to separate out conflicting styles of thinking. They enable and encourage a group of people to think constructively together in exploring and implementing change, rather than using argument to fight over who is right and who is wrong.

Lightning Decision Jam

Featured courtesy of Jonathan Courtney of AJ&Smart Berlin, Lightning Decision Jam is one of those strategies that should be in every facilitation toolbox. Exploring problems and finding solutions is often creative in nature, though as with any creative process, there is the potential to lose focus and get lost.

Unstructured discussions might get you there in the end, but it’s much more effective to use a method that creates a clear process and team focus.

In Lightning Decision Jam, participants are invited to begin by writing challenges, concerns, or mistakes on post-its without discussing them before then being invited by the moderator to present them to the group.

From there, the team vote on which problems to solve and are guided through steps that will allow them to reframe those problems, create solutions and then decide what to execute on.

By deciding the problems that need to be solved as a team before moving on, this group process is great for ensuring the whole team is aligned and can take ownership over the next stages.

Lightning Decision Jam (LDJ) #action #decision making #problem solving #issue analysis #innovation #design #remote-friendly It doesn’t matter where you work and what your job role is, if you work with other people together as a team, you will always encounter the same challenges: Unclear goals and miscommunication that cause busy work and overtime Unstructured meetings that leave attendants tired, confused and without clear outcomes. Frustration builds up because internal challenges to productivity are not addressed Sudden changes in priorities lead to a loss of focus and momentum Muddled compromise takes the place of clear decision- making, leaving everybody to come up with their own interpretation. In short, a lack of structure leads to a waste of time and effort, projects that drag on for too long and frustrated, burnt out teams. AJ&Smart has worked with some of the most innovative, productive companies in the world. What sets their teams apart from others is not better tools, bigger talent or more beautiful offices. The secret sauce to becoming a more productive, more creative and happier team is simple: Replace all open discussion or brainstorming with a structured process that leads to more ideas, clearer decisions and better outcomes. When a good process provides guardrails and a clear path to follow, it becomes easier to come up with ideas, make decisions and solve problems. This is why AJ&Smart created Lightning Decision Jam (LDJ). It’s a simple and short, but powerful group exercise that can be run either in-person, in the same room, or remotely with distributed teams.

Problem Definition Process

While problems can be complex, the problem-solving methods you use to identify and solve those problems can often be simple in design.

By taking the time to truly identify and define a problem before asking the group to reframe the challenge as an opportunity, this method is a great way to enable change.

Begin by identifying a focus question and exploring the ways in which it manifests before splitting into five teams who will each consider the problem using a different method: escape, reversal, exaggeration, distortion or wishful. Teams develop a problem objective and create ideas in line with their method before then feeding them back to the group.

This method is great for enabling in-depth discussions while also creating space for finding creative solutions too!

Problem Definition #problem solving #idea generation #creativity #online #remote-friendly A problem solving technique to define a problem, challenge or opportunity and to generate ideas.

The 5 Whys

Sometimes, a group needs to go further with their strategies and analyze the root cause at the heart of organizational issues. An RCA or root cause analysis is the process of identifying what is at the heart of business problems or recurring challenges.

The 5 Whys is a simple and effective method of helping a group go find the root cause of any problem or challenge and conduct analysis that will deliver results.

By beginning with the creation of a problem statement and going through five stages to refine it, The 5 Whys provides everything you need to truly discover the cause of an issue.

The 5 Whys #hyperisland #innovation This simple and powerful method is useful for getting to the core of a problem or challenge. As the title suggests, the group defines a problems, then asks the question “why” five times, often using the resulting explanation as a starting point for creative problem solving.

World Cafe is a simple but powerful facilitation technique to help bigger groups to focus their energy and attention on solving complex problems.

World Cafe enables this approach by creating a relaxed atmosphere where participants are able to self-organize and explore topics relevant and important to them which are themed around a central problem-solving purpose. Create the right atmosphere by modeling your space after a cafe and after guiding the group through the method, let them take the lead!

Making problem-solving a part of your organization’s culture in the long term can be a difficult undertaking. More approachable formats like World Cafe can be especially effective in bringing people unfamiliar with workshops into the fold.

World Cafe #hyperisland #innovation #issue analysis World Café is a simple yet powerful method, originated by Juanita Brown, for enabling meaningful conversations driven completely by participants and the topics that are relevant and important to them. Facilitators create a cafe-style space and provide simple guidelines. Participants then self-organize and explore a set of relevant topics or questions for conversation.

Discovery & Action Dialogue (DAD)

One of the best approaches is to create a safe space for a group to share and discover practices and behaviors that can help them find their own solutions.

With DAD, you can help a group choose which problems they wish to solve and which approaches they will take to do so. It’s great at helping remove resistance to change and can help get buy-in at every level too!

This process of enabling frontline ownership is great in ensuring follow-through and is one of the methods you will want in your toolbox as a facilitator.

Discovery & Action Dialogue (DAD) #idea generation #liberating structures #action #issue analysis #remote-friendly DADs make it easy for a group or community to discover practices and behaviors that enable some individuals (without access to special resources and facing the same constraints) to find better solutions than their peers to common problems. These are called positive deviant (PD) behaviors and practices. DADs make it possible for people in the group, unit, or community to discover by themselves these PD practices. DADs also create favorable conditions for stimulating participants’ creativity in spaces where they can feel safe to invent new and more effective practices. Resistance to change evaporates as participants are unleashed to choose freely which practices they will adopt or try and which problems they will tackle. DADs make it possible to achieve frontline ownership of solutions.

Design Sprint 2.0

Want to see how a team can solve big problems and move forward with prototyping and testing solutions in a few days? The Design Sprint 2.0 template from Jake Knapp, author of Sprint, is a complete agenda for a with proven results.

Developing the right agenda can involve difficult but necessary planning. Ensuring all the correct steps are followed can also be stressful or time-consuming depending on your level of experience.

Use this complete 4-day workshop template if you are finding there is no obvious solution to your challenge and want to focus your team around a specific problem that might require a shortcut to launching a minimum viable product or waiting for the organization-wide implementation of a solution.

Open space technology

Open space technology- developed by Harrison Owen – creates a space where large groups are invited to take ownership of their problem solving and lead individual sessions. Open space technology is a great format when you have a great deal of expertise and insight in the room and want to allow for different takes and approaches on a particular theme or problem you need to be solved.

Start by bringing your participants together to align around a central theme and focus their efforts. Explain the ground rules to help guide the problem-solving process and then invite members to identify any issue connecting to the central theme that they are interested in and are prepared to take responsibility for.

Once participants have decided on their approach to the core theme, they write their issue on a piece of paper, announce it to the group, pick a session time and place, and post the paper on the wall. As the wall fills up with sessions, the group is then invited to join the sessions that interest them the most and which they can contribute to, then you’re ready to begin!

Everyone joins the problem-solving group they’ve signed up to, record the discussion and if appropriate, findings can then be shared with the rest of the group afterward.

Open Space Technology #action plan #idea generation #problem solving #issue analysis #large group #online #remote-friendly Open Space is a methodology for large groups to create their agenda discerning important topics for discussion, suitable for conferences, community gatherings and whole system facilitation

Techniques to identify and analyze problems

Using a problem-solving method to help a team identify and analyze a problem can be a quick and effective addition to any workshop or meeting.

While further actions are always necessary, you can generate momentum and alignment easily, and these activities are a great place to get started.

We’ve put together this list of techniques to help you and your team with problem identification, analysis, and discussion that sets the foundation for developing effective solutions.

Let’s take a look!

Fishbone Analysis

Organizational or team challenges are rarely simple, and it’s important to remember that one problem can be an indication of something that goes deeper and may require further consideration to be solved.

Fishbone Analysis helps groups to dig deeper and understand the origins of a problem. It’s a great example of a root cause analysis method that is simple for everyone on a team to get their head around.

Participants in this activity are asked to annotate a diagram of a fish, first adding the problem or issue to be worked on at the head of a fish before then brainstorming the root causes of the problem and adding them as bones on the fish.

Using abstractions such as a diagram of a fish can really help a team break out of their regular thinking and develop a creative approach.

Fishbone Analysis #problem solving ##root cause analysis #decision making #online facilitation A process to help identify and understand the origins of problems, issues or observations.

Problem Tree

Encouraging visual thinking can be an essential part of many strategies. By simply reframing and clarifying problems, a group can move towards developing a problem solving model that works for them.

In Problem Tree, groups are asked to first brainstorm a list of problems – these can be design problems, team problems or larger business problems – and then organize them into a hierarchy. The hierarchy could be from most important to least important or abstract to practical, though the key thing with problem solving games that involve this aspect is that your group has some way of managing and sorting all the issues that are raised.

Once you have a list of problems that need to be solved and have organized them accordingly, you’re then well-positioned for the next problem solving steps.

Problem tree #define intentions #create #design #issue analysis A problem tree is a tool to clarify the hierarchy of problems addressed by the team within a design project; it represents high level problems or related sublevel problems.

SWOT Analysis

Chances are you’ve heard of the SWOT Analysis before. This problem-solving method focuses on identifying strengths, weaknesses, opportunities, and threats is a tried and tested method for both individuals and teams.

Start by creating a desired end state or outcome and bare this in mind – any process solving model is made more effective by knowing what you are moving towards. Create a quadrant made up of the four categories of a SWOT analysis and ask participants to generate ideas based on each of those quadrants.

Once you have those ideas assembled in their quadrants, cluster them together based on their affinity with other ideas. These clusters are then used to facilitate group conversations and move things forward.

SWOT analysis #gamestorming #problem solving #action #meeting facilitation The SWOT Analysis is a long-standing technique of looking at what we have, with respect to the desired end state, as well as what we could improve on. It gives us an opportunity to gauge approaching opportunities and dangers, and assess the seriousness of the conditions that affect our future. When we understand those conditions, we can influence what comes next.

Agreement-Certainty Matrix

Not every problem-solving approach is right for every challenge, and deciding on the right method for the challenge at hand is a key part of being an effective team.

The Agreement Certainty matrix helps teams align on the nature of the challenges facing them. By sorting problems from simple to chaotic, your team can understand what methods are suitable for each problem and what they can do to ensure effective results.

If you are already using Liberating Structures techniques as part of your problem-solving strategy, the Agreement-Certainty Matrix can be an invaluable addition to your process. We’ve found it particularly if you are having issues with recurring problems in your organization and want to go deeper in understanding the root cause.

Agreement-Certainty Matrix #issue analysis #liberating structures #problem solving You can help individuals or groups avoid the frequent mistake of trying to solve a problem with methods that are not adapted to the nature of their challenge. The combination of two questions makes it possible to easily sort challenges into four categories: simple, complicated, complex , and chaotic . A problem is simple when it can be solved reliably with practices that are easy to duplicate. It is complicated when experts are required to devise a sophisticated solution that will yield the desired results predictably. A problem is complex when there are several valid ways to proceed but outcomes are not predictable in detail. Chaotic is when the context is too turbulent to identify a path forward. A loose analogy may be used to describe these differences: simple is like following a recipe, complicated like sending a rocket to the moon, complex like raising a child, and chaotic is like the game “Pin the Tail on the Donkey.” The Liberating Structures Matching Matrix in Chapter 5 can be used as the first step to clarify the nature of a challenge and avoid the mismatches between problems and solutions that are frequently at the root of chronic, recurring problems.

Organizing and charting a team’s progress can be important in ensuring its success. SQUID (Sequential Question and Insight Diagram) is a great model that allows a team to effectively switch between giving questions and answers and develop the skills they need to stay on track throughout the process.

Begin with two different colored sticky notes – one for questions and one for answers – and with your central topic (the head of the squid) on the board. Ask the group to first come up with a series of questions connected to their best guess of how to approach the topic. Ask the group to come up with answers to those questions, fix them to the board and connect them with a line. After some discussion, go back to question mode by responding to the generated answers or other points on the board.

It’s rewarding to see a diagram grow throughout the exercise, and a completed SQUID can provide a visual resource for future effort and as an example for other teams.

SQUID #gamestorming #project planning #issue analysis #problem solving When exploring an information space, it’s important for a group to know where they are at any given time. By using SQUID, a group charts out the territory as they go and can navigate accordingly. SQUID stands for Sequential Question and Insight Diagram.

To continue with our nautical theme, Speed Boat is a short and sweet activity that can help a team quickly identify what employees, clients or service users might have a problem with and analyze what might be standing in the way of achieving a solution.

Methods that allow for a group to make observations, have insights and obtain those eureka moments quickly are invaluable when trying to solve complex problems.

In Speed Boat, the approach is to first consider what anchors and challenges might be holding an organization (or boat) back. Bonus points if you are able to identify any sharks in the water and develop ideas that can also deal with competitors!

Speed Boat #gamestorming #problem solving #action Speedboat is a short and sweet way to identify what your employees or clients don’t like about your product/service or what’s standing in the way of a desired goal.

The Journalistic Six

Some of the most effective ways of solving problems is by encouraging teams to be more inclusive and diverse in their thinking.

Based on the six key questions journalism students are taught to answer in articles and news stories, The Journalistic Six helps create teams to see the whole picture. By using who, what, when, where, why, and how to facilitate the conversation and encourage creative thinking, your team can make sure that the problem identification and problem analysis stages of the are covered exhaustively and thoughtfully. Reporter’s notebook and dictaphone optional.

The Journalistic Six – Who What When Where Why How #idea generation #issue analysis #problem solving #online #creative thinking #remote-friendly A questioning method for generating, explaining, investigating ideas.

Individual and group perspectives are incredibly important, but what happens if people are set in their minds and need a change of perspective in order to approach a problem more effectively?

Flip It is a method we love because it is both simple to understand and run, and allows groups to understand how their perspectives and biases are formed.

Participants in Flip It are first invited to consider concerns, issues, or problems from a perspective of fear and write them on a flip chart. Then, the group is asked to consider those same issues from a perspective of hope and flip their understanding.

No problem and solution is free from existing bias and by changing perspectives with Flip It, you can then develop a problem solving model quickly and effectively.

Flip It! #gamestorming #problem solving #action Often, a change in a problem or situation comes simply from a change in our perspectives. Flip It! is a quick game designed to show players that perspectives are made, not born.

LEGO Challenge

Now for an activity that is a little out of the (toy) box. LEGO Serious Play is a facilitation methodology that can be used to improve creative thinking and problem-solving skills.

The LEGO Challenge includes giving each member of the team an assignment that is hidden from the rest of the group while they create a structure without speaking.

What the LEGO challenge brings to the table is a fun working example of working with stakeholders who might not be on the same page to solve problems. Also, it’s LEGO! Who doesn’t love LEGO!

LEGO Challenge #hyperisland #team A team-building activity in which groups must work together to build a structure out of LEGO, but each individual has a secret “assignment” which makes the collaborative process more challenging. It emphasizes group communication, leadership dynamics, conflict, cooperation, patience and problem solving strategy.

What, So What, Now What?

If not carefully managed, the problem identification and problem analysis stages of the problem-solving process can actually create more problems and misunderstandings.

The What, So What, Now What? problem-solving activity is designed to help collect insights and move forward while also eliminating the possibility of disagreement when it comes to identifying, clarifying, and analyzing organizational or work problems.

Facilitation is all about bringing groups together so that might work on a shared goal and the best problem-solving strategies ensure that teams are aligned in purpose, if not initially in opinion or insight.

Throughout the three steps of this game, you give everyone on a team to reflect on a problem by asking what happened, why it is important, and what actions should then be taken.

This can be a great activity for bringing our individual perceptions about a problem or challenge and contextualizing it in a larger group setting. This is one of the most important problem-solving skills you can bring to your organization.

W³ – What, So What, Now What? #issue analysis #innovation #liberating structures You can help groups reflect on a shared experience in a way that builds understanding and spurs coordinated action while avoiding unproductive conflict. It is possible for every voice to be heard while simultaneously sifting for insights and shaping new direction. Progressing in stages makes this practical—from collecting facts about What Happened to making sense of these facts with So What and finally to what actions logically follow with Now What . The shared progression eliminates most of the misunderstandings that otherwise fuel disagreements about what to do. Voila!

Journalists

Problem analysis can be one of the most important and decisive stages of all problem-solving tools. Sometimes, a team can become bogged down in the details and are unable to move forward.

Journalists is an activity that can avoid a group from getting stuck in the problem identification or problem analysis stages of the process.

In Journalists, the group is invited to draft the front page of a fictional newspaper and figure out what stories deserve to be on the cover and what headlines those stories will have. By reframing how your problems and challenges are approached, you can help a team move productively through the process and be better prepared for the steps to follow.

Journalists #vision #big picture #issue analysis #remote-friendly This is an exercise to use when the group gets stuck in details and struggles to see the big picture. Also good for defining a vision.

Problem-solving techniques for brainstorming solutions

Now you have the context and background of the problem you are trying to solving, now comes the time to start ideating and thinking about how you’ll solve the issue.

Here, you’ll want to encourage creative, free thinking and speed. Get as many ideas out as possible and explore different perspectives so you have the raw material for the next step.

Looking at a problem from a new angle can be one of the most effective ways of creating an effective solution. TRIZ is a problem-solving tool that asks the group to consider what they must not do in order to solve a challenge.

By reversing the discussion, new topics and taboo subjects often emerge, allowing the group to think more deeply and create ideas that confront the status quo in a safe and meaningful way. If you’re working on a problem that you’ve tried to solve before, TRIZ is a great problem-solving method to help your team get unblocked.

Making Space with TRIZ #issue analysis #liberating structures #issue resolution You can clear space for innovation by helping a group let go of what it knows (but rarely admits) limits its success and by inviting creative destruction. TRIZ makes it possible to challenge sacred cows safely and encourages heretical thinking. The question “What must we stop doing to make progress on our deepest purpose?” induces seriously fun yet very courageous conversations. Since laughter often erupts, issues that are otherwise taboo get a chance to be aired and confronted. With creative destruction come opportunities for renewal as local action and innovation rush in to fill the vacuum. Whoosh!

Mindspin

Brainstorming is part of the bread and butter of the problem-solving process and all problem-solving strategies benefit from getting ideas out and challenging a team to generate solutions quickly.

With Mindspin, participants are encouraged not only to generate ideas but to do so under time constraints and by slamming down cards and passing them on. By doing multiple rounds, your team can begin with a free generation of possible solutions before moving on to developing those solutions and encouraging further ideation.

This is one of our favorite problem-solving activities and can be great for keeping the energy up throughout the workshop. Remember the importance of helping people become engaged in the process – energizing problem-solving techniques like Mindspin can help ensure your team stays engaged and happy, even when the problems they’re coming together to solve are complex.

MindSpin #teampedia #idea generation #problem solving #action A fast and loud method to enhance brainstorming within a team. Since this activity has more than round ideas that are repetitive can be ruled out leaving more creative and innovative answers to the challenge.

The Creativity Dice

One of the most useful problem solving skills you can teach your team is of approaching challenges with creativity, flexibility, and openness. Games like The Creativity Dice allow teams to overcome the potential hurdle of too much linear thinking and approach the process with a sense of fun and speed.

In The Creativity Dice, participants are organized around a topic and roll a dice to determine what they will work on for a period of 3 minutes at a time. They might roll a 3 and work on investigating factual information on the chosen topic. They might roll a 1 and work on identifying the specific goals, standards, or criteria for the session.

Encouraging rapid work and iteration while asking participants to be flexible are great skills to cultivate. Having a stage for idea incubation in this game is also important. Moments of pause can help ensure the ideas that are put forward are the most suitable.

The Creativity Dice #creativity #problem solving #thiagi #issue analysis Too much linear thinking is hazardous to creative problem solving. To be creative, you should approach the problem (or the opportunity) from different points of view. You should leave a thought hanging in mid-air and move to another. This skipping around prevents premature closure and lets your brain incubate one line of thought while you consciously pursue another.

Idea and Concept Development

Brainstorming without structure can quickly become chaotic or frustrating. In a problem-solving context, having an ideation framework to follow can help ensure your team is both creative and disciplined.

In this method, you’ll find an idea generation process that encourages your group to brainstorm effectively before developing their ideas and begin clustering them together. By using concepts such as Yes and…, more is more and postponing judgement, you can create the ideal conditions for brainstorming with ease.

Idea & Concept Development #hyperisland #innovation #idea generation Ideation and Concept Development is a process for groups to work creatively and collaboratively to generate creative ideas. It’s a general approach that can be adapted and customized to suit many different scenarios. It includes basic principles for idea generation and several steps for groups to work with. It also includes steps for idea selection and development.

Problem-solving techniques for developing and refining solutions

The success of any problem-solving process can be measured by the solutions it produces. After you’ve defined the issue, explored existing ideas, and ideated, it’s time to develop and refine your ideas in order to bring them closer to a solution that actually solves the problem.

Use these problem-solving techniques when you want to help your team think through their ideas and refine them as part of your problem solving process.

Improved Solutions

After a team has successfully identified a problem and come up with a few solutions, it can be tempting to call the work of the problem-solving process complete. That said, the first solution is not necessarily the best, and by including a further review and reflection activity into your problem-solving model, you can ensure your group reaches the best possible result.

One of a number of problem-solving games from Thiagi Group, Improved Solutions helps you go the extra mile and develop suggested solutions with close consideration and peer review. By supporting the discussion of several problems at once and by shifting team roles throughout, this problem-solving technique is a dynamic way of finding the best solution.

Improved Solutions #creativity #thiagi #problem solving #action #team You can improve any solution by objectively reviewing its strengths and weaknesses and making suitable adjustments. In this creativity framegame, you improve the solutions to several problems. To maintain objective detachment, you deal with a different problem during each of six rounds and assume different roles (problem owner, consultant, basher, booster, enhancer, and evaluator) during each round. At the conclusion of the activity, each player ends up with two solutions to her problem.

Four Step Sketch

Creative thinking and visual ideation does not need to be confined to the opening stages of your problem-solving strategies. Exercises that include sketching and prototyping on paper can be effective at the solution finding and development stage of the process, and can be great for keeping a team engaged.

By going from simple notes to a crazy 8s round that involves rapidly sketching 8 variations on their ideas before then producing a final solution sketch, the group is able to iterate quickly and visually. Problem-solving techniques like Four-Step Sketch are great if you have a group of different thinkers and want to change things up from a more textual or discussion-based approach.

Four-Step Sketch #design sprint #innovation #idea generation #remote-friendly The four-step sketch is an exercise that helps people to create well-formed concepts through a structured process that includes: Review key information Start design work on paper, Consider multiple variations , Create a detailed solution . This exercise is preceded by a set of other activities allowing the group to clarify the challenge they want to solve. See how the Four Step Sketch exercise fits into a Design Sprint

Ensuring that everyone in a group is able to contribute to a discussion is vital during any problem solving process. Not only does this ensure all bases are covered, but its then easier to get buy-in and accountability when people have been able to contribute to the process.

1-2-4-All is a tried and tested facilitation technique where participants are asked to first brainstorm on a topic on their own. Next, they discuss and share ideas in a pair before moving into a small group. Those groups are then asked to present the best idea from their discussion to the rest of the team.

This method can be used in many different contexts effectively, though I find it particularly shines in the idea development stage of the process. Giving each participant time to concretize their ideas and develop them in progressively larger groups can create a great space for both innovation and psychological safety.

1-2-4-All #idea generation #liberating structures #issue analysis With this facilitation technique you can immediately include everyone regardless of how large the group is. You can generate better ideas and more of them faster than ever before. You can tap the know-how and imagination that is distributed widely in places not known in advance. Open, generative conversation unfolds. Ideas and solutions are sifted in rapid fashion. Most importantly, participants own the ideas, so follow-up and implementation is simplified. No buy-in strategies needed! Simple and elegant!

15% Solutions

Some problems are simpler than others and with the right problem-solving activities, you can empower people to take immediate actions that can help create organizational change.

Part of the liberating structures toolkit, 15% solutions is a problem-solving technique that focuses on finding and implementing solutions quickly. A process of iterating and making small changes quickly can help generate momentum and an appetite for solving complex problems.

Problem-solving strategies can live and die on whether people are onboard. Getting some quick wins is a great way of getting people behind the process.

It can be extremely empowering for a team to realize that problem-solving techniques can be deployed quickly and easily and delineate between things they can positively impact and those things they cannot change.

15% Solutions #action #liberating structures #remote-friendly You can reveal the actions, however small, that everyone can do immediately. At a minimum, these will create momentum, and that may make a BIG difference. 15% Solutions show that there is no reason to wait around, feel powerless, or fearful. They help people pick it up a level. They get individuals and the group to focus on what is within their discretion instead of what they cannot change. With a very simple question, you can flip the conversation to what can be done and find solutions to big problems that are often distributed widely in places not known in advance. Shifting a few grains of sand may trigger a landslide and change the whole landscape.

Problem-solving techniques for making decisions and planning

After your group is happy with the possible solutions you’ve developed, now comes the time to choose which to implement. There’s more than one way to make a decision and the best option is often dependant on the needs and set-up of your group.

Sometimes, it’s the case that you’ll want to vote as a group on what is likely to be the most impactful solution. Other times, it might be down to a decision maker or major stakeholder to make the final decision. Whatever your process, here’s some techniques you can use to help you make a decision during your problem solving process.

How-Now-Wow Matrix

The problem-solving process is often creative, as complex problems usually require a change of thinking and creative response in order to find the best solutions. While it’s common for the first stages to encourage creative thinking, groups can often gravitate to familiar solutions when it comes to the end of the process.

When selecting solutions, you don’t want to lose your creative energy! The How-Now-Wow Matrix from Gamestorming is a great problem-solving activity that enables a group to stay creative and think out of the box when it comes to selecting the right solution for a given problem.

Problem-solving techniques that encourage creative thinking and the ideation and selection of new solutions can be the most effective in organisational change. Give the How-Now-Wow Matrix a go, and not just for how pleasant it is to say out loud.

How-Now-Wow Matrix #gamestorming #idea generation #remote-friendly When people want to develop new ideas, they most often think out of the box in the brainstorming or divergent phase. However, when it comes to convergence, people often end up picking ideas that are most familiar to them. This is called a ‘creative paradox’ or a ‘creadox’. The How-Now-Wow matrix is an idea selection tool that breaks the creadox by forcing people to weigh each idea on 2 parameters.

Impact and Effort Matrix

All problem-solving techniques hope to not only find solutions to a given problem or challenge but to find the best solution. When it comes to finding a solution, groups are invited to put on their decision-making hats and really think about how a proposed idea would work in practice.

The Impact and Effort Matrix is one of the problem-solving techniques that fall into this camp, empowering participants to first generate ideas and then categorize them into a 2×2 matrix based on impact and effort.

Activities that invite critical thinking while remaining simple are invaluable. Use the Impact and Effort Matrix to move from ideation and towards evaluating potential solutions before then committing to them.

Impact and Effort Matrix #gamestorming #decision making #action #remote-friendly In this decision-making exercise, possible actions are mapped based on two factors: effort required to implement and potential impact. Categorizing ideas along these lines is a useful technique in decision making, as it obliges contributors to balance and evaluate suggested actions before committing to them.

If you’ve followed each of the problem-solving steps with your group successfully, you should move towards the end of your process with heaps of possible solutions developed with a specific problem in mind. But how do you help a group go from ideation to putting a solution into action?

Dotmocracy – or Dot Voting -is a tried and tested method of helping a team in the problem-solving process make decisions and put actions in place with a degree of oversight and consensus.

One of the problem-solving techniques that should be in every facilitator’s toolbox, Dot Voting is fast and effective and can help identify the most popular and best solutions and help bring a group to a decision effectively.

Dotmocracy #action #decision making #group prioritization #hyperisland #remote-friendly Dotmocracy is a simple method for group prioritization or decision-making. It is not an activity on its own, but a method to use in processes where prioritization or decision-making is the aim. The method supports a group to quickly see which options are most popular or relevant. The options or ideas are written on post-its and stuck up on a wall for the whole group to see. Each person votes for the options they think are the strongest, and that information is used to inform a decision.

Straddling the gap between decision making and planning, MoSCoW is a simple and effective method that allows a group team to easily prioritize a set of possible options.

Use this method in a problem solving process by collecting and summarizing all your possible solutions and then categorize them into 4 sections: “Must have”, “Should have”, “Could have”, or “Would like but won‘t get”.

This method is particularly useful when its less about choosing one possible solution and more about prioritorizing which to do first and which may not fit in the scope of your project. In my experience, complex challenges often require multiple small fixes, and this method can be a great way to move from a pile of things you’d all like to do to a structured plan.

MoSCoW #define intentions #create #design #action #remote-friendly MoSCoW is a method that allows the team to prioritize the different features that they will work on. Features are then categorized into “Must have”, “Should have”, “Could have”, or “Would like but won‘t get”. To be used at the beginning of a timeslot (for example during Sprint planning) and when planning is needed.

When it comes to managing the rollout of a solution, clarity and accountability are key factors in ensuring the success of the project. The RAACI chart is a simple but effective model for setting roles and responsibilities as part of a planning session.

Start by listing each person involved in the project and put them into the following groups in order to make it clear who is responsible for what during the rollout of your solution.

Responsibility (Which person and/or team will be taking action?)
Authority (At what “point” must the responsible person check in before going further?)
Accountability (Who must the responsible person check in with?)
Consultation (Who must be consulted by the responsible person before decisions are made?)
Information (Who must be informed of decisions, once made?)

Ensure this information is easily accessible and use it to inform who does what and who is looped into discussions and kept up to date.

RAACI #roles and responsibility #teamwork #project management Clarifying roles and responsibilities, levels of autonomy/latitude in decision making, and levels of engagement among diverse stakeholders.

Problem-solving warm-up activities

All facilitators know that warm-ups and icebreakers are useful for any workshop or group process. Problem-solving workshops are no different.

Use these problem-solving techniques to warm up a group and prepare them for the rest of the process. Activating your group by tapping into some of the top problem-solving skills can be one of the best ways to see great outcomes from your session.

Check-in / Check-out

Solid processes are planned from beginning to end, and the best facilitators know that setting the tone and establishing a safe, open environment can be integral to a successful problem-solving process. Check-in / Check-out is a great way to begin and/or bookend a problem-solving workshop. Checking in to a session emphasizes that everyone will be seen, heard, and expected to contribute.

If you are running a series of meetings, setting a consistent pattern of checking in and checking out can really help your team get into a groove. We recommend this opening-closing activity for small to medium-sized groups though it can work with large groups if they’re disciplined!

Check-in / Check-out #team #opening #closing #hyperisland #remote-friendly Either checking-in or checking-out is a simple way for a team to open or close a process, symbolically and in a collaborative way. Checking-in/out invites each member in a group to be present, seen and heard, and to express a reflection or a feeling. Checking-in emphasizes presence, focus and group commitment; checking-out emphasizes reflection and symbolic closure.

Doodling Together

Thinking creatively and not being afraid to make suggestions are important problem-solving skills for any group or team, and warming up by encouraging these behaviors is a great way to start.

Doodling Together is one of our favorite creative ice breaker games – it’s quick, effective, and fun and can make all following problem-solving steps easier by encouraging a group to collaborate visually. By passing cards and adding additional items as they go, the workshop group gets into a groove of co-creation and idea development that is crucial to finding solutions to problems.

Doodling Together #collaboration #creativity #teamwork #fun #team #visual methods #energiser #icebreaker #remote-friendly Create wild, weird and often funny postcards together & establish a group’s creative confidence.

Show and Tell

You might remember some version of Show and Tell from being a kid in school and it’s a great problem-solving activity to kick off a session.

Asking participants to prepare a little something before a workshop by bringing an object for show and tell can help them warm up before the session has even begun! Games that include a physical object can also help encourage early engagement before moving onto more big-picture thinking.

By asking your participants to tell stories about why they chose to bring a particular item to the group, you can help teams see things from new perspectives and see both differences and similarities in the way they approach a topic. Great groundwork for approaching a problem-solving process as a team!

Show and Tell #gamestorming #action #opening #meeting facilitation Show and Tell taps into the power of metaphors to reveal players’ underlying assumptions and associations around a topic The aim of the game is to get a deeper understanding of stakeholders’ perspectives on anything—a new project, an organizational restructuring, a shift in the company’s vision or team dynamic.

Constellations

Who doesn’t love stars? Constellations is a great warm-up activity for any workshop as it gets people up off their feet, energized, and ready to engage in new ways with established topics. It’s also great for showing existing beliefs, biases, and patterns that can come into play as part of your session.

Using warm-up games that help build trust and connection while also allowing for non-verbal responses can be great for easing people into the problem-solving process and encouraging engagement from everyone in the group. Constellations is great in large spaces that allow for movement and is definitely a practical exercise to allow the group to see patterns that are otherwise invisible.

Constellations #trust #connection #opening #coaching #patterns #system Individuals express their response to a statement or idea by standing closer or further from a central object. Used with teams to reveal system, hidden patterns, perspectives.

Draw a Tree

Problem-solving games that help raise group awareness through a central, unifying metaphor can be effective ways to warm-up a group in any problem-solving model.

Draw a Tree is a simple warm-up activity you can use in any group and which can provide a quick jolt of energy. Start by asking your participants to draw a tree in just 45 seconds – they can choose whether it will be abstract or realistic.

Once the timer is up, ask the group how many people included the roots of the tree and use this as a means to discuss how we can ignore important parts of any system simply because they are not visible.

All problem-solving strategies are made more effective by thinking of problems critically and by exposing things that may not normally come to light. Warm-up games like Draw a Tree are great in that they quickly demonstrate some key problem-solving skills in an accessible and effective way.

Draw a Tree #thiagi #opening #perspectives #remote-friendly With this game you can raise awarness about being more mindful, and aware of the environment we live in.

Closing activities for a problem-solving process

Each step of the problem-solving workshop benefits from an intelligent deployment of activities, games, and techniques. Bringing your session to an effective close helps ensure that solutions are followed through on and that you also celebrate what has been achieved.

Here are some problem-solving activities you can use to effectively close a workshop or meeting and ensure the great work you’ve done can continue afterward.

One Breath Feedback

Maintaining attention and focus during the closing stages of a problem-solving workshop can be tricky and so being concise when giving feedback can be important. It’s easy to incur “death by feedback” should some team members go on for too long sharing their perspectives in a quick feedback round.

One Breath Feedback is a great closing activity for workshops. You give everyone an opportunity to provide feedback on what they’ve done but only in the space of a single breath. This keeps feedback short and to the point and means that everyone is encouraged to provide the most important piece of feedback to them.

One breath feedback #closing #feedback #action This is a feedback round in just one breath that excels in maintaining attention: each participants is able to speak during just one breath … for most people that’s around 20 to 25 seconds … unless of course you’ve been a deep sea diver in which case you’ll be able to do it for longer.

Who What When Matrix

Matrices feature as part of many effective problem-solving strategies and with good reason. They are easily recognizable, simple to use, and generate results.

The Who What When Matrix is a great tool to use when closing your problem-solving session by attributing a who, what and when to the actions and solutions you have decided upon. The resulting matrix is a simple, easy-to-follow way of ensuring your team can move forward.

Great solutions can’t be enacted without action and ownership. Your problem-solving process should include a stage for allocating tasks to individuals or teams and creating a realistic timeframe for those solutions to be implemented or checked out. Use this method to keep the solution implementation process clear and simple for all involved.

Who/What/When Matrix #gamestorming #action #project planning With Who/What/When matrix, you can connect people with clear actions they have defined and have committed to.

Response cards

Group discussion can comprise the bulk of most problem-solving activities and by the end of the process, you might find that your team is talked out!

Providing a means for your team to give feedback with short written notes can ensure everyone is head and can contribute without the need to stand up and talk. Depending on the needs of the group, giving an alternative can help ensure everyone can contribute to your problem-solving model in the way that makes the most sense for them.

Response Cards is a great way to close a workshop if you are looking for a gentle warm-down and want to get some swift discussion around some of the feedback that is raised.

Response Cards #debriefing #closing #structured sharing #questions and answers #thiagi #action It can be hard to involve everyone during a closing of a session. Some might stay in the background or get unheard because of louder participants. However, with the use of Response Cards, everyone will be involved in providing feedback or clarify questions at the end of a session.

Tips for effective problem solving

Problem-solving activities are only one part of the puzzle. While a great method can help unlock your team’s ability to solve problems, without a thoughtful approach and strong facilitation the solutions may not be fit for purpose.

Let’s take a look at some problem-solving tips you can apply to any process to help it be a success!

Clearly define the problem

Jumping straight to solutions can be tempting, though without first clearly articulating a problem, the solution might not be the right one. Many of the problem-solving activities below include sections where the problem is explored and clearly defined before moving on.

This is a vital part of the problem-solving process and taking the time to fully define an issue can save time and effort later. A clear definition helps identify irrelevant information and it also ensures that your team sets off on the right track.

Don’t jump to conclusions

It’s easy for groups to exhibit cognitive bias or have preconceived ideas about both problems and potential solutions. Be sure to back up any problem statements or potential solutions with facts, research, and adequate forethought.

The best techniques ask participants to be methodical and challenge preconceived notions. Make sure you give the group enough time and space to collect relevant information and consider the problem in a new way. By approaching the process with a clear, rational mindset, you’ll often find that better solutions are more forthcoming.

Try different approaches

Problems come in all shapes and sizes and so too should the methods you use to solve them. If you find that one approach isn’t yielding results and your team isn’t finding different solutions, try mixing it up. You’ll be surprised at how using a new creative activity can unblock your team and generate great solutions.

Don’t take it personally

Depending on the nature of your team or organizational problems, it’s easy for conversations to get heated. While it’s good for participants to be engaged in the discussions, ensure that emotions don’t run too high and that blame isn’t thrown around while finding solutions.

You’re all in it together, and even if your team or area is seeing problems, that isn’t necessarily a disparagement of you personally. Using facilitation skills to manage group dynamics is one effective method of helping conversations be more constructive.

Get the right people in the room

Your problem-solving method is often only as effective as the group using it. Getting the right people on the job and managing the number of people present is important too!

If the group is too small, you may not get enough different perspectives to effectively solve a problem. If the group is too large, you can go round and round during the ideation stages.

Creating the right group makeup is also important in ensuring you have the necessary expertise and skillset to both identify and follow up on potential solutions. Carefully consider who to include at each stage to help ensure your problem-solving method is followed and positioned for success.

Create psychologically safe spaces for discussion

Identifying a problem accurately also requires that all members of a group are able to contribute their views in an open and safe manner.

It can be tough for people to stand up and contribute if the problems or challenges are emotive or personal in nature. Try and create a psychologically safe space for these kinds of discussions and where possible, create regular opportunities for challenges to be brought up organically.

Document everything

The best solutions can take refinement, iteration, and reflection to come out. Get into a habit of documenting your process in order to keep all the learnings from the session and to allow ideas to mature and develop. Many of the methods below involve the creation of documents or shared resources. Be sure to keep and share these so everyone can benefit from the work done!

Bring a facilitator

Facilitation is all about making group processes easier. With a subject as potentially emotive and important as problem-solving, having an impartial third party in the form of a facilitator can make all the difference in finding great solutions and keeping the process moving. Consider bringing a facilitator to your problem-solving session to get better results and generate meaningful solutions!

Develop your problem-solving skills

It takes time and practice to be an effective problem solver. While some roles or participants might more naturally gravitate towards problem-solving, it can take development and planning to help everyone create better solutions.

You might develop a training program, run a problem-solving workshop or simply ask your team to practice using the techniques below. Check out our post on problem-solving skills to see how you and your group can develop the right mental process and be more resilient to issues too!

Design a great agenda

Workshops are a great format for solving problems. With the right approach, you can focus a group and help them find the solutions to their own problems. But designing a process can be time-consuming and finding the right activities can be difficult.

Check out our workshop planning guide to level-up your agenda design and start running more effective workshops. Need inspiration? Check out templates designed by expert facilitators to help you kickstart your process!

Save time and effort creating an effective problem solving process

A structured problem solving process is a surefire way of solving tough problems, discovering creative solutions and driving organizational change. But how can you design for successful outcomes?

With SessionLab, it’s easy to design engaging workshops that deliver results. Drag, drop and reorder blocks to build your agenda. When you make changes or update your agenda, your session timing adjusts automatically , saving you time on manual adjustments.

Collaborating with stakeholders or clients? Share your agenda with a single click and collaborate in real-time. No more sending documents back and forth over email.

Explore how to use SessionLab to design effective problem solving workshops or watch this five minute video to see the planner in action!

Over to you

The problem-solving process can often be as complicated and multifaceted as the problems they are set-up to solve. With the right problem-solving techniques and a mix of exercises designed to guide discussion and generate purposeful ideas, we hope we’ve given you the tools to find the best solutions as simply and easily as possible.

Is there a problem-solving technique that you are missing here? Do you have a favorite activity or method you use when facilitating? Let us know in the comments below, we’d love to hear from you!

James Smart is Head of Content at SessionLab. He’s also a creative facilitator who has run workshops and designed courses for establishments like the National Centre for Writing, UK. He especially enjoys working with young people and empowering others in their creative practice.

thank you very much for these excellent techniques

Certainly wonderful article, very detailed. Shared!

Your list of techniques for problem solving can be helpfully extended by adding TRIZ to the list of techniques. TRIZ has 40 problem solving techniques derived from methods inventros and patent holders used to get new patents. About 10-12 are general approaches. many organization sponsor classes in TRIZ that are used to solve business problems or general organiztational problems. You can take a look at TRIZ and dwonload a free internet booklet to see if you feel it shound be included per your selection process.

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What is Problem Solving? (Steps, Techniques, Examples)

What is problem solving, definition and importance.

Problem solving is the process of finding solutions to obstacles or challenges you encounter in your life or work. It is a crucial skill that allows you to tackle complex situations, adapt to changes, and overcome difficulties with ease. Mastering this ability will contribute to both your personal and professional growth, leading to more successful outcomes and better decision-making.

Problem-Solving Steps

The problem-solving process typically includes the following steps:

Identify the issue : Recognize the problem that needs to be solved.
Analyze the situation : Examine the issue in depth, gather all relevant information, and consider any limitations or constraints that may be present.
Generate potential solutions : Brainstorm a list of possible solutions to the issue, without immediately judging or evaluating them.
Evaluate options : Weigh the pros and cons of each potential solution, considering factors such as feasibility, effectiveness, and potential risks.
Select the best solution : Choose the option that best addresses the problem and aligns with your objectives.
Implement the solution : Put the selected solution into action and monitor the results to ensure it resolves the issue.
Review and learn : Reflect on the problem-solving process, identify any improvements or adjustments that can be made, and apply these learnings to future situations.

Defining the Problem

To start tackling a problem, first, identify and understand it. Analyzing the issue thoroughly helps to clarify its scope and nature. Ask questions to gather information and consider the problem from various angles. Some strategies to define the problem include:

Brainstorming with others
Asking the 5 Ws and 1 H (Who, What, When, Where, Why, and How)
Analyzing cause and effect
Creating a problem statement

Generating Solutions

Once the problem is clearly understood, brainstorm possible solutions. Think creatively and keep an open mind, as well as considering lessons from past experiences. Consider:

Creating a list of potential ideas to solve the problem
Grouping and categorizing similar solutions
Prioritizing potential solutions based on feasibility, cost, and resources required
Involving others to share diverse opinions and inputs

Evaluating and Selecting Solutions

Evaluate each potential solution, weighing its pros and cons. To facilitate decision-making, use techniques such as:

SWOT analysis (Strengths, Weaknesses, Opportunities, Threats)
Decision-making matrices
Pros and cons lists
Risk assessments

After evaluating, choose the most suitable solution based on effectiveness, cost, and time constraints.

Implementing and Monitoring the Solution

Implement the chosen solution and monitor its progress. Key actions include:

Communicating the solution to relevant parties
Setting timelines and milestones
Assigning tasks and responsibilities
Monitoring the solution and making adjustments as necessary
Evaluating the effectiveness of the solution after implementation

Utilize feedback from stakeholders and consider potential improvements. Remember that problem-solving is an ongoing process that can always be refined and enhanced.

Problem-Solving Techniques

During each step, you may find it helpful to utilize various problem-solving techniques, such as:

Brainstorming : A free-flowing, open-minded session where ideas are generated and listed without judgment, to encourage creativity and innovative thinking.
Root cause analysis : A method that explores the underlying causes of a problem to find the most effective solution rather than addressing superficial symptoms.
SWOT analysis : A tool used to evaluate the strengths, weaknesses, opportunities, and threats related to a problem or decision, providing a comprehensive view of the situation.
Mind mapping : A visual technique that uses diagrams to organize and connect ideas, helping to identify patterns, relationships, and possible solutions.

Brainstorming

When facing a problem, start by conducting a brainstorming session. Gather your team and encourage an open discussion where everyone contributes ideas, no matter how outlandish they may seem. This helps you:

Generate a diverse range of solutions
Encourage all team members to participate
Foster creative thinking

When brainstorming, remember to:

Reserve judgment until the session is over
Encourage wild ideas
Combine and improve upon ideas

Root Cause Analysis

For effective problem-solving, identifying the root cause of the issue at hand is crucial. Try these methods:

5 Whys : Ask “why” five times to get to the underlying cause.
Fishbone Diagram : Create a diagram representing the problem and break it down into categories of potential causes.
Pareto Analysis : Determine the few most significant causes underlying the majority of problems.

SWOT Analysis

SWOT analysis helps you examine the Strengths, Weaknesses, Opportunities, and Threats related to your problem. To perform a SWOT analysis:

List your problem’s strengths, such as relevant resources or strong partnerships.
Identify its weaknesses, such as knowledge gaps or limited resources.
Explore opportunities, like trends or new technologies, that could help solve the problem.
Recognize potential threats, like competition or regulatory barriers.

SWOT analysis aids in understanding the internal and external factors affecting the problem, which can help guide your solution.

Mind Mapping

A mind map is a visual representation of your problem and potential solutions. It enables you to organize information in a structured and intuitive manner. To create a mind map:

Write the problem in the center of a blank page.
Draw branches from the central problem to related sub-problems or contributing factors.
Add more branches to represent potential solutions or further ideas.

Mind mapping allows you to visually see connections between ideas and promotes creativity in problem-solving.

Examples of Problem Solving in Various Contexts

In the business world, you might encounter problems related to finances, operations, or communication. Applying problem-solving skills in these situations could look like:

Identifying areas of improvement in your company’s financial performance and implementing cost-saving measures
Resolving internal conflicts among team members by listening and understanding different perspectives, then proposing and negotiating solutions
Streamlining a process for better productivity by removing redundancies, automating tasks, or re-allocating resources

In educational contexts, problem-solving can be seen in various aspects, such as:

Addressing a gap in students’ understanding by employing diverse teaching methods to cater to different learning styles
Developing a strategy for successful time management to balance academic responsibilities and extracurricular activities
Seeking resources and support to provide equal opportunities for learners with special needs or disabilities

Everyday life is full of challenges that require problem-solving skills. Some examples include:

Overcoming a personal obstacle, such as improving your fitness level, by establishing achievable goals, measuring progress, and adjusting your approach accordingly
Navigating a new environment or city by researching your surroundings, asking for directions, or using technology like GPS to guide you
Dealing with a sudden change, like a change in your work schedule, by assessing the situation, identifying potential impacts, and adapting your plans to accommodate the change.
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Open access
Published: 05 September 2024

The effectiveness of training teachers in problem-based learning implementation on students’ outcomes: a mixed-method study

Nawaf Awadh K. Alreshidi ORCID: orcid.org/0000-0002-7934-4724 1 &
Victor Lally 2

Humanities and Social Sciences Communications volume 11 , Article number: 1137 ( 2024 ) Cite this article

Metrics details

The aim of this study was to understand the effect of training teachers in problem-based learning (PBL) implementation on students’ outcomes. Mixed methods were used to analyse the quasi-experimental study data. 127 students were divided into three groups: Group A ( N = 52) was taught by a trained teacher using the PBL teaching strategy, group B ( N = 39) was taught by an untrained teacher using traditional teaching methods, and group C ( N = 36) was taught by an untrained teacher using the PBL teaching strategy. The results showed that students whose teachers received training in PBL implementation significantly improved in terms of applying knowledge compared with students whose teachers used traditional teaching methods. The findings also provide robust evidence to show that using PBL teaching methods significantly improves students’ attitudes towards mathematics compared with traditional teaching methods, regardless of the teacher training effect. The key element in training teachers in PBL to improve students’ application of mathematics is training teachers in using metacognitive strategies that facilitate students’ learning processes.

Fostering twenty-first century skills among primary school students through math project-based learning

A meta-analysis to gauge the impact of pedagogies employed in mixed-ability high school biology classrooms

Secondary school students’ attitude towards mathematics word problems

Introduction.

Problem-based learning (PBL) is a teaching strategy in which a facilitator assists students to solve real-world problems as they work in small groups; the facilitator’s aim is to help the students to gain new knowledge and improve their problem-solving skills (see Barrows, 1986 ; Goodman, 2010 ). PBL aims to improve students’ knowledge application (Hmelo, 1998 ; Hmelo and Lin, 2000 ; Schmidt et al., 1996 ), and attitudes towards learning the subject (Hung, 2006 ; Westwood, 2011 ).

In mathematics, PBL is an instructional strategy that contextualises mathematics knowledge (i.e., real-life problems) in a way that helps students to understand where, when and how to apply knowledge. In PBL, when students encounter a real-life problem, they should identify what they have already learned about the problem (i.e., activating their prior knowledge) and establish what they need to know in order to solve the problem (i.e., missing information). They have to search for missing information and then combine it with what they already know (i.e., relevant prior knowledge), applying this to a new context (Bokonjic et al., 2007 ). Therefore, using a PBL teaching strategy in mathematics should reflect on students’ improvement in applying mathematics. Applying mathematics is the concept of using mathematics in real life (Mumcu, 2016 ).

Contextualising knowledge can be prepared by embedding learning opportunities in real-life contexts, which could it also be of interest for students, and it shows students the value of the function of the subject matter in the real world (Hung, 2006 ; Westwood, 2011 ). In the mathematics context, the content of PBL settings (real-life problems) shows the function of mathematics in reality and gives meaning to learning mathematics (Westwood, 2011 ). This should place value on learning mathematics for students, leading to an increase in positive attitudes towards learning mathematics. Attitudes towards mathematics is a negative or positive emotional disposition toward mathematics (Zan and Di Martino, 2007 ). In a systematic review and meta-analysis, Suparman et al. ( 2021 ) determined that PBL is one of the best teaching strategies for primary school mathematics teachers to enhance students’ mathematical abilities. However, students’ learning processes need to be facilitated by teachers in their approach to solving problems (Collins et al., 1989 ; Hmelo-Silver and Barrows, 2006 ; Hung, 2011 ). Thus, it is essential for teachers to be able to do this effectively to produce a noticeable improvement in students’ outcomes. This might require teachers to complete training in facilitation processes. To date, little is known about how the training of teachers in PBL implementation affects students’ outcomes. The results of the present study will help educational decision-makers to understand how training teachers in implementing PBL affects students’ mathematical applications and attitudes towards mathematics.

This article begins with a review of previous studies on PBL, followed by a discussion of teacher training in PBL implementation. The experiment conducted as part of this research examined the effects of training teachers on students’ knowledge application in mathematics and students’ attitudes towards mathematics.

Previous studies in problem-based learning

The overall review of empirical studies shows that PBL tends to significantly improve knowledge application (Abdalqader and Khalid, 2014 ; Primadoni et al., 2020 ; Tong et al., 2021 ; Wirkala and Kuhn, 2011 ; Wong and Day, 2009 ) and generate positive attitudes among students compared with traditional teaching methods (TTM; i.e., teacher-centred instruction) in kindergarten to 12th grade (K–12) settings (Goodnough and Cashion, 2006 ; Lou et al., 2011 ; Merritt et al., 2017 ; Nowak, 2001 ; Tong et al. 2021 ). For example, a quasi-experimental study including control groups conducted by Tong et al. ( 2021 ) examined the effectiveness of PBL on 10th-grade students’ mathematical application knowledge and their attitudes towards mathematics. The results showed that the students taught by the PBL group improved significantly in the application of knowledge and attitudes towards mathematics compared to the students taught by conventional methods. The real-life problems used with PBL are expected to drive students’ curiosity and capture their interest (Schmidt et al. 2009 ); therefore, PBL pedagogy and content could enhance students’ interest and promote their knowledge application.

Most of the literature pertaining to PBL has been conducted in the field of medicine and its allied contexts at universities. A limited number of studies have been carried out in K–12 contexts, and very few studies have been conducted in primary schools see (Alshhrany and Mohammed ( 2010 ); Eviyanti et al., 2017 ). Additional empirical research is needed to investigate the effects of PBL on the outcomes of younger students.

Training in PBL implementation

Although training teachers to implement PBL is generally viewed as critical for improving students’ achievement (Arani et al., 2023 ; Barrows, 1996 ; Fernandes, 2021 ; Hmelo-Silver and Barrows, 2006 ; Leary et al., 2009 ; Wosinski et al., 2018 ) the effects of teacher training on students’ performance are still ambiguous. The agreement on the importance of training is supported by literature outside of PBL, where reports have shown that the most effective teachers are trained in how to use facilitation skills (Leary et al., 2009 ). A meta-analysis was conducted to investigate the relationship between teacher training and students’ learning outcomes, and 94 studies were selected for inclusion in the study. The results showed a significant relationship between teacher training and students’ achievement. The study suggested that untrained teachers have similar student outcomes to those of teachers who use TTM (Leary et al., 2013 ). The researchers concluded that the facilitator may be a key factor in students’ outcomes. In another study, Tawfik and Kolodner ( 2016 ) revisited PBL’s foundations from a case-based reasoning perspective suggested that novices must be trained to facilitate scaffolding students during PBL. Maxwell et al., ( 2005 ) suggested that PBL instruction can improve learning compared with conventional methods when teachers are trained well in PBL. El-Aziz El Naggar et al., ( 2013 ) found that training was necessary to improve facilitators’ skills in collaborative learning and self-directed environments. However, there is a lack of research studies that have experimentally examined the effects of teacher training on student learning. More primary research is required to measure the effects on students’ outcomes of training teachers in PBL.

The aim of training teachers in PBL is to develop teachers in their professional role (Friedman and Woodhead, 2008 ; Villegas-Reimers, 2003 ). Both teachers and students have a role in PBL. To delineate the role of teachers, first, we have to identify the role of students. In PBL, the role of students is to go through the PBL process. Students work in small groups to understand the problem, identify and learn what they need to know and generate hypotheses to solve the problem (Hmelo-Silver, 2004 ). The role of students also involves questioning, researching and using critical thinking in an active way to solve problems (Cerezo, 2004 ). Students are required to take responsibility for their learning and engage in meaning-making in terms of their knowledge (English and Kitsantas, 2013 ). For effective engagement in PBL, students must be responsible for their learning, and they must actively participate in constructing knowledge and making meaningful processes (English and Kitsantas, 2013 ). However, many students cannot easily shift into this role because they have developed ingrained habits from the typical traditional classroom experiences, and they rely on the passive receiving of knowledge (English and Kitsantas, 2013 ; Hung, 2011 ; Ronis, 2008 ). To shift effectively to the new role, students must develop self-regulated learning (SRL) skills (English and Kitsantas, 2013 ).

SRL refers to the extent to which the learner is motivationally, metacognitively and behaviourally active in their learning processes (Zimmerman, 1989 ). Self-regulated learners can set goals and plans, identify appropriate strategies, and self-monitor and self-evaluate their learning; they are intrinsically motivated to learn. Thus, for effective learning in PBL, SRL is an essential skill (English and Kitsantas, 2013 ). In PBL, teachers can consciously activate students’ behaviours, leading to SRL. When it comes to promoting students’ skills to be able to do this, the role of teachers is to structure activities to stimulate students’ motivation, encourage reflection and facilitate their learning processes through guidance, scaffolding feedback and prompting independent thinking (English and Kitsantas, 2013 ). The role of the teacher in PBL is to facilitate collaborative knowledge construction by students, monitor learning processes, model desired behaviours and concentrate students’ efforts on critical thinking (Hmelo-Silver and Barrows, 2006 , 2008 ); this can be done by raising awareness of students’ higher cognitive thinking (Barrows, 1998 ).

Effective teachers should know how to facilitate groups’ learning processes (Dolmans et al., 2002 ; El-Aziz El Naggar et al., 2013 ). To enhance cooperation and production within groups, teachers should use intervention strategies, such as making decisions on what, when and how to intervene (Bosse et al., 2010 ). Teachers may need to be trained to implement such strategies in such a way as to facilitate tutorial processes, since it is teachers’ responsibility to guide students’ learning (Yew et al., 2011 ). In this study, we attempt to understand the effect of training in implementing PBL on students’ outcomes. We address the following questions:

How do trained and untrained teachers in PBL techniques implement PBL?

What are the effects of teacher training in implementing PBL on students’ mathematical applications?

What are the effects of teacher training in implementing PBL on students’ attitudes towards mathematics?

Study design

A quasi-experimental design was adopted in this study as the main quantitative approach to minimise bias in estimating the difference between traditional instruction and PBL classes. In addition, a qualitative approach was used during the intervention using field observation notes and after the intervention using interviews, as a secondary approach (see Fig. 1 ).

The figure illustrates the study design; mathematical test and attitudes towards mathematics were applied before and after the intervention, while during the quasi-experimental implementation, field observation notes were taken, and at the end of the intervention semi-structured interviews were conducted with the teachers.

Figure 1 illustrates the study design; during the quasi-experimental implementation, field observation notes documenting the authors’ observations were taken with the aim of observing how teachers implemented PBL, while semi-structured interviews were conducted with both types of the teachers who only implemented PBL (trained and untrained teachers) after the implementation of PBL as a supplement, with the aim of being used as part of the triangulation method for the author’s observations in how teachers implemented PBL.

School and participating students

The school was located in an urban district in a major city, Hail, which is situated in the north of Saudi Arabia. The school was randomly selected from ten private schools. Then, seven of the third-grade classes out of nine in the selected school were randomly chosen. The third grade is an important level, as it is the final grade of lower primary school. The classes were instructed by three teachers; one taught three classes, and the others taught two classes each. These classes comprised the three following groups: group A (three classes taught by a trained teacher using a PBL teaching strategy), group B (two classes taught by an untrained teacher using TTM) and group C (two classes taught by an untrained teacher using a PBL teaching strategy; see the study design in Table 1 ).

Ethical approval was obtained, and all participants signed consent forms to participate. They were informed that they could withdraw any time with no need to justify their decision, nor would there be any consequences of withdrawal.

In total, 127 pupils participated in the study, and their ages ranged from eight to nine years old. They were in the last semester of the third grade. Most of the students at the school were Saudis; in each group, two to four students had Arab backgrounds, such as from Syria, Egypt and Sudan. All students had a middle-class socioeconomic status. Academic school records and pre-test’ scores were used to ensure that the groups were similar in terms of mathematical achievement. Within each group, students showed a wide range of academic achievements; the students spanned from very low to very high achievers. There were no special education pupils within the groups.

Three teachers were randomly selected from one large primary school to take part in this study. The first teacher was randomly selected to receive training courses in using the PBL teaching strategy. The second teacher did not receive any training, but he was provided with PBL materials—specifically, design problems and guidelines for implementing PBL; he was asked to conduct self-directed learning (SDL) to implement PBL in his classrooms. The aim of including a trained and an untrained teacher using PBL was to measure the effects of training teachers on students’ outcomes. The third teacher was not trained in PBL and was asked to teach students using TTM.

The teachers had similar characteristics in terms of qualifications, experience and expertise, as well as in their beliefs and perspectives on PBL and TTM. They are all male and they believed that the aim of teaching mathematics is to conduct real-life problem solving, and they considered active learning to be important for students. They had been teaching mathematics to third-grade school students for 10 years. They all had a first degree in mathematics. They were all Egyptians and aged in their late thirties. According to the teachers and the administration of the school, the teachers had all attended the same training courses in different aspects of education, such as active learning. However, none of them had ever been trained in using PBL teaching strategies.

The topic covered in the classes was ‘data display’. It covered representation through codes, interpretation of representation through codes, representation in columns and interpretation of representation in columns. The content was new to the students. The instruction took place during ten class sessions (45 min each) comprising four sessions per week over for two and a half weeks, with a total of 7.5 h for each group. To control for the time factor, all groups, whether PBL or traditional, were given the same amount of time.

Instruments

Six multiple-choice questions, short answer questions, fill-in table questions and drawing tests were applied at the beginning of the study (pre-test) and in the final experiment (post-test). Mathematics items were selected from Trends in International Mathematics and Science Study (TIMSS) 2003 , 2007 and 2011 (see Mullis et al., 2012 ). The TIMSS items that were selected matched the objectives of lessons for knowledge application exactly; they had already been examined for the purpose of the test. We chose TIMSS mathematics items because they were verified as appropriate for the students’ ages. The students had nearly finished the third grade, and the curriculum for that grade contained many TIMSS topics (see TIMSS, n.d. ). Each item on the test received a score of either one or zero. An example of the items is given in Appendix A . The measure ‘attitudes towards mathematics’ of TIMSS 2007 (Mullis et al., 2008 ) contains four items, as follows:

I would like to take more mathematics in school

I enjoy learning mathematics.

Mathematics is boring (reverse-coded).

I like mathematics.

This measure was adopted and assumed to meet the standard of a valid and reliable test (see, Mullis et al., 2008 ). Attitudes were assessed using four items applied twice as pre- and post-measures; four items with 4-point Likert scales (disagree a lot, disagree a little, agree a little, and agree a lot) were presented. Each item score ranged from 1 to 4. The total marks ranged from the number of items of the measure to multiply them by 4; the measure consisted of four items, so the total scores ranged from 4 to 16. Some items were reverse-coded; for example, for ‘mathematics is boring’, ‘disagree a lot’ would receive a score of 4, whereas ‘agree a lot’ would receive a score of 1.

The face validity method was used to assess the validity of the tests and attitude measures. Eight arbitrators checked and gave their opinions on the adequacy, clarity, and relevance of the items’ content. The opinions of the arbitrators were considered and included in the preparation of the final image of the tests and attitudes. However, no changes were reported, and face validity confirmed the tests’ validity. In addition, test-retest reliability was used to assess the reliability of the tests and attitude measures. The levels of reliability were acceptable, with a score of 0.86 for the mathematics test and 0.88 for the attitude measure. For further reliability, Cronbach’s alpha was used for each scale of the test and attitudes and for the whole test and attitudes. The results show that all items correlated with a good degree of total scales (no items scored less than 0.3), and the reliability for the test was 0.747, whereas that for attitude was 0.808. Therefore, the measures became high valid for the purposes of this study.

In qualitative methods, filed observation and semi-structured interview were used to assess teachers’ performance in PBL implementation. After filed observations completed, post- semi-structured interviews were conducted for the teachers to confirm the results of author observations of how teachers implemented PBL as a supplement for the methodological triangulation of the filed observations. Methodological triangulation involves a researcher using more than one method, such as interviews and observations, for collecting data to understand a phenomenon deeply (Flick et al., 2004 ; Neuman, 2000 ). The teachers’ responses to the questions in the semi-structured interviews were analysed and compared with the analysed observation data to enhance the validity of the study and to gain a deeper understanding of social events. As Neuman ( 2000 ) commented, “Looking at something from several different points gives a more accurate view of it” (p. 521).

The data obtained from qualitative methods were deductively analysed. Prior to conducting data collection from filed work. A structured categorisation matrix was developed by the authors based on a literature review (see Barrows, 1998 ; English and Kitsantas, 2013 ; Hmelo-Silver and Barrows, 2006 , 2008 ). It aimed to assess PBL implementation conducted by teachers and consisted of two main categories: understanding the problem and using metacognitive strategies (see Appendix B ). Field observation notes were used to describe how the teachers implemented PBL. In this study, field observation notes consisted of two parts: descriptive and reflective information (Patton, 1990 ). The descriptive part involved documenting the factual data obtained from inside the classroom. The main author moved between groups to make sure everything was proceeding well; the intention was to monitor the implementation of the study, and the authors had a diary that was used to document any observations, particularly the observations that took place during lessons and were made inside mathematics classrooms. The main focus was on teachers’ performance, particularly with respect to teacher intervention, individual and collective student practices, student responses, group interaction and PBL processes. In the reflective section, the authors reflected on the meaning of the observations outside of the classroom (see Appendix C ). At the end of the experiment, ten lessons by each teacher were observed.

Semi-structured interview questions were developed according to analysed data of class observations which includes: The three main questions:

How was PBL implemented in your teaching strategies?

How did you assess your students in relation to understanding the problem?

How did you support your students to solve the problem?

In semi-structured interview, tape recordings were used for the interviews with each teacher, which ranged from 13 to 23 min in length. The interviews were conducted in Arabic, transcribed and subsequently translated into English by the authors.

The data were deductively coded (i.e., both the interview and observation) by the main author, and according to the identified categories mentioned above. When a deductive content analysis is used, a categorisation matrix is developed; following this, the data are coded according to the categories (Polit and Beck, 2004 ). In addition, if a structured matrix is chosen, only aspects that fit the matrix are selected from the data (Patton, 1990 ).

Professional development

The PBL programme used in this study aimed to train teachers by focusing on how to implement PBL in mathematics classrooms. The programme continued to provide feedback during the implementation after each session, taking advantage of the literature recommendations. Therefore, the trained teacher learned how to facilitate groups’ learning processes and guide students’ learning by adopting strategies such as posing meta-cognitive questions and focusing on the process of learning to model students’ learning strategies. The teacher was trained in intervention strategies, such as making decisions based on what, when and how intervention should occur to enhance cooperation. The programme included examples of PBL implementations. Teacher training lasted for one week (8–10 h), and daily meetings took place during the course of the training to provide an opportunity to present feedback and resolve unexpected problems. The programme for training the teacher to implement PBL in his class was developed by the author. It was expected that, following the teacher’s completion of the programme, the teacher would be able to do the following:

provide scaffolding and feedback as needed

prompt independent thinking

facilitate collaborative knowledge construction for students

monitor learning processes

model desired behaviours

concentrate students’ efforts on critical thinking.

use intervention strategies, such as making decisions on what, when and how to intervene

The programme included three real-life sessions, each lasting 45 min. The teacher was asked to implement the PBL strategy using an ill-structured problem, which was taken from a mathematics textbook and related to the topics that the students had been studying. A group of students from outside the study sample was selected to assess the teacher’s performance and establish whether he was able to implement PBL effectively. This was followed by providing the teacher with extensive feedback, which lasted more than an hour for each session.

The students were trained in two sessions in how to deal with the PBL teaching strategy.

Problem-based learning implementation

Problems were presented to the students. Students worked in small groups of four to six members. They discussed their understanding of the problems, and then the teacher discussed the understanding of the problem with the whole class. This was followed by students solving the problems. Finally, the teacher discussed the solution with all the students.

In this study, the six core characteristics of PBL mentioned by Barrows ( 1996 ) were adopted. These are as follows:

The student is the centre of the learning.

Learning occurs in small groups of students.

At the beginning of the learning, the students are presented with authentic problems.

The problems are used as a means of developing problem-solving skills.

New knowledge is gained through SDL. (Barrows, 1996 )

From the literature review (see Barrows, 1986 ; Gallagher and Stepien, 1996 ; Hung et al., 2008 ), six characteristics were adopted in the problems after reviewing the literature related to the problem of PBL. These were as follows:

the role of students as stakeholders

ill-structured problems

real-life problems

age-appropriate problems

clear and short problems

not too difficult problems

Statistical analysis (quantitative analysis)

The study used mixed-factor analysis of variance (ANOVA) models (Field, 2013 ; Howell, 2012 ) within one factor (time: pre- and post-tests and between). Tukey’s post hoc test (Field, 2013 ; Howell, 2012 ) was applied when appropriate and where significant results were observed—that is, an effect size (partial eta squared [η p 2 ]). The effect size, classified as Cohen suggested, could be small 0.01; medium, 0.06; or large, 0.14. All analyses were performed on IBM SPSS v22 and at a 5% (0.05) level of significance.

A quasi-experimental design was adopted in this study as the main quantitative approach, while a qualitative approach was used during the intervention using class observation notes and interviews, as a secondary approach. In total, 127 pupils participated in the study. They were in the last semester of the third grade. Ethical approval was obtained, and all participants signed consent forms to participate. Three teachers were randomly selected from one large primary school to take part in this study. The first teacher was randomly selected to receive training courses in using the PBL teaching strategy. The second teacher was not trained and asked to conduct SDL to implement PBL in his classrooms. The third teacher was not trained in PBL and was asked to teach students using TTM. The topic covered in the classes was ‘data display’. The content was new to the students. The instruction took place during 10 class sessions. Instruments of the study include mathematics test and attitudes towards mathematics were prepared and verified. Applying a pre-test (a measure of attitudes towards mathematics and an exam to measure mathematics application). Conducting the study took about 2 and a half weeks. Applying for a post-test (a measure of attitudes towards mathematics and an exam to measure mathematics application). During the intervention, class observations were carried out for each lesson.

Problem-based learning implementation of trained and untrained teachers

Unlike the untrained teacher, the trained teacher properly implemented PBL. The differences between their performances lay in differences in ‘giving students sufficient time to understand the problem’ and ‘using more metacognitive strategies to coach students in relation to their thinking skills’.

Table 2 and Fig. 2 summarise the difference between trained and untrained teachers after analysing both the teachers’ interviews and the author’s observations. The two following themes were extracted from the data analyses: ‘understanding the problem’ and ‘using meta-cognitive teaching skills’. These themes are detailed below.

This figure illustrates the difference between trained and untrained teachers' performances in PBL implementation.

Understanding the problem

The trained teacher did not allow students to solve the problem until they demonstrated their understanding of it. The author frequently noted that the trained teacher prevented the students from solving the problem until they demonstrated their understanding of it. When the trained teacher was asked how he knew that the students understood the problem, he replied, ‘I frequently asked random students… : ‘could you please explain to us the problem in your own words?’ If they did not do very well, I asked them how they could understand the problem more deeply? I waited longer … for them to solve the problem and gave them more time to reflect on their understanding and discuss with their group to deeply understand the problem’. The author observed that the teacher frequently and asked ransom students the following question: ‘Could [you] explain the problem [to us in] your own words’. Some students could, while others could not. Then, he encouraged them to understand the problem by asking them the following questions: ‘How can you understand the problem deeply? and Could you identify the obstacles and discuss [them] with your [respective] groups?’ Later, he again asked them whether they could explain the problem. However, the untrained teacher’s students had been given a shorter amount of time to understand the problem than those who were with the trained teacher (author’s observation).

In all lessons, the untrained teacher asked students whether they understood the problem; he often proceeded after hearing anyone shout ‘yes’ (author’s observation). The untrained teacher confirmed this when he was asked how he knew that his students had understood the problem before carrying on: ‘I always ask my students, if they do not understand the problem, to stop me any time and feel free to ask’. He did not ask his students to explain the problem in their own words (author’s observation). It was noted that the trained teacher gave more time for understanding the problem and questioned his students’ understanding more than the untrained teacher did.

Using meta-cognitive teaching skills

The trained teacher used more metacognitive strategies than the untrained teacher. Throughout all the lessons, the author observed that the trained teacher facilitated his students’ learning processes via PBL by using meta-cognitive strategies. He confirmed this in stating:

They [the students] work within groups to solve the problem, and I monitor them and coach their thinking with meta-cognitive questions …. For example, I ask students: what they did so far, and what next, did they consider this or that … and so on…. Sometimes, I think aloud and model right behaviours to let them engage in learning processes.

It was observed that students gradually began to depend on their own selves to solve the problems when they found their teacher pushed them to be independent. The trained teacher confirmed the following:

I did not want my students to depend on me. I never give them the solution, but encouraged them to depend on their own effort … And I found coaching their thinking improved their independence.

In contrast, the untrained teacher showed less ability to use meta-cognitive strategies through implementing PBL (author’s observation). The untrained teacher said: ‘They [the students] worked with their groups to solve the problem, and I helped them to solve the problem by indirectly explaining any difficulties, for example, by giving them some examples’. He explained the difficulties and led his students to solve the problem. He did not explain the solution directly, but he gave similar examples, which led them to the correct answer (author’s observation). In some ways, this strategy may be considered a metacognitive activation strategy.

The author observed that students frequently asked their teachers to give them more examples to understand how to solve the problems. The untrained teacher confirmed this: ‘My students are allowed to ask me to give examples to solve the problems, and I always meet their needs’.

Knowledge application in mathematics

From Table 3 , it can be seen that the improvement in the ‘applying achievement’ mean scores increased in all groups. From the mixed-measures ANOVA, as shown in Table 4 , it was found that a statistically significant improvement occurred for the average of students’ scores in knowledge application, F (2, 121) = 76.795, p = 0.000, with a large effect size at 0.388 (see row 1). However, when time was interacted with the groups (PBL with trained teacher, PBL with untrained teacher and TTM) the result showed a statistically significant effect, F (3, 121) = 4.333, p = 0.015. The partial eta squared effect size for this statistically significant result was medium, at 0.067 (see row 2). This effect shows that there was an effect on at least one group, but further analysis was needed to identify which group(s) might be affected. Tukey’s post hoc test was applied to determine which of the groups was statistically significantly different from the others. This test found that the mean scores of the group of students taught using the PBL teaching strategy by the trained teacher were statistically significantly different only from the scores of the students taught using TTM, p = 0.009 (see row 3). This indicates that the average of the PBL group’s scores with the trained teacher significantly improved more than the average of the traditional group’s scores did in ‘applying mathematics’.

Attitudes towards mathematics

From Table 5 , it can be seen that the mean score for ‘attitudes towards mathematics’ increased in groups A and C, while the scores of group B, the traditional group, decreased.

From the mixed-measures ANOVA analysis, as shown in Table 6 , there was no statistically significant improvement occurring for the average of students’ scores in attitudes towards mathematics, F (2, 121) = 0.480, p = 0.490 (see row 1). However, when time was interacted with groups (PBL with trained teacher, PBL with untrained teacher, and TTM), the result showed a statistically significant effect, F (3, 121) = 12.486, p = 0.000. The partial eta squared effect size for this statistically significant result was large, at 0.171 (see row 2). Tukey’s post hoc test was applied to determine which of the groups was significantly different from the others in attitudes towards mathematics. This test showed that using PBL with the trained teacher group was significantly different from using TTM, p = 0.000; using PBL with the untrained teacher group was also significantly different from using TTM, p = 0.008. However, there was no statistically significant difference between using PBL with the trained and untrained teachers (see row 3). This means that there was a statistically significant difference between the groups attributed to the types of treatment (PBL and TTM) in ‘attitudes towards mathematics’ and in favour of the PBL group, regardless of the different abilities of teachers in PBL implementation.

The study aimed to assess the effect of teacher training on students’ knowledge application and attitudes towards mathematics. The trained teacher demonstrated his ability to facilitate his students’ learning processes by using more metacognitive strategies than the untrained teacher. This result was expected, as many scholars think that training teachers on PBL implementation is critical for success (Barrows, 1996 ; Hmelo-Silver and Barrows, 2006 ; Leary et al., 2009 ; Wosinski et al., 2018 ). The results of the analyses of the interview data and the class observations were convergent. No noticeable difference was identified between the data analyses of class observation and the teachers’ interviews. Below, we consider how the teacher training affected student outcomes. Below, we consider how the teacher training affected student outcomes.

The current study’s quantitative results suggest that when PBL is taught by a teacher who can facilitate the students’ learning processes by using more meta-cognitive strategies, this could improve the application of mathematical knowledge of third-grade students’ significantly more than when they are taught using TTM (see Table 4 ). PBL theorists claim that, when compared with TTM, PBL is more successful in improving knowledge application (Hmelo-Silver, 2004 ; Hmelo-Silver and Barrows, 2008 ). This is because, with PBL, students engage in SDL by using their meta-cognitive learning strategies to solve real-life and ill-structured problems as a way of learning (Chin and Chia, 2006 ). This should reflect some improvement in the students’ ‘application’ ability over TTM (Fogarty, 1994 ). However, for such a method to be effective, skilled teachers who are also able to effectively use meta-cognitive strategies must be present to activate students’ meta-cognitive learning strategies. The trained teacher in PBL is better able to do so.

The role of the teacher in PBL is to facilitate learning processes (Hmelo-Silver and Barrows, 2006 , 2008 ). The shift to PBL requires new teaching roles and skills (Wilkerson and Hundert, 1997 ). Teachers can facilitate PBL processes if they are using meta-cognitive strategies, such as ‘thinking aloud with students’ and ‘modelling behaviours’ (Delisle, 1997 ). In the current study, these skills were shown effectively by the trained teacher; consequently, such strategies were reflected in the improvements to the students’ ‘application’ achievements. However, when students were taught by an untrained teacher, their learning processes were less facilitated. He only responded to difficulties they were experiencing by explaining similar situations (i.e., an example). Even though this approach is considered a metacognitive activation strategy, the students’ solutions were led by these examples. Thus, the teacher’s performance is an important factor that will affect the application of mathematical knowledge among third-grade students.

In terms of teacher training, the findings of the present study are supported by the results of the meta-analysis conducted by Leary et al. ( 2013 ), which showed a statistically significant positive relationship between teacher training and student achievement. The study also suggested that untrained teachers resulted in student outcomes similar to those attained by teachers who use TTM. This is also supported by the results of the current study. Moreover, this study’s findings are in line with those of Maxwell et al. ( 2005 ); these researchers’ conclusion suggests that PBL instruction can improve learning more than TTM can when teachers are well trained in using the PBL strategy. However, the results of the current study support the conclusions of several studies that found students taught via PBL outperformed students taught via TTM in terms of application knowledge (see Tong et al., 2021 ; Wirkala and Kuhn, 2011 ; Wong and Day, 2009 ).

The current study’s results suggested that PBL could significantly improve third-grade students’ attitudes towards mathematics compared with TTM (see Table 6 ). This is supported by the findings of (Lou et al., ( 2011 ) and Tong et al. ( 2021 ). For example, Tong et al. ( 2021 ) suggested that students taught via PBL improved their attitudes towards mathematics more significantly than those taught via TTM. The reason for this is that the students liked active learning and working in groups. This idea was supported by Goodnough and Cashion ( 2006 ), who suggested that young students like this strategy because it encourages active learning, supports working in groups and provides students with a variety of learning approaches and methods. In addition, real-life problems that interest students can be used to motivate students to engage deeply in learning processes when students fully understand them. These kinds of problems are expected to drive students’ curiosity and capture their interest, resulting in more effective student engagement in SDL in order to solve the problems (Schmidt et al., 2009 ).

In this study, the role of the problem was to motivate the students in all lessons taught by teachers trained in implementing PBL. Students became intrinsically motivated when they worked on tasks that stimulated their interests and sense of satisfaction or that challenged them (Hmelo-Silver, 2004 ). The possible reason for this is that the untrained teachers did not give students sufficient time to understand the problem, in contrast with the trained teacher (teachers’ interview and author’s observations).

In sum, PBL could be an effective teaching strategy for improving students’ attitudes towards learning mathematics; this effect is probably due to PBL content (i.e., real-life problems) and the nature of the PBL environment (i.e., eliciting active learning). In addition, PBL could be an effective teaching strategy for improving students’ mathematics application when students’ processes are effectively facilitated; without such facilitation, the effect of PBL instruction will not differ from that of TTM.

Limitations of the study

This study had several limitations. Because of the study design, results could be generated only for young students and for learning mathematics. The sample selection was not completely random, which could also decrease the opportunity to generalise the results of this study. Because of the gender segregation system that is currently operational in Saudi Arabia, the study participants were all male students. Therefore, the results of this study should be generalised with caution, taking these contextualising factors into account.

This study attempted to assess how training teachers in PBL implementation affects student outcomes, including knowledge application and students’ attitudes towards learning mathematics compared with TTM. Overall, the third-grade students who were taught using PBL showed more positive attitudes towards learning mathematics, regardless of whether they were taught by trained or untrained teachers. The study provides evidence that supports the necessity of training teachers to implement PBL effectively, as this will improve students’ mathematics application.

Data availability

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

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Four of the biggest problems facing education—and four trends that could make a difference

Eduardo velez bustillo, harry a. patrinos.

In 2022, we published, Lessons for the education sector from the COVID-19 pandemic , which was a follow up to, Four Education Trends that Countries Everywhere Should Know About , which summarized views of education experts around the world on how to handle the most pressing issues facing the education sector then. We focused on neuroscience, the role of the private sector, education technology, inequality, and pedagogy.

Unfortunately, we think the four biggest problems facing education today in developing countries are the same ones we have identified in the last decades .

1. The learning crisis was made worse by COVID-19 school closures

Low quality instruction is a major constraint and prior to COVID-19, the learning poverty rate in low- and middle-income countries was 57% (6 out of 10 children could not read and understand basic texts by age 10). More dramatic is the case of Sub-Saharan Africa with a rate even higher at 86%. Several analyses show that the impact of the pandemic on student learning was significant, leaving students in low- and middle-income countries way behind in mathematics, reading and other subjects. Some argue that learning poverty may be close to 70% after the pandemic , with a substantial long-term negative effect in future earnings. This generation could lose around $21 trillion in future salaries, with the vulnerable students affected the most.

2. Countries are not paying enough attention to early childhood care and education (ECCE)

At the pre-school level about two-thirds of countries do not have a proper legal framework to provide free and compulsory pre-primary education. According to UNESCO, only a minority of countries, mostly high-income, were making timely progress towards SDG4 benchmarks on early childhood indicators prior to the onset of COVID-19. And remember that ECCE is not only preparation for primary school. It can be the foundation for emotional wellbeing and learning throughout life; one of the best investments a country can make.

3. There is an inadequate supply of high-quality teachers

Low quality teaching is a huge problem and getting worse in many low- and middle-income countries. In Sub-Saharan Africa, for example, the percentage of trained teachers fell from 84% in 2000 to 69% in 2019 . In addition, in many countries teachers are formally trained and as such qualified, but do not have the minimum pedagogical training. Globally, teachers for science, technology, engineering, and mathematics (STEM) subjects are the biggest shortfalls.

4. Decision-makers are not implementing evidence-based or pro-equity policies that guarantee solid foundations

It is difficult to understand the continued focus on non-evidence-based policies when there is so much that we know now about what works. Two factors contribute to this problem. One is the short tenure that top officials have when leading education systems. Examples of countries where ministers last less than one year on average are plentiful. The second and more worrisome deals with the fact that there is little attention given to empirical evidence when designing education policies.

To help improve on these four fronts, we see four supporting trends:

1. Neuroscience should be integrated into education policies

Policies considering neuroscience can help ensure that students get proper attention early to support brain development in the first 2-3 years of life. It can also help ensure that children learn to read at the proper age so that they will be able to acquire foundational skills to learn during the primary education cycle and from there on. Inputs like micronutrients, early child stimulation for gross and fine motor skills, speech and language and playing with other children before the age of three are cost-effective ways to get proper development. Early grade reading, using the pedagogical suggestion by the Early Grade Reading Assessment model, has improved learning outcomes in many low- and middle-income countries. We now have the tools to incorporate these advances into the teaching and learning system with AI , ChatGPT , MOOCs and online tutoring.

2. Reversing learning losses at home and at school

There is a real need to address the remaining and lingering losses due to school closures because of COVID-19. Most students living in households with incomes under the poverty line in the developing world, roughly the bottom 80% in low-income countries and the bottom 50% in middle-income countries, do not have the minimum conditions to learn at home . These students do not have access to the internet, and, often, their parents or guardians do not have the necessary schooling level or the time to help them in their learning process. Connectivity for poor households is a priority. But learning continuity also requires the presence of an adult as a facilitator—a parent, guardian, instructor, or community worker assisting the student during the learning process while schools are closed or e-learning is used.

To recover from the negative impact of the pandemic, the school system will need to develop at the student level: (i) active and reflective learning; (ii) analytical and applied skills; (iii) strong self-esteem; (iv) attitudes supportive of cooperation and solidarity; and (v) a good knowledge of the curriculum areas. At the teacher (instructor, facilitator, parent) level, the system should aim to develop a new disposition toward the role of teacher as a guide and facilitator. And finally, the system also needs to increase parental involvement in the education of their children and be active part in the solution of the children’s problems. The Escuela Nueva Learning Circles or the Pratham Teaching at the Right Level (TaRL) are models that can be used.

3. Use of evidence to improve teaching and learning

We now know more about what works at scale to address the learning crisis. To help countries improve teaching and learning and make teaching an attractive profession, based on available empirical world-wide evidence , we need to improve its status, compensation policies and career progression structures; ensure pre-service education includes a strong practicum component so teachers are well equipped to transition and perform effectively in the classroom; and provide high-quality in-service professional development to ensure they keep teaching in an effective way. We also have the tools to address learning issues cost-effectively. The returns to schooling are high and increasing post-pandemic. But we also have the cost-benefit tools to make good decisions, and these suggest that structured pedagogy, teaching according to learning levels (with and without technology use) are proven effective and cost-effective .

4. The role of the private sector

When properly regulated the private sector can be an effective education provider, and it can help address the specific needs of countries. Most of the pedagogical models that have received international recognition come from the private sector. For example, the recipients of the Yidan Prize on education development are from the non-state sector experiences (Escuela Nueva, BRAC, edX, Pratham, CAMFED and New Education Initiative). In the context of the Artificial Intelligence movement, most of the tools that will revolutionize teaching and learning come from the private sector (i.e., big data, machine learning, electronic pedagogies like OER-Open Educational Resources, MOOCs, etc.). Around the world education technology start-ups are developing AI tools that may have a good potential to help improve quality of education .

After decades asking the same questions on how to improve the education systems of countries, we, finally, are finding answers that are very promising. Governments need to be aware of this fact.

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The Hidden Goldmine: Why Your Niche Is The Key To Profit

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One of the most important decisions you will make when starting your business is choosing your niche. Your niche determines not only what type of customers you will serve but also how successful you will be in building a profitable, sustainable business. Many new entrepreneurs overlook the importance of this step but choosing the right niche can be the difference between struggling to make ends meet and building a thriving company.

Don’t rush this step. Your niche is your business’s identity, and by selecting wisely, you’ll ensure that you’re entering a market where success is not only possible but highly likely.

Here are some tips on finding the right niche for your business:

1. focus on profitability.

While passion is important, profitability should always be at the forefront when deciding on a niche. A hobby might be fun, but if people aren’t willing to pay for the products or services you offer, your business will not survive. You must select a niche with proven demand if you want to make money. This means looking at market trends and understanding which industries are growing and where consumers are spending their money.

2. In-Demand Niches Have Built-in Customers

One of the benefits of choosing an in-demand niche is that you don’t have to convince people they need what you offer. They already want it. Your job becomes connecting the dots between their needs and your solutions. To find an in-demand niche, research what people are already talking about, what problems they’re trying to solve, and where they’re spending their money.

For example, niches like health, personal finance, and digital marketing are consistently in demand because people are always looking for ways to improve their well-being, manage their money, or grow their businesses. An in-demand niche also gives you the opportunity to create tailored products or services that meet specific needs, increasing your chances of success.

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Nyt ‘strands’ hints, spangram and answers for monday, september 9th, used tesla cybertruck price continues to crash, 3. avoid overcrowded niches.

While it’s important to choose an in-demand niche, it’s equally important to avoid one that’s overcrowded. Entering an overcrowded market means you’ll face fierce competition from well-established businesses. This can make it much harder for your business to stand out, especially when bigger players already dominate the space.

To avoid an overcrowded niche, look for opportunities within a larger market where there are gaps. These gaps often exist in sub-niches, where fewer businesses operate. For example, instead of entering the general “fitness” market, you could focus on a sub-niche like fitness coaching for women over 50 or fitness programs for busy professionals. By narrowing your focus, you can carve out a space where your business becomes the go-to expert.

4. Customers Must Be Willing to Pay

You may have a great idea, but if customers aren’t willing to pay for your product or service, you’ll struggle to build a profitable business . To ensure your niche will generate income, it’s important to assess whether potential customers will spend money on the solutions you provide.

Research the buying habits of your target audience to see what they’re willing to invest in. Are they paying for products and services similar to what you offer? If the answer is yes, that’s a strong indicator of a profitable niche. If the answer is no, you might need to rethink how you position your offering or consider another niche altogether.

5. You Can Become the Expert in a Targeted Niche

Choosing a profitable niche doesn’t just allow you to make money; it also gives you the chance to position yourself as an expert. When you select a niche that is in demand but not overcrowded, you can become the go-to authority in your field. This is important because people prefer to work with experts. They are more likely to trust you, recommend you to others, and pay premium prices for your services.

For example, if you enter a niche that is specific, like eco-friendly home organizing, you can build a brand that stands out as the expert in that area. Over time, as your reputation grows, you can charge more for your services and attract a loyal customer base.

6. Profitability Comes from Solving Problems

The most successful businesses are those that solve specific problems for their customers. When choosing a niche, it’s essential to identify the problems that exist in that market and create solutions that customers will pay for. A profitable niche is not just about selling products; it’s about offering value.

Your target audience is experiencing pain from the problem they have. Think about what keeps them up at night. What are they struggling with? Once you understand their problems, position your business as the solution. This approach not only ensures profitability but also builds long-term relationships with your customers, as they’ll see you as someone who genuinely cares about helping them.

The bottom line is that when starting a business, choosing the right niche can make or break your success. A profitable, in-demand niche that’s not overcrowded and one that people are willing to pay for is the foundation for a sustainable business. Take the time to research the market, understand your audience’s needs, and position your business as the expert in your field. By doing so, you’ll set yourself up for long-term profitability and growth.

Melissa Houston, CPA is the author of Cash Confident: An Entrepreneur’s Guide to Creating a Profitable Business and the founder of She Means Profit . As a Business Strategist for small business owners, Melissa helps women making mid-career shifts, to launch their dream businesses, and also guides established business owners to grow their businesses to more profitably.

The opinions expressed in this article are not intended to replace any professional or expert accounting and/or tax advice whatsoever.

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