teaching about problem solving

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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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..

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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Teaching problem solving: Let students get ‘stuck’ and ‘unstuck’

Subscribe to the center for universal education bulletin, kate mills and km kate mills literacy interventionist - red bank primary school helyn kim helyn kim former brookings expert @helyn_kim.

October 31, 2017

This is the second in a six-part blog series on teaching 21st century skills , including problem solving , metacognition , critical thinking , and collaboration , in classrooms.

In the real world, students encounter problems that are complex, not well defined, and lack a clear solution and approach. They need to be able to identify and apply different strategies to solve these problems. However, problem solving skills do not necessarily develop naturally; they need to be explicitly taught in a way that can be transferred across multiple settings and contexts.

Here’s what Kate Mills, who taught 4 th grade for 10 years at Knollwood School in New Jersey and is now a Literacy Interventionist at Red Bank Primary School, has to say about creating a classroom culture of problem solvers:

Helping my students grow to be people who will be successful outside of the classroom is equally as important as teaching the curriculum. From the first day of school, I intentionally choose language and activities that help to create a classroom culture of problem solvers. I want to produce students who are able to think about achieving a particular goal and manage their mental processes . This is known as metacognition , and research shows that metacognitive skills help students become better problem solvers.

I begin by “normalizing trouble” in the classroom. Peter H. Johnston teaches the importance of normalizing struggle , of naming it, acknowledging it, and calling it what it is: a sign that we’re growing. The goal is for the students to accept challenge and failure as a chance to grow and do better.

I look for every chance to share problems and highlight how the students— not the teachers— worked through those problems. There is, of course, coaching along the way. For example, a science class that is arguing over whose turn it is to build a vehicle will most likely need a teacher to help them find a way to the balance the work in an equitable way. Afterwards, I make it a point to turn it back to the class and say, “Do you see how you …” By naming what it is they did to solve the problem , students can be more independent and productive as they apply and adapt their thinking when engaging in future complex tasks.

After a few weeks, most of the class understands that the teachers aren’t there to solve problems for the students, but to support them in solving the problems themselves. With that important part of our classroom culture established, we can move to focusing on the strategies that students might need.

Here’s one way I do this in the classroom:

I show the broken escalator video to the class. Since my students are fourth graders, they think it’s hilarious and immediately start exclaiming, “Just get off! Walk!”

When the video is over, I say, “Many of us, probably all of us, are like the man in the video yelling for help when we get stuck. When we get stuck, we stop and immediately say ‘Help!’ instead of embracing the challenge and trying new ways to work through it.” I often introduce this lesson during math class, but it can apply to any area of our lives, and I can refer to the experience and conversation we had during any part of our day.

Research shows that just because students know the strategies does not mean they will engage in the appropriate strategies. Therefore, I try to provide opportunities where students can explicitly practice learning how, when, and why to use which strategies effectively so that they can become self-directed learners.

For example, I give students a math problem that will make many of them feel “stuck”. I will say, “Your job is to get yourselves stuck—or to allow yourselves to get stuck on this problem—and then work through it, being mindful of how you’re getting yourselves unstuck.” As students work, I check-in to help them name their process: “How did you get yourself unstuck?” or “What was your first step? What are you doing now? What might you try next?” As students talk about their process, I’ll add to a list of strategies that students are using and, if they are struggling, help students name a specific process. For instance, if a student says he wrote the information from the math problem down and points to a chart, I will say: “Oh that’s interesting. You pulled the important information from the problem out and organized it into a chart.” In this way, I am giving him the language to match what he did, so that he now has a strategy he could use in other times of struggle.

The charts grow with us over time and are something that we refer to when students are stuck or struggling. They become a resource for students and a way for them to talk about their process when they are reflecting on and monitoring what did or did not work.

For me, as a teacher, it is important that I create a classroom environment in which students are problem solvers. This helps tie struggles to strategies so that the students will not only see value in working harder but in working smarter by trying new and different strategies and revising their process. In doing so, they will more successful the next time around.

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.

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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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. 

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5 Teaching Mathematics Through Problem Solving

Janet Stramel

In his book “How to Solve It,” George Pólya (1945) said, “One of the most important tasks of the teacher is to help his students. This task is not quite easy; it demands time, practice, devotion, and sound principles. The student should acquire as much experience of independent work as possible. But if he is left alone with his problem without any help, he may make no progress at all. If the teacher helps too much, nothing is left to the student. The teacher should help, but not too much and not too little, so that the student shall have a reasonable share of the work.” (page 1)

What is a problem in mathematics? A problem is “any task or activity for which the students have no prescribed or memorized rules or methods, nor is there a perception by students that there is a specific ‘correct’ solution method” (Hiebert, et. al., 1997). Problem solving in mathematics is one of the most important topics to teach; learning to problem solve helps students develop a sense of solving real-life problems and apply mathematics to real world situations. It is also used for a deeper understanding of mathematical concepts. Learning “math facts” is not enough; students must also learn how to use these facts to develop their thinking skills.

According to NCTM (2010), the term “problem solving” refers to mathematical tasks that have the potential to provide intellectual challenges for enhancing students’ mathematical understanding and development. When you first hear “problem solving,” what do you think about? Story problems or word problems? Story problems may be limited to and not “problematic” enough. For example, you may ask students to find the area of a rectangle, given the length and width. This type of problem is an exercise in computation and can be completed mindlessly without understanding the concept of area. Worthwhile problems includes problems that are truly problematic and have the potential to provide contexts for students’ mathematical development.

There are three ways to solve problems: teaching for problem solving, teaching about problem solving, and teaching through problem solving.

Teaching for problem solving begins with learning a skill. For example, students are learning how to multiply a two-digit number by a one-digit number, and the story problems you select are multiplication problems. Be sure when you are teaching for problem solving, you select or develop tasks that can promote the development of mathematical understanding.

Teaching about problem solving begins with suggested strategies to solve a problem. For example, “draw a picture,” “make a table,” etc. You may see posters in teachers’ classrooms of the “Problem Solving Method” such as: 1) Read the problem, 2) Devise a plan, 3) Solve the problem, and 4) Check your work. There is little or no evidence that students’ problem-solving abilities are improved when teaching about problem solving. Students will see a word problem as a separate endeavor and focus on the steps to follow rather than the mathematics. In addition, students will tend to use trial and error instead of focusing on sense making.

Teaching through problem solving focuses students’ attention on ideas and sense making and develops mathematical practices. Teaching through problem solving also develops a student’s confidence and builds on their strengths. It allows for collaboration among students and engages students in their own learning.

Consider the following worthwhile-problem criteria developed by Lappan and Phillips (1998):

The problem has important, useful mathematics embedded in it.
The problem requires high-level thinking and problem solving.
The problem contributes to the conceptual development of students.
The problem creates an opportunity for the teacher to assess what his or her students are learning and where they are experiencing difficulty.
The problem can be approached by students in multiple ways using different solution strategies.
The problem has various solutions or allows different decisions or positions to be taken and defended.
The problem encourages student engagement and discourse.
The problem connects to other important mathematical ideas.
The problem promotes the skillful use of mathematics.
The problem provides an opportunity to practice important skills.

Of course, not every problem will include all of the above. Sometimes, you will choose a problem because your students need an opportunity to practice a certain skill.

Key features of a good mathematics problem includes:

It must begin where the students are mathematically.
The feature of the problem must be the mathematics that students are to learn.
It must require justifications and explanations for both answers and methods of solving.

Problem solving is not a neat and orderly process. Think about needlework. On the front side, it is neat and perfect and pretty.

But look at the b ack.

It is messy and full of knots and loops. Problem solving in mathematics is also like this and we need to help our students be “messy” with problem solving; they need to go through those knots and loops and learn how to solve problems with the teacher’s guidance.

When you teach through problem solving , your students are focused on ideas and sense-making and they develop confidence in mathematics!

Mathematics Tasks and Activities that Promote Teaching through Problem Solving

Choosing the Right Task

Selecting activities and/or tasks is the most significant decision teachers make that will affect students’ learning. Consider the following questions:

Teachers must do the activity first. What is problematic about the activity? What will you need to do BEFORE the activity and AFTER the activity? Additionally, think how your students would do the activity.
What mathematical ideas will the activity develop? Are there connections to other related mathematics topics, or other content areas?
Can the activity accomplish your learning objective/goals?

Low Floor High Ceiling Tasks

By definition, a “ low floor/high ceiling task ” is a mathematical activity where everyone in the group can begin and then work on at their own level of engagement. Low Floor High Ceiling Tasks are activities that everyone can begin and work on based on their own level, and have many possibilities for students to do more challenging mathematics. One gauge of knowing whether an activity is a Low Floor High Ceiling Task is when the work on the problems becomes more important than the answer itself, and leads to rich mathematical discourse [Hover: ways of representing, thinking, talking, agreeing, and disagreeing; the way ideas are exchanged and what the ideas entail; and as being shaped by the tasks in which students engage as well as by the nature of the learning environment].

The strengths of using Low Floor High Ceiling Tasks:

Allows students to show what they can do, not what they can’t.
Provides differentiation to all students.
Promotes a positive classroom environment.
Advances a growth mindset in students
Aligns with the Standards for Mathematical Practice

Examples of some Low Floor High Ceiling Tasks can be found at the following sites:

YouCubed – under grades choose Low Floor High Ceiling
NRICH Creating a Low Threshold High Ceiling Classroom
Inside Mathematics Problems of the Month

Math in 3-Acts

Math in 3-Acts was developed by Dan Meyer to spark an interest in and engage students in thought-provoking mathematical inquiry. Math in 3-Acts is a whole-group mathematics task consisting of three distinct parts:

Act One is about noticing and wondering. The teacher shares with students an image, video, or other situation that is engaging and perplexing. Students then generate questions about the situation.

In Act Two , the teacher offers some information for the students to use as they find the solutions to the problem.

Act Three is the “reveal.” Students share their thinking as well as their solutions.

“Math in 3 Acts” is a fun way to engage your students, there is a low entry point that gives students confidence, there are multiple paths to a solution, and it encourages students to work in groups to solve the problem. Some examples of Math in 3-Acts can be found at the following websites:

Dan Meyer’s Three-Act Math Tasks
Graham Fletcher3-Act Tasks ]
Math in 3-Acts: Real World Math Problems to Make Math Contextual, Visual and Concrete

Number Talks

Number talks are brief, 5-15 minute discussions that focus on student solutions for a mental math computation problem. Students share their different mental math processes aloud while the teacher records their thinking visually on a chart or board. In addition, students learn from each other’s strategies as they question, critique, or build on the strategies that are shared.. To use a “number talk,” you would include the following steps:

The teacher presents a problem for students to solve mentally.
Provide adequate “ wait time .”
The teacher calls on a students and asks, “What were you thinking?” and “Explain your thinking.”
For each student who volunteers to share their strategy, write their thinking on the board. Make sure to accurately record their thinking; do not correct their responses.
Invite students to question each other about their strategies, compare and contrast the strategies, and ask for clarification about strategies that are confusing.

“Number Talks” can be used as an introduction, a warm up to a lesson, or an extension. Some examples of Number Talks can be found at the following websites:

Inside Mathematics Number Talks
Number Talks Build Numerical Reasoning

Saying “This is Easy”

“This is easy.” Three little words that can have a big impact on students. What may be “easy” for one person, may be more “difficult” for someone else. And saying “this is easy” defeats the purpose of a growth mindset classroom, where students are comfortable making mistakes.

When the teacher says, “this is easy,” students may think,

“Everyone else understands and I don’t. I can’t do this!”
Students may just give up and surrender the mathematics to their classmates.
Students may shut down.

Instead, you and your students could say the following:

“I think I can do this.”
“I have an idea I want to try.”
“I’ve seen this kind of problem before.”

Tracy Zager wrote a short article, “This is easy”: The Little Phrase That Causes Big Problems” that can give you more information. Read Tracy Zager’s article here.

Using “Worksheets”

Do you want your students to memorize concepts, or do you want them to understand and apply the mathematics for different situations?

What is a “worksheet” in mathematics? It is a paper and pencil assignment when no other materials are used. A worksheet does not allow your students to use hands-on materials/manipulatives [Hover: physical objects that are used as teaching tools to engage students in the hands-on learning of mathematics]; and worksheets are many times “naked number” with no context. And a worksheet should not be used to enhance a hands-on activity.

Students need time to explore and manipulate materials in order to learn the mathematics concept. Worksheets are just a test of rote memory. Students need to develop those higher-order thinking skills, and worksheets will not allow them to do that.

One productive belief from the NCTM publication, Principles to Action (2014), states, “Students at all grade levels can benefit from the use of physical and virtual manipulative materials to provide visual models of a range of mathematical ideas.”

You may need an “activity sheet,” a “graphic organizer,” etc. as you plan your mathematics activities/lessons, but be sure to include hands-on manipulatives. Using manipulatives can

Provide your students a bridge between the concrete and abstract
Serve as models that support students’ thinking
Provide another representation
Support student engagement
Give students ownership of their own learning.

Adapted from “ The Top 5 Reasons for Using Manipulatives in the Classroom ”.

any task or activity for which the students have no prescribed or memorized rules or methods, nor is there a perception by students that there is a specific ‘correct’ solution method

should be intriguing and contain a level of challenge that invites speculation and hard work, and directs students to investigate important mathematical ideas and ways of thinking toward the learning

involves teaching a skill so that a student can later solve a story problem

when we teach students how to problem solve

teaching mathematics content through real contexts, problems, situations, and models

a mathematical activity where everyone in the group can begin and then work on at their own level of engagement

20 seconds to 2 minutes for students to make sense of questions

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6 Tips for Teaching Math Problem-Solving Skills

Solving word problems is tougher than computing with numbers, but elementary teachers can guide students to do the deep thinking involved.

Photo of elementary school teacher with students

A growing concern with students is the ability to problem-solve, especially with complex, multistep problems. Data shows that students struggle more when solving word problems than they do with computation , and so problem-solving should be considered separately from computation. Why?

Consider this. When we’re on the way to a new destination and we plug in our location to a map on our phone, it tells us what lane to be in and takes us around any detours or collisions, sometimes even buzzing our watch to remind us to turn. When I experience this as a driver, I don’t have to do the thinking. I can think about what I’m going to cook for dinner, not paying much attention to my surroundings other than to follow those directions. If I were to be asked to go there again, I wouldn’t be able to remember, and I would again seek help.

If we can switch to giving students strategies that require them to think instead of giving them too much support throughout the journey to the answer, we may be able to give them the ability to learn the skills to read a map and have several ways to get there.

Here are six ways we can start letting students do this thinking so that they can go through rigorous problem-solving again and again, paving their own way to the solution.

1. Link problem-solving to reading

When we can remind students that they already have many comprehension skills and strategies they can easily use in math problem-solving, it can ease the anxiety surrounding the math problem. For example, providing them with strategies to practice, such as visualizing, acting out the problem with math tools like counters or base 10 blocks, drawing a quick sketch of the problem, retelling the story in their own words, etc., can really help them to utilize the skills they already have to make the task less daunting.

We can break these skills into specific short lessons so students have a bank of strategies to try on their own. Here's an example of an anchor chart that they can use for visualizing . Breaking up comprehension into specific skills can increase student independence and help teachers to be much more targeted in their problem-solving instruction. This allows students to build confidence and break down the barriers between reading and math to see they already have so many strengths that are transferable to all problems.

2. Avoid boxing students into choosing a specific operation

It can be so tempting to tell students to look for certain words that might mean a certain operation. This might even be thoroughly successful in kindergarten and first grade, but just like when our map tells us where to go, that limits students from becoming deep thinkers. It also expires once they get into the upper grades, where those words could be in a problem multiple times, creating more confusion when students are trying to follow a rule that may not exist in every problem.

We can encourage a variety of ways to solve problems instead of choosing the operation first. In first grade, a problem might say, “Joceline has 13 stuffed animals and Jordan has 17. How many more does Jordan have?” Some students might choose to subtract, but a lot of students might just count to find the amount in between. If we tell them that “how many more” means to subtract, we’re taking the thinking out of the problem altogether, allowing them to go on autopilot without truly solving the problem or using their comprehension skills to visualize it.

3. Revisit ‘representation’

The word “representation” can be misleading. It seems like something to do after the process of solving. When students think they have to go straight to solving, they may not realize that they need a step in between to be able to support their understanding of what’s actually happening in the problem first.

Using an anchor chart like one of these ( lower grade , upper grade ) can help students to choose a representation that most closely matches what they’re visualizing in their mind. Once they sketch it out, it can give them a clearer picture of different ways they could solve the problem.

Think about this problem: “Varush went on a trip with his family to his grandmother’s house. It was 710 miles away. On the way there, three people took turns driving. His mom drove 214 miles. His dad drove 358 miles. His older sister drove the rest. How many miles did his sister drive?”

If we were to show this student the anchor chart, they would probably choose a number line or a strip diagram to help them understand what’s happening.

If we tell students they must always draw base 10 blocks in a place value chart, that doesn’t necessarily match the concept of this problem. When we ask students to match our way of thinking, we rob them of critical thinking practice and sometimes confuse them in the process.

4. Give time to process

Sometimes as educators, we can feel rushed to get to everyone and everything that’s required. When solving a complex problem, students need time to just sit with a problem and wrestle with it, maybe even leaving it and coming back to it after a period of time.

This might mean we need to give them fewer problems but go deeper with those problems we give them. We can also speed up processing time when we allow for collaboration and talk time with peers on problem-solving tasks.

5. Ask questions that let Students do the thinking

Questions or prompts during problem-solving should be very open-ended to promote thinking. Telling a student to reread the problem or to think about what tools or resources would help them solve it is a way to get them to try something new but not take over their thinking.

These skills are also transferable across content, and students will be reminded, “Good readers and mathematicians reread.”

6. Spiral concepts so students frequently use problem-solving skills

When students don’t have to switch gears in between concepts, they’re not truly using deep problem-solving skills. They already kind of know what operation it might be or that it’s something they have at the forefront of their mind from recent learning. Being intentional within their learning stations and assessments about having a variety of rigorous problem-solving skills will refine their critical thinking abilities while building more and more resilience throughout the school year as they retain content learning in the process.

Problem-solving skills are so abstract, and it can be tough to pinpoint exactly what students need. Sometimes we have to go slow to go fast. Slowing down and helping students have tools when they get stuck and enabling them to be critical thinkers will prepare them for life and allow them multiple ways to get to their own destination.

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The Problem-solving Classroom

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How to Teach Kids Problem-Solving Skills

KidStock / Blend Images / Getty Images

Steps to Follow
Allow Consequences

Whether your child can't find their math homework or has forgotten their lunch, good problem-solving skills are the key to helping them manage their life.

A 2010 study published in Behaviour Research and Therapy found that kids who lack problem-solving skills may be at a higher risk of depression and suicidality. Additionally, the researchers found that teaching a child problem-solving skills can improve mental health .

You can begin teaching basic problem-solving skills during preschool and help your child sharpen their skills into high school and beyond.

Why Problem-Solving Skills Matter

Kids face a variety of problems every day, ranging from academic difficulties to problems on the sports field. Yet few of them have a formula for solving those problems.

Kids who lack problem-solving skills may avoid taking action when faced with a problem.

Rather than put their energy into solving the problem, they may invest their time in avoiding the issue. That's why many kids fall behind in school or struggle to maintain friendships .

Other kids who lack problem-solving skills spring into action without recognizing their choices. A child may hit a peer who cuts in front of them in line because they are not sure what else to do.

Or, they may walk out of class when they are being teased because they can't think of any other ways to make it stop. Those impulsive choices may create even bigger problems in the long run.

The 5 Steps of Problem-Solving

Kids who feel overwhelmed or hopeless often won't attempt to address a problem. But when you give them a clear formula for solving problems, they'll feel more confident in their ability to try. Here are the steps to problem-solving:

Identify the problem . Just stating the problem out loud can make a big difference for kids who are feeling stuck. Help your child state the problem, such as, "You don't have anyone to play with at recess," or "You aren't sure if you should take the advanced math class."
Develop at least five possible solutions . Brainstorm possible ways to solve the problem. Emphasize that all the solutions don't necessarily need to be good ideas (at least not at this point). Help your child develop solutions if they are struggling to come up with ideas. Even a silly answer or far-fetched idea is a possible solution. The key is to help them see that with a little creativity, they can find many different potential solutions.
Identify the pros and cons of each solution . Help your child identify potential positive and negative consequences for each potential solution they identified.
Pick a solution. Once your child has evaluated the possible positive and negative outcomes, encourage them to pick a solution.
Test it out . Tell them to try a solution and see what happens. If it doesn't work out, they can always try another solution from the list that they developed in step two.

Practice Solving Problems

When problems arise, don’t rush to solve your child’s problems for them. Instead, help them walk through the problem-solving steps. Offer guidance when they need assistance, but encourage them to solve problems on their own. If they are unable to come up with a solution, step in and help them think of some. But don't automatically tell them what to do.

When you encounter behavioral issues, use a problem-solving approach. Sit down together and say, "You've been having difficulty getting your homework done lately. Let's problem-solve this together." You might still need to offer a consequence for misbehavior, but make it clear that you're invested in looking for a solution so they can do better next time.

Use a problem-solving approach to help your child become more independent.

If they forgot to pack their soccer cleats for practice, ask, "What can we do to make sure this doesn't happen again?" Let them try to develop some solutions on their own.

Kids often develop creative solutions. So they might say, "I'll write a note and stick it on my door so I'll remember to pack them before I leave," or "I'll pack my bag the night before and I'll keep a checklist to remind me what needs to go in my bag."

Provide plenty of praise when your child practices their problem-solving skills.

Allow for Natural Consequences

Natural consequences may also teach problem-solving skills. So when it's appropriate, allow your child to face the natural consequences of their action. Just make sure it's safe to do so.

For example, let your teenager spend all of their money during the first 10 minutes you're at an amusement park if that's what they want. Then, let them go for the rest of the day without any spending money.

This can lead to a discussion about problem-solving to help them make a better choice next time. Consider these natural consequences as a teachable moment to help work together on problem-solving.

Becker-Weidman EG, Jacobs RH, Reinecke MA, Silva SG, March JS. Social problem-solving among adolescents treated for depression . Behav Res Ther . 2010;48(1):11-18. doi:10.1016/j.brat.2009.08.006

Pakarinen E, Kiuru N, Lerkkanen M-K, Poikkeus A-M, Ahonen T, Nurmi J-E. Instructional support predicts childrens task avoidance in kindergarten . Early Child Res Q . 2011;26(3):376-386. doi:10.1016/j.ecresq.2010.11.003

Schell A, Albers L, von Kries R, Hillenbrand C, Hennemann T. Preventing behavioral disorders via supporting social and emotional competence at preschool age . Dtsch Arztebl Int . 2015;112(39):647–654. doi:10.3238/arztebl.2015.0647

Cheng SC, She HC, Huang LY. The impact of problem-solving instruction on middle school students’ physical science learning: Interplays of knowledge, reasoning, and problem solving . EJMSTE . 2018;14(3):731-743.

Vlachou A, Stavroussi P. Promoting social inclusion: A structured intervention for enhancing interpersonal problem‐solving skills in children with mild intellectual disabilities . Support Learn . 2016;31(1):27-45. doi:10.1111/1467-9604.12112

Öğülmüş S, Kargı E. The interpersonal cognitive problem solving approach for preschoolers . Turkish J Educ . 2015;4(17347):19-28. doi:10.19128/turje.181093

American Academy of Pediatrics. What's the best way to discipline my child? .

Kashani-Vahid L, Afrooz G, Shokoohi-Yekta M, Kharrazi K, Ghobari B. Can a creative interpersonal problem solving program improve creative thinking in gifted elementary students? . Think Skills Creat . 2017;24:175-185. doi:10.1016/j.tsc.2017.02.011

Shokoohi-Yekta M, Malayeri SA. Effects of advanced parenting training on children's behavioral problems and family problem solving . Procedia Soc Behav Sci . 2015;205:676-680. doi:10.1016/j.sbspro.2015.09.106

By Amy Morin, LCSW Amy Morin, LCSW, is the Editor-in-Chief of Verywell Mind. She's also a psychotherapist, an international bestselling author of books on mental strength and host of The Verywell Mind Podcast. She delivered one of the most popular TEDx talks of all time.

Problem-Solving

Jabberwocky

Problem-solving is the ability to identify and solve problems by applying appropriate skills systematically.

Problem-solving is a process—an ongoing activity in which we take what we know to discover what we don't know. It involves overcoming obstacles by generating hypo-theses, testing those predictions, and arriving at satisfactory solutions.

Problem-solving involves three basic functions:

Seeking information

Generating new knowledge

Making decisions

Problem-solving is, and should be, a very real part of the curriculum. It presupposes that students can take on some of the responsibility for their own learning and can take personal action to solve problems, resolve conflicts, discuss alternatives, and focus on thinking as a vital element of the curriculum. It provides students with opportunities to use their newly acquired knowledge in meaningful, real-life activities and assists them in working at higher levels of thinking (see Levels of Questions ).

Here is a five-stage model that most students can easily memorize and put into action and which has direct applications to many areas of the curriculum as well as everyday life:

Expert Opinion

Here are some techniques that will help students understand the nature of a problem and the conditions that surround it:

List all related relevant facts.
Make a list of all the given information.
Restate the problem in their own words.
List the conditions that surround a problem.
Describe related known problems.

It's Elementary

For younger students, illustrations are helpful in organizing data, manipulating information, and outlining the limits of a problem and its possible solution(s). Students can use drawings to help them look at a problem from many different perspectives.

Understand the problem. It's important that students understand the nature of a problem and its related goals. Encourage students to frame a problem in their own words.

Describe any barriers. Students need to be aware of any barriers or constraints that may be preventing them from achieving their goal. In short, what is creating the problem? Encouraging students to verbalize these impediments is always an important step.

Identify various solutions. After the nature and parameters of a problem are understood, students will need to select one or more appropriate strategies to help resolve the problem. Students need to understand that they have many strategies available to them and that no single strategy will work for all problems. Here are some problem-solving possibilities:

Create visual images. Many problem-solvers find it useful to create “mind pictures” of a problem and its potential solutions prior to working on the problem. Mental imaging allows the problem-solvers to map out many dimensions of a problem and “see” it clearly.

Guesstimate. Give students opportunities to engage in some trial-and-error approaches to problem-solving. It should be understood, however, that this is not a singular approach to problem-solving but rather an attempt to gather some preliminary data.

Create a table. A table is an orderly arrangement of data. When students have opportunities to design and create tables of information, they begin to understand that they can group and organize most data relative to a problem.

Use manipulatives. By moving objects around on a table or desk, students can develop patterns and organize elements of a problem into recognizable and visually satisfying components.

Work backward. It's frequently helpful for students to take the data presented at the end of a problem and use a series of computations to arrive at the data presented at the beginning of the problem.

Look for a pattern. Looking for patterns is an important problem-solving strategy because many problems are similar and fall into predictable patterns. A pattern, by definition, is a regular, systematic repetition and may be numerical, visual, or behavioral.

Create a systematic list. Recording information in list form is a process used quite frequently to map out a plan of attack for defining and solving problems. Encourage students to record their ideas in lists to determine regularities, patterns, or similarities between problem elements.

Try out a solution. When working through a strategy or combination of strategies, it will be important for students to …

Keep accurate and up-to-date records of their thoughts, proceedings, and procedures. Recording the data collected, the predictions made, and the strategies used is an important part of the problem solving process.

Try to work through a selected strategy or combination of strategies until it becomes evident that it's not working, it needs to be modified, or it is yielding inappropriate data. As students become more proficient problem-solvers, they should feel comfortable rejecting potential strategies at any time during their quest for solutions.

Monitor with great care the steps undertaken as part of a solution. Although it might be a natural tendency for students to “rush” through a strategy to arrive at a quick answer, encourage them to carefully assess and monitor their progress.

Feel comfortable putting a problem aside for a period of time and tackling it at a later time. For example, scientists rarely come up with a solution the first time they approach a problem. Students should also feel comfortable letting a problem rest for a while and returning to it later.

Evaluate the results. It's vitally important that students have multiple opportunities to assess their own problem-solving skills and the solutions they generate from using those skills. Frequently, students are overly dependent upon teachers to evaluate their performance in the classroom. The process of self-assessment is not easy, however. It involves risk-taking, self-assurance, and a certain level of independence. But it can be effectively promoted by asking students questions such as “How do you feel about your progress so far?” “Are you satisfied with the results you obtained?” and “Why do you believe this is an appropriate response to the problem?”

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Teaching Problem Solving in Math

Freebies , Math , Planning

Every year my students can be fantastic at math…until they start to see math with words. For some reason, once math gets translated into reading, even my best readers start to panic. There is just something about word problems, or problem-solving, that causes children to think they don’t know how to complete them.

Every year in math, I start off by teaching my students problem-solving skills and strategies. Every year they moan and groan that they know them. Every year – paragraph one above. It was a vicious cycle. I needed something new.

$Problem solving tends to REALLY throw students for a loop when they're first introduced to it. Up until this point, math has been numbers, but now, math is numbers and words. I discuss four important steps I take in teaching problem solving, and I provide you with examples as I go. You can also check out my math workshop problem solving unit for third grade!$

I put together a problem-solving unit that would focus a bit more on strategies and steps in hopes that that would create problem-solving stars.

The Problem Solving Strategies

First, I wanted to make sure my students all learned the different strategies to solve problems, such as guess-and-check, using visuals (draw a picture, act it out, and modeling it), working backward, and organizational methods (tables, charts, and lists). In the past, I had used worksheet pages that would introduce one and provide the students with plenty of problems practicing that one strategy. I did like that because students could focus more on practicing the strategy itself, but I also wanted students to know when to use it, too, so I made sure they had both to practice.

I provided students with plenty of practice of the strategies, such as in this guess-and-check game.

Problem solving tends to REALLY throw students for a loop when they're first introduced to it. Up until this point, math has been numbers, but now, math is numbers and words. I discuss four important steps I take in teaching problem solving, and I provide you with examples as I go. You can also check out my math workshop problem solving unit for third grade!

There’s also this visuals strategy wheel practice.

I also provided them with paper dolls and a variety of clothing to create an organized list to determine just how many outfits their “friend” would have.

Then, as I said above, we practiced in a variety of ways to make sure we knew exactly when to use them. I really wanted to make sure they had this down!

Anyway, after I knew they had down the various strategies and when to use them, then we went into the actual problem-solving steps.

The Problem Solving Steps

I wanted students to understand that when they see a story problem, it isn’t scary. Really, it’s just the equation written out in words in a real-life situation. Then, I provided them with the “keys to success.”

S tep 1 – Understand the Problem. To help students understand the problem, I provided them with sample problems, and together we did five important things:

read the problem carefully
restated the problem in our own words
crossed out unimportant information
circled any important information
stated the goal or question to be solved

We did this over and over with example problems.

Once I felt the students had it down, we practiced it in a game of problem-solving relay. Students raced one another to see how quickly they could get down to the nitty-gritty of the word problems. We weren’t solving the problems – yet.

Then, we were on to Step 2 – Make a Plan . We talked about how this was where we were going to choose which strategy we were going to use. We also discussed how this was where we were going to figure out what operation to use. I taught the students Sheila Melton’s operation concept map.

We talked about how if you know the total and know if it is equal or not, that will determine what operation you are doing. So, we took an example problem, such as:

Sheldon wants to make a cupcake for each of his 28 classmates. He can make 7 cupcakes with one box of cupcake mix. How many boxes will he need to buy?

We started off by asking ourselves, “Do we know the total?” We know there are a total of 28 classmates. So, yes, we are separating. Then, we ask, “Is it equal?” Yes, he wants to make a cupcake for EACH of his classmates. So, we are dividing: 28 divided by 7 = 4. He will need to buy 4 boxes. (I actually went ahead and solved it here – which is the next step, too.)

Step 3 – Solving the problem . We talked about how solving the problem involves the following:

taking our time
working the problem out
showing all our work
estimating the answer
using thinking strategies

We talked specifically about thinking strategies. Just like in reading, there are thinking strategies in math. I wanted students to be aware that sometimes when we are working on a problem, a particular strategy may not be working, and we may need to switch strategies. We also discussed that sometimes we may need to rethink the problem, to think of related content, or to even start over. We discussed these thinking strategies:

switch strategies or try a different one
rethink the problem
think of related content
decide if you need to make changes
check your work
but most important…don’t give up!

To make sure they were getting in practice utilizing these thinking strategies, I gave each group chart paper with a letter from a fellow “student” (not a real student), and they had to give advice on how to help them solve their problem using the thinking strategies above.

Finally, Step 4 – Check It. This is the step that students often miss. I wanted to emphasize just how important it is! I went over it with them, discussing that when they check their problems, they should always look for these things:

compare your answer to your estimate
check for reasonableness
check your calculations
add the units
restate the question in the answer
explain how you solved the problem

Then, I gave students practice cards. I provided them with example cards of “students” who had completed their assignments already, and I wanted them to be the teacher. They needed to check the work and make sure it was completed correctly. If it wasn’t, then they needed to tell what they missed and correct it.

To demonstrate their understanding of the entire unit, we completed an adorable lap book (my first time ever putting together one or even creating one – I was surprised how well it turned out, actually). It was a great way to put everything we discussed in there.

Once we were all done, students were officially Problem Solving S.T.A.R.S. I just reminded students frequently of this acronym.

Stop – Don’t rush with any solution; just take your time and look everything over.

Think – Take your time to think about the problem and solution.

Act – Act on a strategy and try it out.

Review – Look it over and see if you got all the parts.

Wow, you are a true trooper sticking it out in this lengthy post! To sum up the majority of what I have written here, I have some problem-solving bookmarks FREE to help you remember and to help your students!

You can grab these problem-solving bookmarks for FREE by clicking here .

You can do any of these ideas without having to purchase anything. However, if you are looking to save some time and energy, then they are all found in my Math Workshop Problem Solving Unit . The unit is for grade three, but it may work for other grade levels. The practice problems are all for the early third-grade level.

freebie , Math Workshop , Problem Solving

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Problem-Solving Method in Teaching

The problem-solving method is a highly effective teaching strategy that is designed to help students develop critical thinking skills and problem-solving abilities . It involves providing students with real-world problems and challenges that require them to apply their knowledge, skills, and creativity to find solutions. This method encourages active learning, promotes collaboration, and allows students to take ownership of their learning.

Definition of problem-solving method.

Problem-solving is a process of identifying, analyzing, and resolving problems. The problem-solving method in teaching involves providing students with real-world problems that they must solve through collaboration and critical thinking. This method encourages students to apply their knowledge and creativity to develop solutions that are effective and practical.

Meaning of Problem-Solving Method

The meaning and Definition of problem-solving are given by different Scholars. These are-

Woodworth and Marquis(1948) : Problem-solving behavior occurs in novel or difficult situations in which a solution is not obtainable by the habitual methods of applying concepts and principles derived from past experience in very similar situations.

Skinner (1968): Problem-solving is a process of overcoming difficulties that appear to interfere with the attainment of a goal. It is the procedure of making adjustments in spite of interference

Benefits of Problem-Solving Method

The problem-solving method has several benefits for both students and teachers. These benefits include:

Encourages active learning: The problem-solving method encourages students to actively participate in their own learning by engaging them in real-world problems that require critical thinking and collaboration
Promotes collaboration: Problem-solving requires students to work together to find solutions. This promotes teamwork, communication, and cooperation.
Builds critical thinking skills: The problem-solving method helps students develop critical thinking skills by providing them with opportunities to analyze and evaluate problems
Increases motivation: When students are engaged in solving real-world problems, they are more motivated to learn and apply their knowledge.
Enhances creativity: The problem-solving method encourages students to be creative in finding solutions to problems.

Steps in Problem-Solving Method

The problem-solving method involves several steps that teachers can use to guide their students. These steps include

Identifying the problem: The first step in problem-solving is identifying the problem that needs to be solved. Teachers can present students with a real-world problem or challenge that requires critical thinking and collaboration.
Analyzing the problem: Once the problem is identified, students should analyze it to determine its scope and underlying causes.
Generating solutions: After analyzing the problem, students should generate possible solutions. This step requires creativity and critical thinking.
Evaluating solutions: The next step is to evaluate each solution based on its effectiveness and practicality
Selecting the best solution: The final step is to select the best solution and implement it.

Verification of the concluded solution or Hypothesis

The solution arrived at or the conclusion drawn must be further verified by utilizing it in solving various other likewise problems. In case, the derived solution helps in solving these problems, then and only then if one is free to agree with his finding regarding the solution. The verified solution may then become a useful product of his problem-solving behavior that can be utilized in solving further problems. The above steps can be utilized in solving various problems thereby fostering creative thinking ability in an individual.

The problem-solving method is an effective teaching strategy that promotes critical thinking, creativity, and collaboration. It provides students with real-world problems that require them to apply their knowledge and skills to find solutions. By using the problem-solving method, teachers can help their students develop the skills they need to succeed in school and in life.

Jonassen, D. (2011). Learning to solve problems: A handbook for designing problem-solving learning environments. Routledge.
Hmelo-Silver, C. E. (2004). Problem-based learning: What and how do students learn? Educational Psychology Review, 16(3), 235-266.
Mergendoller, J. R., Maxwell, N. L., & Bellisimo, Y. (2006). The effectiveness of problem-based instruction: A comparative study of instructional methods and student characteristics. Interdisciplinary Journal of Problem-based Learning, 1(2), 49-69.
Richey, R. C., Klein, J. D., & Tracey, M. W. (2011). The instructional design knowledge base: Theory, research, and practice. Routledge.
Savery, J. R., & Duffy, T. M. (2001). Problem-based learning: An instructional model and its constructivist framework. CRLT Technical Report No. 16-01, University of Michigan. Wojcikowski, J. (2013). Solving real-world problems through problem-based learning. College Teaching, 61(4), 153-156

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Teaching Through Problem-solving

An elementary-age male student points while his female teacher stands beside him and observes

TTP in Action

What is Teaching Through Problem-Solving?

In Teaching Through Problem-solving (TTP), students learn new mathematics by solving problems. Students grapple with a novel problem, present and discuss solution strategies, and together build the next concept or procedure in the mathematics curriculum.

Teaching Through Problem-solving is widespread in Japan, where students solve problems before a solution method or procedure is taught. In contrast, U.S. students spend most of their time doing exercises– completing problems for which a solution method has already been taught.

Why Teaching Through Problem-Solving?

As students build their mathematical knowledge, they also:

Learn to reason mathematically, using prior knowledge to build new ideas
See the power of their explanations and carefully written work to spark insights for themselves and their classmates
Expect mathematics to make sense
Enjoy solving unfamiliar problems
Experience mathematical discoveries that naturally deepen their perseverance

Phases of a TTP Lesson

Teaching Through Problem-solving flows through four phases as students 1. Grasp the problem, 2. Try to solve the problem independently, 3. Present and discuss their work (selected strategies), and 4. Summarize and reflect.

Click on the arrows below to find out what students and teachers do during each phase and to see video examples.

1. Grasp the Problem
2. Try to Solve
3. Present & Discuss
4. Summarize & Reflect
New Learning

WHAT STUDENTS DO

Understand the problem and develop interest in solving it.
Consider what they know that might help them solve the problem.

WHAT TEACHERS DO

Show several student journal reflections from the prior lesson.
Pose a problem that students do not yet know how to solve.
Interest students in the problem and in thinking about their own related knowledge.
Independently try to solve the problem.
Do not simply following the teacher’s solution example.
Allow classmates to provide input after some independent thinking time.
Circulate, using seating chart to note each student’s solution approach.
Identify work to be presented and discussed at board.
Ask individual questions to spark more thinking if some students finish quickly or don’t get started.
Present and explain solution ideas at the board, are questioned by classmates and teacher. (2-3 students per lesson)
Actively make sense of the presented work and draw out key mathematical points. (All students)
Strategically select and sequence student presentations of work at the board, to build the new mathematics. (Incorrect approaches may be included.)
Monitor student discussion: Are all students noticing the important mathematical ideas?
Add teacher moves (questions, turn-and-talk, votes) as needed to build important mathematics.
Consider what they learned and share their thoughts with class, to help formulate class summary of learning. Copy summary into journal.
Write journal reflection on their own learning from the lesson.
Write on the board a brief summary of what the class learned during the lesson, using student ideas and words where possible.
Ask students to write in their journals about what they learned during the lesson.

How Do Teachers Support Problem-solving?

Although students do much of the talking and questioning in a TTP lesson, teachers play a crucial role. The widely-known 5 Practices for Orchestrating Mathematical Discussions were based in part on TTP . Teachers study the curriculum, anticipate student thinking, and select and sequence the student presentations that allow the class to build the new mathematics. Classroom routines for presentation and discussion of student work, board organization, and reflective mathematics journals work together to allow students to do the mathematical heavy lifting. To learn more about journals, board work, and discussion in TTP, as well as see other TTP resources and examples of TTP in action, click on the respective tabs near the top of this page.

Additional Readings

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What is Lesson Study?
Why Lesson Study?
Teacher Learning
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Teaching Through Problem-solving (TTP)
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10 Best Problem-Solving Therapy Worksheets & Activities

Cognitive science tells us that we regularly face not only well-defined problems but, importantly, many that are ill defined (Eysenck & Keane, 2015).

Sometimes, we find ourselves unable to overcome our daily problems or the inevitable (though hopefully infrequent) life traumas we face.

Problem-Solving Therapy aims to reduce the incidence and impact of mental health disorders and improve wellbeing by helping clients face life’s difficulties (Dobson, 2011).

This article introduces Problem-Solving Therapy and offers techniques, activities, and worksheets that mental health professionals can use with clients.

Before you continue, we thought you might like to download our three Positive Psychology Exercises for free . These science-based exercises explore fundamental aspects of positive psychology, including strengths, values, and self-compassion, and will give you the tools to enhance the wellbeing of your clients, students, or employees.

This Article Contains:

What is problem-solving therapy, 14 steps for problem-solving therapy, 3 best interventions and techniques, 7 activities and worksheets for your session, fascinating books on the topic, resources from positivepsychology.com, a take-home message.

Problem-Solving Therapy assumes that mental disorders arise in response to ineffective or maladaptive coping. By adopting a more realistic and optimistic view of coping, individuals can understand the role of emotions and develop actions to reduce distress and maintain mental wellbeing (Nezu & Nezu, 2009).

“Problem-solving therapy (PST) is a psychosocial intervention, generally considered to be under a cognitive-behavioral umbrella” (Nezu, Nezu, & D’Zurilla, 2013, p. ix). It aims to encourage the client to cope better with day-to-day problems and traumatic events and reduce their impact on mental and physical wellbeing.

Clinical research, counseling, and health psychology have shown PST to be highly effective in clients of all ages, ranging from children to the elderly, across multiple clinical settings, including schizophrenia, stress, and anxiety disorders (Dobson, 2011).

Can it help with depression?

PST appears particularly helpful in treating clients with depression. A recent analysis of 30 studies found that PST was an effective treatment with a similar degree of success as other successful therapies targeting depression (Cuijpers, Wit, Kleiboer, Karyotaki, & Ebert, 2020).

Other studies confirm the value of PST and its effectiveness at treating depression in multiple age groups and its capacity to combine with other therapies, including drug treatments (Dobson, 2011).

The major concepts

Effective coping varies depending on the situation, and treatment typically focuses on improving the environment and reducing emotional distress (Dobson, 2011).

PST is based on two overlapping models:

Social problem-solving model

This model focuses on solving the problem “as it occurs in the natural social environment,” combined with a general coping strategy and a method of self-control (Dobson, 2011, p. 198).

The model includes three central concepts:

Social problem-solving
The problem
The solution

The model is a “self-directed cognitive-behavioral process by which an individual, couple, or group attempts to identify or discover effective solutions for specific problems encountered in everyday living” (Dobson, 2011, p. 199).

Relational problem-solving model

The theory of PST is underpinned by a relational problem-solving model, whereby stress is viewed in terms of the relationships between three factors:

Stressful life events
Emotional distress and wellbeing
Problem-solving coping

Therefore, when a significant adverse life event occurs, it may require “sweeping readjustments in a person’s life” (Dobson, 2011, p. 202).

Enhance positive problem orientation
Decrease negative orientation
Foster ability to apply rational problem-solving skills
Reduce the tendency to avoid problem-solving
Minimize the tendency to be careless and impulsive

D’Zurilla’s and Nezu’s model includes (modified from Dobson, 2011):

Initial structuring Establish a positive therapeutic relationship that encourages optimism and explains the PST approach.
Assessment Formally and informally assess areas of stress in the client’s life and their problem-solving strengths and weaknesses.
Obstacles to effective problem-solving Explore typically human challenges to problem-solving, such as multitasking and the negative impact of stress. Introduce tools that can help, such as making lists, visualization, and breaking complex problems down.
Problem orientation – fostering self-efficacy Introduce the importance of a positive problem orientation, adopting tools, such as visualization, to promote self-efficacy.
Problem orientation – recognizing problems Help clients recognize issues as they occur and use problem checklists to ‘normalize’ the experience.
Problem orientation – seeing problems as challenges Encourage clients to break free of harmful and restricted ways of thinking while learning how to argue from another point of view.
Problem orientation – use and control emotions Help clients understand the role of emotions in problem-solving, including using feelings to inform the process and managing disruptive emotions (such as cognitive reframing and relaxation exercises).
Problem orientation – stop and think Teach clients how to reduce impulsive and avoidance tendencies (visualizing a stop sign or traffic light).
Problem definition and formulation Encourage an understanding of the nature of problems and set realistic goals and objectives.
Generation of alternatives Work with clients to help them recognize the wide range of potential solutions to each problem (for example, brainstorming).
Decision-making Encourage better decision-making through an improved understanding of the consequences of decisions and the value and likelihood of different outcomes.
Solution implementation and verification Foster the client’s ability to carry out a solution plan, monitor its outcome, evaluate its effectiveness, and use self-reinforcement to increase the chance of success.
Guided practice Encourage the application of problem-solving skills across multiple domains and future stressful problems.
Rapid problem-solving Teach clients how to apply problem-solving questions and guidelines quickly in any given situation.

Success in PST depends on the effectiveness of its implementation; using the right approach is crucial (Dobson, 2011).

Problem-solving therapy – Baycrest

The following interventions and techniques are helpful when implementing more effective problem-solving approaches in client’s lives.

First, it is essential to consider if PST is the best approach for the client, based on the problems they present.

Is PPT appropriate?

It is vital to consider whether PST is appropriate for the client’s situation. Therapists new to the approach may require additional guidance (Nezu et al., 2013).

Therapists should consider the following questions before beginning PST with a client (modified from Nezu et al., 2013):

Has PST proven effective in the past for the problem? For example, research has shown success with depression, generalized anxiety, back pain, Alzheimer’s disease, cancer, and supporting caregivers (Nezu et al., 2013).
Is PST acceptable to the client?
Is the individual experiencing a significant mental or physical health problem?

All affirmative answers suggest that PST would be a helpful technique to apply in this instance.

Five problem-solving steps

The following five steps are valuable when working with clients to help them cope with and manage their environment (modified from Dobson, 2011).

Ask the client to consider the following points (forming the acronym ADAPT) when confronted by a problem:

Attitude Aim to adopt a positive, optimistic attitude to the problem and problem-solving process.
Define Obtain all required facts and details of potential obstacles to define the problem.
Alternatives Identify various alternative solutions and actions to overcome the obstacle and achieve the problem-solving goal.
Predict Predict each alternative’s positive and negative outcomes and choose the one most likely to achieve the goal and maximize the benefits.
Try out Once selected, try out the solution and monitor its effectiveness while engaging in self-reinforcement.

If the client is not satisfied with their solution, they can return to step ‘A’ and find a more appropriate solution.

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Positive self-statements

When dealing with clients facing negative self-beliefs, it can be helpful for them to use positive self-statements.

Use the following (or add new) self-statements to replace harmful, negative thinking (modified from Dobson, 2011):

I can solve this problem; I’ve tackled similar ones before.
I can cope with this.
I just need to take a breath and relax.
Once I start, it will be easier.
It’s okay to look out for myself.
I can get help if needed.
Other people feel the same way I do.
I’ll take one piece of the problem at a time.
I can keep my fears in check.
I don’t need to please everyone.

5 Worksheets and workbooks

Problem-solving self-monitoring form.

Answering the questions in the Problem-Solving Self-Monitoring Form provides the therapist with necessary information regarding the client’s overall and specific problem-solving approaches and reactions (Dobson, 2011).

Ask the client to complete the following:

Describe the problem you are facing.
What is your goal?
What have you tried so far to solve the problem?
What was the outcome?

Reactions to Stress

It can be helpful for the client to recognize their own experiences of stress. Do they react angrily, withdraw, or give up (Dobson, 2011)?

The Reactions to Stress worksheet can be given to the client as homework to capture stressful events and their reactions. By recording how they felt, behaved, and thought, they can recognize repeating patterns.

What Are Your Unique Triggers?

Helping clients capture triggers for their stressful reactions can encourage emotional regulation.

When clients can identify triggers that may lead to a negative response, they can stop the experience or slow down their emotional reaction (Dobson, 2011).

The What Are Your Unique Triggers ? worksheet helps the client identify their triggers (e.g., conflict, relationships, physical environment, etc.).

Problem-Solving worksheet

Imagining an existing or potential problem and working through how to resolve it can be a powerful exercise for the client.

Use the Problem-Solving worksheet to state a problem and goal and consider the obstacles in the way. Then explore options for achieving the goal, along with their pros and cons, to assess the best action plan.

Getting the Facts

Clients can become better equipped to tackle problems and choose the right course of action by recognizing facts versus assumptions and gathering all the necessary information (Dobson, 2011).

Use the Getting the Facts worksheet to answer the following questions clearly and unambiguously:

Who is involved?
What did or did not happen, and how did it bother you?
Where did it happen?
When did it happen?
Why did it happen?
How did you respond?

2 Helpful Group Activities

While therapists can use the worksheets above in group situations, the following two interventions work particularly well with more than one person.

Generating Alternative Solutions and Better Decision-Making

A group setting can provide an ideal opportunity to share a problem and identify potential solutions arising from multiple perspectives.

Use the Generating Alternative Solutions and Better Decision-Making worksheet and ask the client to explain the situation or problem to the group and the obstacles in the way.

Once the approaches are captured and reviewed, the individual can share their decision-making process with the group if they want further feedback.

Visualization

Visualization can be performed with individuals or in a group setting to help clients solve problems in multiple ways, including (Dobson, 2011):

Clarifying the problem by looking at it from multiple perspectives
Rehearsing a solution in the mind to improve and get more practice
Visualizing a ‘safe place’ for relaxation, slowing down, and stress management

Guided imagery is particularly valuable for encouraging the group to take a ‘mental vacation’ and let go of stress.

Ask the group to begin with slow, deep breathing that fills the entire diaphragm. Then ask them to visualize a favorite scene (real or imagined) that makes them feel relaxed, perhaps beside a gently flowing river, a summer meadow, or at the beach.

The more the senses are engaged, the more real the experience. Ask the group to think about what they can hear, see, touch, smell, and even taste.

Encourage them to experience the situation as fully as possible, immersing themselves and enjoying their place of safety.

Such feelings of relaxation may be able to help clients fall asleep, relieve stress, and become more ready to solve problems.

We have included three of our favorite books on the subject of Problem-Solving Therapy below.

1. Problem-Solving Therapy: A Treatment Manual – Arthur Nezu, Christine Maguth Nezu, and Thomas D’Zurilla

This is an incredibly valuable book for anyone wishing to understand the principles and practice behind PST.

Written by the co-developers of PST, the manual provides powerful toolkits to overcome cognitive overload, emotional dysregulation, and the barriers to practical problem-solving.

Find the book on Amazon .

2. Emotion-Centered Problem-Solving Therapy: Treatment Guidelines – Arthur Nezu and Christine Maguth Nezu

Another, more recent, book from the creators of PST, this text includes important advances in neuroscience underpinning the role of emotion in behavioral treatment.

Along with clinical examples, the book also includes crucial toolkits that form part of a stepped model for the application of PST.

3. Handbook of Cognitive-Behavioral Therapies – Keith Dobson and David Dozois

This is the fourth edition of a hugely popular guide to Cognitive-Behavioral Therapies and includes a valuable and insightful section on Problem-Solving Therapy.

This is an important book for students and more experienced therapists wishing to form a high-level and in-depth understanding of the tools and techniques available to Cognitive-Behavioral Therapists.

For even more tools to help strengthen your clients’ problem-solving skills, check out the following free worksheets from our blog.

Case Formulation Worksheet This worksheet presents a four-step framework to help therapists and their clients come to a shared understanding of the client’s presenting problem.
Understanding Your Default Problem-Solving Approach This worksheet poses a series of questions helping clients reflect on their typical cognitive, emotional, and behavioral responses to problems.
Social Problem Solving: Step by Step This worksheet presents a streamlined template to help clients define a problem, generate possible courses of action, and evaluate the effectiveness of an implemented solution.

If you’re looking for more science-based ways to help others enhance their wellbeing, check out this signature collection of 17 validated positive psychology tools for practitioners. Use them to help others flourish and thrive.

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The Positive Psychology Toolkit© is a groundbreaking practitioner resource containing over 500 science-based exercises , activities, interventions, questionnaires, and assessments created by experts using the latest positive psychology research.

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While we are born problem-solvers, facing an incredibly diverse set of challenges daily, we sometimes need support.

Problem-Solving Therapy aims to reduce stress and associated mental health disorders and improve wellbeing by improving our ability to cope. PST is valuable in diverse clinical settings, ranging from depression to schizophrenia, with research suggesting it as a highly effective treatment for teaching coping strategies and reducing emotional distress.

Many PST techniques are available to help improve clients’ positive outlook on obstacles while reducing avoidance of problem situations and the tendency to be careless and impulsive.

The PST model typically assesses the client’s strengths, weaknesses, and coping strategies when facing problems before encouraging a healthy experience of and relationship with problem-solving.

Why not use this article to explore the theory behind PST and try out some of our powerful tools and interventions with your clients to help them with their decision-making, coping, and problem-solving?

We hope you enjoyed reading this article. Don’t forget to download our three Positive Psychology Exercises for free .

Cuijpers, P., Wit, L., Kleiboer, A., Karyotaki, E., & Ebert, D. (2020). Problem-solving therapy for adult depression: An updated meta-analysis. European P sychiatry , 48 (1), 27–37.
Dobson, K. S. (2011). Handbook of cognitive-behavioral therapies (3rd ed.). Guilford Press.
Dobson, K. S., & Dozois, D. J. A. (2021). Handbook of cognitive-behavioral therapies (4th ed.). Guilford Press.
Eysenck, M. W., & Keane, M. T. (2015). Cognitive psychology: A student’s handbook . Psychology Press.
Nezu, A. M., & Nezu, C. M. (2009). Problem-solving therapy DVD . Retrieved September 13, 2021, from https://www.apa.org/pubs/videos/4310852
Nezu, A. M., & Nezu, C. M. (2018). Emotion-centered problem-solving therapy: Treatment guidelines. Springer.
Nezu, A. M., Nezu, C. M., & D’Zurilla, T. J. (2013). Problem-solving therapy: A treatment manual . Springer.

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Top 10 Challenges to Teaching Math and Science Using Real Problems

Nine in ten educators believe that using a problem-solving approach to teaching math and science can be motivating for students, according to an EdWeek Research Center survey.

But that doesn’t mean it’s easy.

Teachers perceive lack of time as a big hurdle. In fact, a third of educators—35 percent—worry that teaching math or science through real-world problems—rather than focusing on procedures—eats up too many precious instructional minutes.

Other challenges: About another third of educators said they weren’t given sufficient professional development in how to teach using a real-world problem-solving approach. Nearly a third say reading and writing take priority over STEM, leaving little bandwidth for this kind of instruction. About a quarter say that it’s tough to find instructional materials that embrace a problem-solving perspective.

Nearly one in five cited teachers’ lack of confidence in their own problem solving, the belief that this approach isn’t compatible with standardized tests, low parent support, and the belief that student behavior is so poor that this approach would not be feasible.

The nationally representative survey included 1,183 district leaders, school leaders, and teachers, and was conducted from March 27 to April 14. (Note: The chart below lists 11 challenges because the last two on the list—dealing with teacher preparation and student behavior—received the exact percentage of responses.)

Trying to incorporate a problem-solving approach to tackling math can require rethinking long-held beliefs about how students learn, said Elham Kazemi, a professor in the teacher education program at the University of Washington.

Most teachers were taught math using a procedural perspective when they were in school. While Kazemi believes that approach has merit, she advocates for exposing students to both types of instruction.

Many educators have “grown up around a particular model of thinking of teaching and learning as the teacher in the front of the room, imparting knowledge, showing kids how to do things,” Kazemi said.

To be sure, some teachers have figured out how to incorporate some real-world problem solving alongside more traditional methods. But it can be tough for their colleagues to learn from them because “teachers don’t have a lot of time to collaborate with one another and see each other teach,” Kazemi said.

What’s more, there are limited instructional materials emphasizing problem solving, Kazemi said.

Though that’s changing, many of the resources available have “reinforced the idea that the teacher demonstrates solutions for kids,” Kazemi said.

Molly Daley, a regional math coordinator for Education Service District 112, which serves about 30 districts near Vancouver, Wash., has heard teachers raise concerns that teaching math from a problem-solving perspective takes too long—particularly given the pressure to get through all the material students will need to perform well on state tests.

Daley believes, however, that being taught to think about math in a deeper way will help students tackle math questions on state assessments that may look different from what they’ve seen before.

“It’s myth that it’s possible to cover everything that will be on the test,” as it will appear, she said. “There’s actually no way to make sure that kids have seen every single possible thing the way it will show up. That’s kind of a losing proposition.”

But rushing through the material in a purely procedural way may actually be counterproductive, she said.

Teachers don’t want kids to “sit down at the test and say, ‘I haven’t seen this and therefore I can’t do it,’” Daley said. “I think a lot of times teachers can unintentionally foster that because they’re so urgently trying to cover everything. That’s where the kind of mindless [teaching] approaches come in.”

Teachers may think to themselves: “’OK, I’m gonna make this as simple as possible, make sure everyone knows how to follow the steps and then when they see it, they can follow it,” Daley said.

But that strategy might “take away their students’ confidence that they can figure out what to do when they don’t know what to do, which is really what you want them to be thinking when they go to approach a test,” Daley said.

Data analysis for this article was provided by the EdWeek Research Center. Learn more about the center’s work.

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A Better Framework for Solving Tough Problems

Start with trust and end with speed.

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When it comes to solving complicated problems, the default for many organizational leaders is to take their time to work through the issues at hand. Unfortunately, that often leads to patchwork solutions or problems not truly getting resolved.

But Anne Morriss offers a different framework. In this episode, she outlines a five-step process for solving any problem and explains why starting with trust and ending with speed is so important for effective change leadership. As she says, “Let’s get into dialogue with the people who are also impacted by the problem before we start running down the path of solving it.”

Morriss is an entrepreneur and leadership coach. She’s also the coauthor of the book, Move Fast and Fix Things: The Trusted Leader’s Guide to Solving Hard Problems .

Key episode topics include: strategy, decision making and problem solving, strategy execution, managing people, collaboration and teams, trustworthiness, organizational culture, change leadership, problem solving, leadership.

HBR On Strategy curates the best case studies and conversations with the world’s top business and management experts, to help you unlock new ways of doing business. New episodes every week.

Listen to the full HBR IdeaCast episode: How to Solve Tough Problems Better and Faster (2023)
Find more episodes of HBR IdeaCast
Discover 100 years of Harvard Business Review articles, case studies, podcasts, and more at HBR.org .

HANNAH BATES: Welcome to HBR On Strategy , case studies and conversations with the world’s top business and management experts, hand-selected to help you unlock new ways of doing business.

When it comes to solving complicated problems, many leaders only focus on the most apparent issues. Unfortunately that often leads to patchwork or partial solutions. But Anne Morriss offers a different framework that aims to truly tackle big problems by first leaning into trust and then focusing on speed.

Morriss is an entrepreneur and leadership coach. She’s also the co-author of the book, Move Fast and Fix Things: The Trusted Leader’s Guide to Solving Hard Problems . In this episode, she outlines a five-step process for solving any problem. Some, she says, can be solved in a week, while others take much longer. She also explains why starting with trust and ending with speed is so important for effective change leadership.

This episode originally aired on HBR IdeaCast in October 2023. Here it is.

CURT NICKISCH: Welcome to the HBR IdeaCast from Harvard Business Review. I’m Curt Nickisch.

Problems can be intimidating. Sure, some problems are fun to dig into. You roll up your sleeves, you just take care of them; but others, well, they’re complicated. Sometimes it’s hard to wrap your brain around a problem, much less fix it.

And that’s especially true for leaders in organizations where problems are often layered and complex. They sometimes demand technical, financial, or interpersonal knowledge to fix. And whether it’s avoidance on the leaders’ part or just the perception that a problem is systemic or even intractable, problems find a way to endure, to keep going, to keep being a problem that everyone tries to work around or just puts up with.

But today’s guest says that just compounds it and makes the problem harder to fix. Instead, she says, speed and momentum are key to overcoming a problem.

Anne Morriss is an entrepreneur, leadership coach and founder of the Leadership Consortium and with Harvard Business School Professor Francis Frei, she wrote the new book, Move Fast and Fix Things: The Trusted Leaders Guide to Solving Hard Problems . Anne, welcome back to the show.

ANNE MORRISS: Curt, thank you so much for having me.

CURT NICKISCH: So, to generate momentum at an organization, you say that you really need speed and trust. We’ll get into those essential ingredients some more, but why are those two essential?

ANNE MORRISS: Yeah. Well, the essential pattern that we observed was that the most effective change leaders out there were building trust and speed, and it didn’t seem to be a well-known observation. We all know the phrase, “Move fast and break things,” but the people who were really getting it right were moving fast and fixing things, and that was really our jumping off point. So when we dug into the pattern, what we observed was they were building trust first and then speed. This foundation of trust was what allowed them to fix more things and break fewer.

CURT NICKISCH: Trust sounds like a slow thing, right? If you talk about building trust, that is something that takes interactions, it takes communication, it takes experiences. Does that run counter to the speed idea?

ANNE MORRISS: Yeah. Well, this issue of trust is something we’ve been looking at for over a decade. One of the headlines in our research is it’s actually something we’re building and rebuilding and breaking all the time. And so instead of being this precious, almost farbege egg, it’s this thing that is constantly in motion and this thing that we can really impact when we’re deliberate about our choices and have some self-awareness around where it’s breaking down and how it’s breaking down.

CURT NICKISCH: You said break trust in there, which is intriguing, right? That you may have to break trust to build trust. Can you explain that a little?

ANNE MORRISS: Yeah, well, I’ll clarify. It’s not that you have to break it in order to build it. It’s just that we all do it some of the time. Most of us are trusted most of the time. Most of your listeners I imagine are trusted most of the time, but all of us have a pattern where we break trust or where we don’t build as much as could be possible.

CURT NICKISCH: I want to talk about speed, this other essential ingredient that’s so intriguing, right? Because you think about solving hard problems as something that just takes a lot of time and thinking and coordination and planning and designing. Explain what you mean by it? And also, just how we maybe approach problems wrong by taking them on too slowly?

ANNE MORRISS: Well, Curt, no one has ever said to us, “I wish I had taken longer and done less.” We hear the opposite all the time, by the way. So what we really set out to do was to create a playbook that anyone can use to take less time to do more of the things that are going to make your teams and organizations stronger.

And the way we set up the book is okay, it’s really a five step process. Speed is the last step. It’s the payoff for the hard work you’re going to do to figure out your problem, build or rebuild trust, expand the team in thoughtful and strategic ways, and then tell a real and compelling story about the change you’re leading.

Only then do you get to go fast, but that’s an essential part of the process, and we find that either people under emphasize it or speed has gotten a bad name in this world of moving fast and breaking things. And part of our mission for sure was to rehabilitate speed’s reputation because it is an essential part of the change leader’s equation. It can be the difference between good intentions and getting anything done at all.

CURT NICKISCH: You know, the fact that nobody ever tells you, “I wish we had done less and taken more time.” I think we all feel that, right? Sometimes we do something and then realize, “Oh, that wasn’t that hard and why did it take me so long to do it? And I wish I’d done this a long time ago.” Is it ever possible to solve a problem too quickly?

ANNE MORRISS: Absolutely. And we see that all the time too. What we push people to do in those scenarios is really take a look at the underlying issue because in most cases, the solution is not to take your foot off the accelerator per se and slow down. The solution is to get into the underlying problem. So if it’s burnout or a strategic disconnect between what you’re building and the marketplace you’re serving, what we find is the anxiety that people attach to speed or the frustration people attach to speed is often misplaced.

CURT NICKISCH: What is a good timeline to think about solving a problem then? Because if we by default take too long or else jump ahead and we don’t fix it right, what’s a good target time to have in your mind for how long solving a problem should take?

ANNE MORRISS: Yeah. Well, we’re playful in the book and talking about the idea that many problems can be solved in a week. We set the book up five chapters. They’re titled Monday, Tuesday, Wednesday, Thursday, Friday, and we’re definitely having fun with that. And yet, if you count the hours in a week, there are a lot of them. Many of our problems, if you were to spend a focused 40 hours of effort on a problem, you’re going to get pretty far.

But our main message is, listen, of course it’s going to depend on the nature of the problem, and you’re going to take weeks and maybe even some cases months to get to the other side. What we don’t want you to do is take years, which tends to be our default timeline for solving hard problems.

CURT NICKISCH: So you say to start with identifying the problem that’s holding you back, seems kind of obvious. But where do companies go right and wrong with this first step of just identifying the problem that’s holding you back?

ANNE MORRISS: And our goal is that all of these are going to feel obvious in retrospect. The problem is we skip over a lot of these steps and this is why we wanted to underline them. So this one is really rooted in our observation and I think the pattern of our species that we tend to be overconfident in the quality of our thoughts, particularly when it comes to diagnosing problems.

And so we want to invite you to start in a very humble and curious place, which tends not to be our default mode when we’re showing up for work. We convince ourselves that we’re being paid for our judgment. That’s exactly what gets reinforced everywhere. And so we tend to counterintuitively, given what we just talked about, we tend to move too quickly through the diagnostic phase.

CURT NICKISCH: “I know what to do, that’s why you hired me.”

ANNE MORRISS: Exactly. “I know what to do. That’s why you hired me. I’ve seen this before. I have a plan. Follow me.” We get rewarded for the expression of confidence and clarity. And so what we’re inviting people to do here is actually pause and really lean into what are the root causes of the problem you’re seeing? What are some alternative explanations? Let’s get into dialogue with the people who are also impacted by the problem before we start running down the path of solving it.

CURT NICKISCH: So what do you recommend for this step, for getting to the root of the problem? What are questions you should ask? What’s the right thought process? What do you do on Monday of the week?

ANNE MORRISS: In our experience of doing this work, people tend to undervalue the power of conversation, particularly with other people in the organization. So we will often advocate putting together a team of problem solvers, make it a temporary team, really pull in people who have a particular perspective on the problem and create the space, make it as psychologically safe as you can for people to really, as Chris Argyris so beautifully articulated, discuss the undiscussable.

And so the conditions for that are going to look different in every organization depending on the problem, but if you can get a space where smart people who have direct experience of a problem are in a room and talking honestly with each other, you can make an extraordinary amount of progress, certainly in a day.

CURT NICKISCH: Yeah, that gets back to the trust piece.

ANNE MORRISS: Definitely.

CURT NICKISCH: How do you like to start that meeting, or how do you like to talk about it? I’m just curious what somebody on that team might hear in that meeting, just to get the sense that it’s psychologically safe, you can discuss the undiscussable and you’re also focusing on the identification part. What’s key to communicate there?

ANNE MORRISS: Yeah. Well, we sometimes encourage people to do a little bit of data gathering before those conversations. So the power of a quick anonymous survey around whatever problem you’re solving, but also be really thoughtful about the questions you’re going to ask in the moment. So a little bit of preparation can go a long way and a little bit of thoughtfulness about the power dynamic. So who’s going to walk in there with license to speak and who’s going to hold back? So being thoughtful about the agenda, about the questions you’re asking about the room, about the facilitation, and then courage is a very infectious emotion.

So if you can early on create the conditions for people to show up bravely in that conversation, then the chance that you’re going to get good information and that you’re going to walk out of that room with new insight in the problem that you didn’t have when you walked in is extraordinarily high.

CURT NICKISCH: Now, in those discussions, you may have people who have different perspectives on what the problem really is. They also bear different costs of addressing the problem or solving it. You talked about the power dynamic, but there’s also an unfairness dynamic of who’s going to actually have to do the work to take care of it, and I wonder how you create a culture in that meeting where it’s the most productive?

ANNE MORRISS: For sure, the burden of work is not going to be equitably distributed around the room. But I would say, Curt, the dynamic that we see most often is that people are deeply relieved that hard problems are being addressed. So it really can create, and more often than not in our experience, it does create this beautiful flywheel of action, creativity, optimism. Often when problems haven’t been addressed, there is a fair amount of anxiety in the organization, frustration, stagnation. And so credible movement towards action and progress is often the best antidote. So even if the plan isn’t super clear yet, if it’s credible, given who’s in the room and their decision rights and mandate, if there’s real momentum coming out of that to make progress, then that tends to be deeply energizing to people.

CURT NICKISCH: I wonder if there’s an organization that you’ve worked with that you could talk about how this rolled out and how this took shape?

ANNE MORRISS: When we started working with Uber, that was wrestling with some very public issues of culture and trust with a range of stakeholders internally, the organization, also external, that work really started with a campaign of listening and really trying to understand where trust was breaking down from the perspective of these stakeholders?

So whether it was female employees or regulators or riders who had safety concerns getting into the car with a stranger. This work, it starts with an honest internal dialogue, but often the problem has threads that go external. And so bringing that same commitment to curiosity and humility and dialogue to anyone who’s impacted by the problem is the fastest way to surface what’s really going on.

CURT NICKISCH: There’s a step in this process that you lay out and that’s communicating powerfully as a leader. So we’ve heard about listening and trust building, but now you’re talking about powerful communication. How do you do this and why is it maybe this step in the process rather than the first thing you do or the last thing you do?

ANNE MORRISS: So in our process, again, it’s the days of the week. On Monday you figured out the problem. Tuesday you really got into the sandbox in figuring out what a good enough plan is for building trust. Wednesday, step three, you made it better. You created an even better plan, bringing in new perspectives. Thursday, this fourth step is the day we’re saying you got to go get buy-in. You got to bring other people along. And again, this is a step where we see people often underinvest in the power and payoff of really executing it well.

CURT NICKISCH: How does that go wrong?

ANNE MORRISS: Yeah, people don’t know the why. Human behavior and the change in human behavior really depends on a strong why. It’s not just a selfish, “What’s in it for me?” Although that’s helpful, but where are we going? I may be invested in a status quo and I need to understand, okay, if you’re going to ask me to change, if you’re going to invite me into this uncomfortable place of doing things differently, why am I here? Help me understand it and articulate the way forward and language that not only I can understand, but also that’s going to be motivating to me.

CURT NICKISCH: And who on my team was part of this process and all that kind of stuff?

ANNE MORRISS: Oh, yeah. I may have some really important questions that may be in the way of my buy-in and commitment to this plan. So certainly creating a space where those questions can be addressed is essential. But what we found is that there is an architecture of a great change story, and it starts with honoring the past, honoring the starting place. Sometimes we’re so excited about the change and animated about the change that what has happened before or what is even happening in the present tense is low on our list of priorities.

Or we want to label it bad, because that’s the way we’ve thought about the change, but really pausing and honoring what came before you and all the reasonable decisions that led up to it, I think can be really helpful to getting people emotionally where you want them to be willing to be guided by you. Going back to Uber, when Dara Khosrowshahi came in.

CURT NICKISCH: This is the new CEO.

ANNE MORRISS: The new CEO.

CURT NICKISCH: Replaced Travis Kalanick, the founder and first CEO, yeah.

ANNE MORRISS: Yeah, and had his first all-hands meeting. One of his key messages, and this is a quote, was that he was going to retain the edge that had made Uber, “A force of nature.” And in that meeting, the crowd went wild because this is also a company that had been beaten up publicly for months and months and months, and it was a really powerful choice. And his predecessor, Travis was in the room, and he also honored Travis’ incredible work and investment in bringing the company to the place where it was.

And I would use words like grace to also describe those choices, but there’s also an incredible strategic value to naming the starting place for everybody in the room because in most cases, most people in that room played a role in getting to that starting place, and you’re acknowledging that.

CURT NICKISCH: You can call it grace. Somebody else might call it diplomatic or strategic. But yeah, I guess like it or not, it’s helpful to call out and honor the complexity of the way things have been done and also the change that’s happening.

ANNE MORRISS: Yeah, and the value. Sometimes honoring the past is also owning what didn’t work or what wasn’t working for stakeholders or segments of the employee team, and we see that around culture change. Sometimes you’ve got to acknowledge that it was not an equitable environment, but whatever the worker, everyone in that room is bringing that pass with them. So again, making it discussable and using it as the jumping off place is where we advise people to start.

Then you’ve earned the right to talk about the change mandate, which we suggest using clear and compelling language about the why. “This is what happened, this is where we are, this is the good and the bad of it, and here’s the case for change.”

And then the last part, which is to describe a rigorous and optimistic way forward. It’s a simple past, present, future arc, which will be familiar to human beings. We love stories as human beings. It’s among the most powerful currency we have to make sense of the world.

CURT NICKISCH: Yeah. Chronological is a pretty powerful order.

ANNE MORRISS: Right. But again, the change leaders we see really get it right, are investing an incredible amount of time into the storytelling part of their job. Ursula Burns, the Head of Xerox is famous for the months and years she spent on the road just telling the story of Xerox’s change, its pivot into services to everyone who would listen, and that was a huge part of her success.

CURT NICKISCH: So Friday or your fifth step, you end with empowering teams and removing roadblocks. That seems obvious, but it’s critical. Can you dig into that a little bit?

ANNE MORRISS: Yeah. Friday is the fun day. Friday’s the release of energy into the system. Again, you’ve now earned the right to go fast. You have a plan, you’re pretty confident it’s going to work. You’ve told the story of change the organization, and now you get to sprint. So this is about really executing with urgency, and it’s about a lot of the tactics of speed is where we focus in the book. So the tactics of empowerment, making tough strategic trade-offs so that your priorities are clear and clearly communicated, creating mechanisms to fast-track progress. At Etsy, CEO Josh Silverman, he labeled these projects ambulances. It’s an unfortunate metaphor, but it’s super memorable. These are the products that get to speed out in front of the other ones because the stakes are high and the clock is sticking.

CURT NICKISCH: You pull over and let it go by.

ANNE MORRISS: Yeah, exactly. And so we have to agree as an organization on how to do something like that. And so we see lots of great examples both in young organizations and big complex biotech companies with lots of regulatory guardrails have still found ways to do this gracefully.

And I think we end with this idea of conflict debt, which is a term we really love. Leanne Davey, who’s a team scholar and researcher, and anyone in a tech company will recognize the idea of tech debt, which is this weight the organization drags around until they resolve it. Conflict debt is a beautiful metaphor because it is this weight that we drag around and slows us down until we decide to clean it up and fix it. The organizations that are really getting speed right have figured out either formally or informally, how to create an environment where conflict and disagreements can be gracefully resolved.

CURT NICKISCH: Well, let’s talk about this speed more, right? Because I think this is one of those places that maybe people go wrong or take too long, and then you lose the awareness of the problem, you lose that urgency. And then that also just makes it less effective, right? It’s not just about getting the problem solved as quickly as possible. It’s also just speed in some ways helps solve the problem.

ANNE MORRISS: Oh, yeah. It really is the difference between imagining the change you want to lead and really being able to bring it to life. Speed is the thing that unlocks your ability to lead change. It needs a foundation, and that’s what Monday through Thursday is all about, steps one through four, but the finish line is executing with urgency, and it’s that urgency that releases the system’s energy, that communicates your priorities, that creates the conditions for your team to make progress.

CURT NICKISCH: Moving fast is something that entrepreneurs and tech companies certainly understand, but there’s also this awareness that with big companies, the bigger the organization, the harder it is to turn the aircraft carrier around, right? Is speed relative when you get at those levels, or do you think this is something that any company should be able to apply equally?

ANNE MORRISS: We think this applies to any company. The culture really lives at the level of team. So we believe you can make a tremendous amount of progress even within your circle of control as a team leader. I want to bring some humility to this and careful of words like universal, but we do think there’s some universal truths here around the value of speed, and then some of the byproducts like keeping fantastic people. Your best people want to solve problems, they want to execute, they want to make progress and speed, and the ability to do that is going to be a variable in their own equation of whether they stay or they go somewhere else where they can have an impact.

CURT NICKISCH: Right. They want to accomplish something before they go or before they retire or finish something out. And if you’re able to just bring more things on the horizon and have it not feel like it’s going to be another two years to do something meaningful.

ANNE MORRISS: People – I mean, they want to make stuff happen and they want to be around the energy and the vitality of making things happen, which again, is also a super infectious phenomenon. One of the most important jobs of a leader, we believe, is to set the metabolic pace of their teams and organizations. And so what we really dig into on Friday is, well, what does that look like to speed something up? What are the tactics of that?

CURT NICKISCH: I wonder if that universal truth, that a body in motion stays in motion applies to organizations, right? If an organization in motion stays in motion, there is something to that.

ANNE MORRISS: Absolutely.

CURT NICKISCH: Do you have a favorite client story to share, just where you saw speed just become a bit of a flywheel or just a positive reinforcement loop for more positive change at the organization?

ANNE MORRISS: Yeah. We work with a fair number of organizations that are on fire. We do a fair amount of firefighting, but we also less dramatically do a lot of fire prevention. So we’re brought into organizations that are working well and want to get better, looking out on the horizon. That work is super gratifying, and there is always a component of, well, how do we speed this up?

What I love about that work is there’s often already a high foundation of trust, and so it’s, well, how do we maintain that foundation but move this flywheel, as you said, even faster? And it’s really energizing because often there’s a lot of pent-up energy that… There’s a lot of loyalty to the organization, but often it’s also frustration and pent-up energy. And so when that gets released, when good people get the opportunity to sprint for the first time in a little while, it’s incredibly energizing, not just for us, but for the whole organization.

CURT NICKISCH: Anne, this is great. I think finding a way to solve problems better but also faster is going to be really helpful. So thanks for coming on the show to talk about it.

ANNE MORRISS: Oh, Curt, it was such a pleasure. This is my favorite conversation. I’m delighted to have it anytime.

HANNAH BATES: That was entrepreneur, leadership coach, and author Anne Morriss – in conversation with Curt Nickisch on HBR IdeaCast.

We’ll be back next Wednesday with another hand-picked conversation about business strategy from Harvard Business Review. If you found this episode helpful, share it with your friends and colleagues, and follow our show on Apple Podcasts, Spotify, or wherever you get your podcasts. While you’re there, be sure to leave us a review.

When you’re ready for more podcasts, articles, case studies, books, and videos with the world’s top business and management experts, you’ll find it all at HBR.org.

This episode was produced by Mary Dooe, Anne Saini, and me, Hannah Bates. Ian Fox is our editor. Special thanks to Rob Eckhardt, Maureen Hoch, Erica Truxler, Ramsey Khabbaz, Nicole Smith, Anne Bartholomew, and you – our listener. See you next week.

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Marines say no more ‘death by PowerPoint’ as Corps overhauls education

WASHINGTON, D.C. ― Marines and those who teach them will see more direct, problem-solving approaches to how they learn and far less “death by PowerPoint” as the Corps overhauls its education methods .

Decades of lecturers “foot stomping” material for Marines to learn, recall and regurgitate on a test before forgetting most of what they heard is being replaced by “outcomes-based” learning, a method that’s been in use in other fields but only recently brought into military training.

“Instead of teaching them what to think, we’re teaching them how to think,” said Col. Karl Arbogast, director of the policy and standards division at training and education command .

Here’s what’s in the Corps’ new training and education plan

New ranges, tougher swimming. inside the corps' new training blueprint..

Arbogast laid out some of the new methods that the command is using at the center for learning and faculty development while speaking at the Modern Day Marine Expo.

“No more death by PowerPoint,” Arbogast said. “No more ‘sage on the stage’ anymore, it’s the ‘guide on the side.’”

To do that, Lt. Col. Chris Devries, director of the learning and faculty center, is a multiyear process in which the Marines have developed two new military occupational specialties, 0951 and 0952.

The exceptional MOS is in addition to their primary MOS but allows the Marines to quickly identify who among their ranks is qualified to teach using the new methods.

Training for those jobs gives instructors, now called facilitators, an entry-level understanding of how to teach in an outcomes-based learning model.

Devries said the long-term goal is to create two more levels of instructor/facilitator that a Marine could return to in their career, a journeyman level and a master level. Those curricula are still under development.

The new method helps facilitators first learn the technology they’ll need to share material with and guide students. It also teaches them more formal assessment tools so they can gauge how well students are performing.

For the students, they can learn at their own pace. If they grasp the material the group is covering, they’re encouraged to advance in their study, rather than wait for the entire group to master the introductory material.

More responsibility is placed on the students. For example, in a land navigation class, a facilitator might share materials for students to review before class on their own and then immediately jump into working with maps, compasses and protractors on land navigation projects in the next class period, said John deForest, learning and development officer at the center.

That creates more time in the field for those Marines to practice the skills in a realistic setting.

Marines with Marine Medium Tiltrotor Squadron (VMM) 268, Marine Aircraft Group 24, 1st Marine Aircraft Wing, fire M240-B machine guns at the Marine Corps Air Station Kaneohe Bay range, Hawaii, March 5. (Lance Cpl. Tania Guerrero/Marine Corps)

For the infantry Marine course, the school split up the large classroom into squad-sized groups led by a sergeant or staff sergeant, allowing for more individual focus and participation among the students, Arbogast said.

“They have to now prepare activities for the learner to be directly involved in their own learning and then they have to steer and guide the learners correct outcome,” said Timothy Heck, director of the center’s West Coast detachment.

The students are creating products and portfolios of activities in their training instead of simply taking a written test, said Justina Kirkland, a facilitator at the West Coast detachment.

Students are also pushed to discuss problems among themselves and troubleshoot scenarios. The role of the facilitator then is to monitor the conversation and ask probing questions to redirect the group if they get off course, Heck said.

That involves more decision games, decision forcing cases and even wargaming, deForest said.

We “put the student in an active learning experience where they have to grapple with uncertainty, where they have to grapple with the technical skills and the knowledge they need,” deForest said.

That makes the learning more about application than recall, he said.

Todd South has written about crime, courts, government and the military for multiple publications since 2004 and was named a 2014 Pulitzer finalist for a co-written project on witness intimidation. Todd is a Marine veteran of the Iraq War.

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Open access
Published: 28 May 2024

Design and practice of blended teaching of internal medicine nursing based on O-AMAS effective teaching model

Anyan Duan 1 , 2 ,
Fen Jiang 1 ,
Ling Li 3 ,
Qun Li 1 , 2 &
Wei Chen 1 , 2

BMC Medical Education volume 24 , Article number: 580 ( 2024 ) Cite this article

156 Accesses

Metrics details

Self-directed learning (SDL) ability is the basis for cultivating nursing students’ ability to find and solve problems, lifelong learning, and providing high-quality nursing talents for healthcare. The O-AMAS (Objective, Activation, Multi-learning, Assessment, Summary) model adheres to the teaching philosophy of student-centered, result-oriented, combines the advantages of online and offline teaching, enriching teaching resources and learning channels, diversifying teaching and evaluation methods, and emphasizing integrating and applying knowledge conducive to improving students’ SDL ability and achieving teaching objectives. This study explored the course design, practical, and application effects under the O-AMAS effective teaching model in internal medicine nursing to provide a basis and reference for combining effective teaching models with blended teaching in future nursing courses.

This study is a self-controlled before-after trial. The participants were 76 nursing undergraduates from Hunan Normal University. This study utilizes the O-AMAS effective teaching model to design internal medicine nursing courses and implement blended online and offline teaching. Main links: The overall course design and application are student-centered, after clarifying macro and micro multi-dimensional learning objectives, with online and offline blended teaching environments activated students’ learning behavior and diversified teachers’ teaching activities, then based on instant and dynamic provide effective feedback; finally, students take the initiate to make a brief and potent summary under the teacher guidance. After the course, a unified assessment of the learning effect of nursing students was conducted, including the evaluation of the SDL ability of nursing students, a final comprehensive evaluation grade, and a teaching satisfaction survey.

The nursing students’ SDL ability scores are higher than before teaching, and the results were statistically significant ( P < 0.05). The final average comprehensive evaluation grade of nursing students was 78.38 ± 7.12. More than 96% of the students are satisfied with this course.

Applying for internal medicine nursing blended teaching integrated with the O-AMAS effective teaching model is conducive to improving nursing students’ SDL ability, academic grades, and teaching satisfaction.

Peer Review reports

The overall purpose of internal medicine course is to cultivate high-quality nursing talents with multi-field adaptive learning ability, cross-field practical ability, and interdisciplinary comprehensive thinking ability to improve the quality of nursing services, meet the increasingly diversified and differentiated nursing needs of people, and achieve the goal of “universal health coverage by 2030” [ 1 , 2 , 3 ]. With the rapid update of medical knowledge and technology, nursing students must constantly improve their knowledge, ability, and quality in theoretical teaching and clinical practice, which puts higher requirements for their self-directed learning ability [ 3 , 4 , 5 , 6 ]. The self-directed learning ability of nursing undergraduates is the ability of undergraduate nursing students to obtain and master the necessary knowledge and skills of nursing services with meta-cognition and objective human and material resources. Its main components are the three abilities of self-management, information, and learning cooperation [ 7 ]. Self-directed learning ability is a core competence that equips nursing students with lifelong learning [ 6 , 8 , 9 , 10 ]. Relevant studies show that the SDL ability enables nursing students to enhance their professional nursing values, self-efficacy, meta-cognitive ability, critical thinking, academic performance, academic resilience, time management tendency, problem-solving ability, health education ability, and resilience [ 11 , 12 , 13 , 14 , 15 , 16 , 17 ]. However, because nursing students in the process of learning are still influenced by the traditional teaching concept, nursing students’ learning mainly depends on teachers’ classroom teaching, still a passive accept knowledge role, lack of learning initiative, do not understand discipline dynamic and master essential knowledge, especially difficult to use theory knowledge analysis and solve the problem of clinical practice, the nursing students overall SDL ability and SDL readiness is still at a low to medium level [ 11 , 15 , 18 , 19 ]. Therefore, educators must reform the traditional teaching mode according to the growth law and the learning needs of contemporary students.

O-AMAS, an online and offline hybrid interactive teaching model, was independently developed and launched by the effective teaching team of Nankai University in 2017. The model has five links: Objective, Activation, Multi-learning, Assessment, and Summary [ 20 ]. The model is oriented by learning results and driven by benign interaction. After clarifying multi-dimensional goals, it realizes the teaching objectives and objects are deeply penetrated and participate in the course, advocates student-centered, pays attention to contextualization, gives full play to students’ enthusiasm and initiative, and inspires students to become knowledge builders and problem solvers. The model has been applied in pharmacology, microbial physiology, and community pharmacist training and achieved good results in improving study objects’ self-directed learning ability, academic grades, and satisfaction [ 21 , 22 , 23 ].

In recent years, blended learning strategies have become the most potential teaching strategy in nursing education [ 24 ]. In 2022, China launched the educational digitization strategy, built an online national intelligent education platform for higher education, and an intelligent overpass for teachers and students to teach and learn [ 25 ]. In 2023, China’s Ministry of Education proposed that the digital reform of higher education should pay great attention to content reform and thus provide high-quality educational content to effectively support the steady development of digital education [ 26 ]. Therefore, the Internet-based online and offline mixed teaching mode offers new ideas for promoting the construction of nursing “golden courses” [ 27 , 28 ]. So, this study combines the O-AMAS effective teaching model and online and offline blended teaching to design the internal medicine nursing course. Given the problems existing in the current teaching, analysis and grasp the students learning characteristics and cognitive way, optimize the online teaching resources construction and offline teaching methods, rebuild the internal medical nursing teaching process, use diversified teaching mode, implement effective evaluation and feedback, finally through a brief but potent summary to promote deep learning, fully arouse the students’ learning, improve students’ SDL ability.

Study design

This study is a self-controlled before-after trial.

Participants

Through cluster sampling, the study defined participants as 76 second year nursing undergraduates from Hunan Normal University, including 11 males and 65 females. All subjects signed an informed consent form before participating in the study.

Tools and measurements

Self-directed learning instrument for nursing students

Self-directed learning instrument for nursing students (SDLI for nursing students) consists of 20 items, using the Likert 5-point scoring method; each item is 1 ~ 5 points, the total score is 20 ~ 100 points, the higher the score, the stronger the self-directed learning ability. The scale contains four dimensions (learning motivation, learning plan and implementation, self-management, and interpersonal communication) [ 29 ].

Curriculum academic grades

According to the course design, the course team has developed a comprehensive assessment and evaluation system, which combines the process evaluation and final evaluation from online and offline, including classroom performance, chapter test, topic discussion, group activities, clinical internship, and final examination, with each part taking different weights.

Teaching satisfaction for nursing student’s questionnaire

The teaching team of this study designed the questionnaire through an extensive review of the literature, examined other satisfaction questionnaires, interviewed nursing students, consulted with academic experts, and then adjusted it according to the course design and practice. The questionnaire comprises eight items on three options (approval, neutrality, and disapproval); the questionnaire assesses aspects such as increased learning interest, engagement, and efficiency. In the current study, the Cronbach’s alpha coefficient was 0.916, indicating a high level of reliability.

Internal medicine nursing is a core and practical clinical course in nursing, but learning it is challenging for most students. On the one hand, the complicated and scattered course content, abstract mechanism, and uneven difficulty hindered learners from activating learning interests and focusing on learning objectives; on the other hand, tight class hours, limited classroom learning resources, and learners cannot reasonably arrange learning resources and formulate learning strategies aren’t conducive to cultivate self-directed learning ability and innovation consciousness [ 30 , 31 ]. So this study chooses internal medicine nursing to explore the application effects of the O-AMAS effective teaching model and provide a basis and reference for combining effective teaching models with blended teaching in future nursing courses.

The internal medicine nursing course adopts the O-AMAS effective teaching model to design and mainly includes five parts. The design is summarized in Fig. 1 . Internal Medicine Nursing (6th edition) is the primary textbook, edited by You Liming and Wu Ying and published by People’s Medical Publishing House. Besides, this course quoted Internal Medicine (9th edition) and relevant literature as references, using the MOOC and Chaoxing of online learning applications to assist teaching.

Flow chart of the design of blended teaching of internal medicine nursing based on the O-AMAS effective teaching model

Assemble a teaching team

This study’s teaching team includes 1 department head, 2 pedagogy experts, 5 internal medicine nursing teachers, and 1 teaching assistant from the Chaoxing learning platform. The department head is responsible for the overall design, implementation, adjustment, and summary of internal medicine nursing; pedagogy experts are responsible for guiding and analyzing students’ learning situation, integrating O-AMAS effective teaching model and blended teaching method design; teachers are responsible for building online teaching platform, course teaching, communicating with students and course evaluation; the teaching assistant is responsible for the smooth combination of online teaching platform and offline courses.

Combining blended teaching with the O-AMAS model effectively

Design effective teaching objectives.

The goal of traditional teaching is unclear; most nursing students aim to pass examinations and get a bachelor’s degree certificate, which leads them to neglect often to cultivate their self-directed learning ability. In the long run, it is not conducive for individuals to adapt to the rapidly changing clinical environment and long-term benign development. Therefore, the course team analyzed the students’ learning characteristics and cognitive methods, and under the guidance of the O-AMAS effective teaching model, according to the SMART principles (Specific, Measurable, Achievable, Realistic, Timed) studied and revised the teaching objectives of the internal medicine nursing course, and formulated the macro objectives of the course. The overall teaching objectives of the course: ① Knowledge objectives: Master the basic theory, knowledge, and skills of internal nursing; master the clinical manifestations, nursing diagnosis, nursing plan, nursing measures, and nursing evaluation of common internal diseases; be familiar with the pathologic and physiological change process, diagnostic points and prevention points of common internal diseases; understand the etiology, pathogenesis, and the related frontier research dynamics. ② Ability objectives: Cultivate the ability of nursing students to exert nursing procedures to achieve holistic care; apply interpersonal communication skills to educate medical patients and their families; and learn internal medicine nursing and other related disciplines independently. ③ Quality objectives: Cultivate students’ professional spirit and professional quality; cultivate a rigorous and realistic scientific attitude and an innovative scientific spirit; possess a high degree of patriotic feelings and cultural, legal, moral, and professional literacy.

Based on understanding the course’s overall teaching objectives and Bloom’s Taxonomy of educational objectives, this study from six bands, including knowledge, comprehension, application, analysis, synthesis, and evaluation, to design each lesson gradually ascend from low to high orders and student-centered micro-teaching objectives, teachers focus on diversified teaching activities to help students to learn independently and building knowledge system effectively.

Take the Transient Ischemic Attacks(TIA) section as an example: ① Pre-class self-directed learning stage: mainly the first order of knowledge and comprehension, memorizing the brain’s blood supply, and grasping the disease characteristics of TIA. ② Cooperative learning stage in the class: mainly the middle and high order of application, analysis, and synthesis. Students can observe and make initial evaluations, judge the condition of TIA patients, and cooperate with doctors to actively treat, raise existing nursing problems, implement effective holistic care, and provide health guidance to individuals and families. ③ Consolidation and promotion stage after class. Based on the high-level evaluation, students can use the knowledge to evaluate whether the nursing measures taken for TIA patients are effective. They can find the existing nursing problems and solutions through books, databases, and other resources.

Effective activation to improve students learning interest

Traditional teaching often uses pre-class previews and class tests to activate students, even in some courses that consider the students’ performance an essential part of academic performance. It may have some positive effects, but it also may cause students anxiety and distraction, especially in pure hybrid teaching; students may quickly get answers by intelligent equipment, which not only weakens the students’ interest in learning but can not achieve effective activation. Effective activation requires exciting ways; the activation tools should be closely related to the learning content, and all students participate so that multi-dimensionally activate students’ physical, emotional, and cognition.

This study adopted role-play about clinical reality to activate students’ bodies. Activate students’ emotions by quoting character stories and news reports, such as the diseases that exist in real heroes and ordinary families taking their precious lives, leading to the country and the family loss of talents and relatives to activate students’ empathy; quote positive clinical cases to activate students responsibility, such as healthcare workers save countless patients struggling in disease through solid fundamental knowledge and meticulous clinical work, the teacher praised students’ and created a positive learning atmosphere to activate students’ confidence based on the student’s performance. Presented clinical micro-video and conducted thematic discussions to activate students’ cognition. For example, the leukemia teaching combined with the teaching objectives and content of this chapter, when talking about “acute leukemia,” the teacher through micro-video to initiate a discussion topic, “Does the blood of patients with leukemia turn white?” to motivate student learning interest and enthusiasm, so that students can quickly get into the learning state. The teacher further used brainstorming to guide the students to state whether the blood of leukemia patients will turn white and analyze the causes on the Chaoxing learning platform; the classroom screen will display each student’s ideas to fully mobilize the students to participate actively in the classroom with enthusiasm.

Diversified teaching methods to enhance students’ motivation

Due to the differences between nursing students in personality, learning habits, learning foundation, and learning methods, teachers are required to build new and diversified learning methods to meet the learning needs of most students. This study, based on students’ learning conditions and specific courses, flexibly adopts multiple teaching methods, such as lectured-based learning(LBL), team-based learning(TBL), problem-based learning(PBL), and case-based learning(CBL) etc. A variety of teaching methods are interspersed. At the same time, teachers guided students to experience various learning methods, such as receptive learning, cooperated and explored learning, independent learning, etc. Suppose students must pass the pre-class quizzes to reach the low-order knowledge and comprehension teaching objectives. In that case, the teachers will focus on the class’s LBL and PBL teaching methods, or the teachers will take students as the leading role, application and analysis as the primary teaching objectives, and CBL and TBL as the central teaching methods.

Take acute coronary syndrome and cerebrovascular disease as an example; since students have comprehended the definition and characteristics of the disease, so the teacher took the progressive cases as the main line to present different scenarios of progressive cases gradually. As the disease progresses, it gradually leads to core knowledge points that include the cause of the disease, clinical manifestations, treatment, and nursing measures, etc., and further through teaching strategies such as questioning, enlightening thinking, and group discussion, encourage and guide students to independently explore the implicit knowledge behind the case scenario (such as the causes and inducements of the disease, typical clinical manifestations, and laboratory changes that contribute to identifying the disease, judgment disease of changes, observe treatment efficacy and care adverse reactions), so then guide students to actively participate in the class, more profoundly and systematically understand the internal logical relationship of disease occurrence and development. Finally, according to the feedback from testing, teachers organized students to discuss the frontier or hot topic of clinical nursing. They guided students to track the latest research results and hotspots of nursing. Besides, in the after-class clinical internship, cooperative learning is the primary method; students enter the ward in groups to collect data, and the teachers observe by the bed and give timely guidance and supplements. After the nursing assessment, the students broached the nursing problems and nursing measures according to the case under the teachers’ guidance, evaluated the implementation effect of the nursing measures, and broached the improvement plan. At the end of the internship, the students completed the internship report, which included nursing medical records and experience.

Effective assessment improve teaching effect

The three elements of effective assessment are assessment design, implementation, and feedback. An effective assessment is not a simple score but an effective feedback activity corresponding to the teaching objectives to promote students’ learning effect. This study combines process assessment and final assessment, attaches importance to process assessment and practical ability assessment, continues to assess teaching activities according to teaching objectives, timely adjusts and improves teaching strategies based on students’ feedback, and the assessment runs through the whole online and offline teaching activities. The assessment methods include before and after classroom evaluation, classroom questions and answers, online engagement in the topic discussion, chapter tests, group activities, and clinical internship performance, etc.; the assessment content includes whether the low-order goals (knowledge and comprehension) and the high-order goals (application, analysis, synthesis, and evaluation) can be achieved. The assessment system of internal medicine nursing is presented in Table 1 . For example, this study adopted multiple assessment forms to achieve practical evaluation and feedback, such as group discussion based on clinical progressive cases, topic discussion, and thinking questions. Students can realize how much knowledge they can master in classroom learning and what aspects they need to make up for the deficiencies; it effectively facilitates students to adjust learning objectives timely. Meanwhile, teachers can also analyze the effect of classroom teaching from a multi-dimensional perspective to improve and further promote effective teaching.

Brief summary to promote in-depth learning

This stage is often at the end of a class. After students focus on learning the vital and challenging points of knowledge in class, they tend to become lax at this stage. Therefore, a short and powerful summary is needed to help students connect the key learning content of a class. With students as the main body, teachers guide students in summarizing the classroom content and integrating the learning emphases. Based on the Chaoxing learning platform, it automatically generates summative hot words, or students summarize the teaching content to form mind mapping to help students review what they have learned, further consolidate, reflect, and deepen knowledge.

Statistical data analysis

Entered and analyzed data using the SPSS 23.0 statistical software, measurement information was expressed as mean ± standard deviation ( $\overline {\rm{X}} {\rm{ \pm S}}$ ), and a paired-sample t-test was used to compare students’ self-directed learning ability before and after teaching. The test level is α = 0.05, 1-β = 0.9, p -value<0.05 was considered statistically significant.

Ethical consideration

Informed consent was obtained from the study participants before they were enrolled in the study. Ethical approval was obtained from the Institutional Review Committee of Hunan Normal University School of Medicine before commencing the study. (Ref no 2,023,415, dated 10th February 2023)

Results of final comprehensive grades

In the teaching process, the Chaoxing learning platform, the classroom learning engagement, and the after-class assessment together form the process grades, which combine the final exam score to get the final comprehensive grades. The course passing rate is higher, as recorded in Table 2 .

Results of evaluation of teaching satisfaction

After teaching, using a self-made questionnaire to evaluate the teaching effect, 100% of students gave feedback; more than 90% of students think it is helpful to promote pre-class preview and after-class review and consolidate; more than 80% of students think it helps to stimulate learning interest and enthusiasm, mobilize learning initiative, help adjust learning methods and improve learning efficiency, and teachers can timely feedback; the course satisfaction rate for all students reached 96.1%. The satisfaction results are presented in Table 3 .

Results of comparison of SDL ability before and after teaching

The after-teaching was superior to the before-teaching in the total score of nursing students’ SDL ability ( P < 0.05). The scores of nursing students’ SDL ability were improved in four dimensions, especially in learning motivation, planning and implementation, and self-management ( P < 0.05). The SDL ability scores before and after teaching are presented in Table 4 .

Existing research results show that the students’ SDL ability is positively associated with health education ability, clinical practice behavior, and learning motivation [ 17 , 32 , 33 , 34 ] and negatively associated with study burnout and academic stress [ 35 ], so improving the nursing students’ SDL ability is beneficial to promote the nursing students’ better master theoretical knowledge and operation skills, integrate into the clinical work, promote professional identity, cultivate consciousness and ability of lifelong learning, improve clinical nursing quality in all aspects, meet the growing social health needs [ 36 ]. The O-AMAS effective teaching model emphasizes the educational philosophy of “student-centered and result-oriented development” in all teaching activities [ 20 ]. This study is based on the digital educational trend, combined with the national Massive Open Online Courses(MOOC), the school Small Private Online Course (SPOC) teaching resources, the Chaoxing learning platform, and the Wisdom Tree Platform teaching tools, which scientifically cover pre-class preview, class teaching, and post-class improve three teaching link, designed and practiced blended teaching of internal medicine nursing teaching based on O-AMAS effective teaching model. Establishing a multi-level oriented multi-dimensional goal in line with Bloom’s Taxonomy of educational objectives; Quickly activating the learning interest and behavior from the three aspects of students’ physical, emotional, and cognitive; adopting multiple teaching methods to guide nursing students learning autonomously based on the needs of diagnostic theory and experimental manipulation; combined with the Chaoxing online learning platform for effective measurement and assessment, multi-dimensional analysis, process evaluation and dynamic feedback on the teaching and learning behaviors generated during the course teaching process, to promote the timely improvement of teaching and learning; finally, teachers take the students as the main body and guide students to generate summarizing hot words or mind mappings, help students review what they have learned, explore the relevant scientific research frontiers, and further consolidate and deepen their reflections, improve the coherence and efficiency of nursing students both in and out of class, reduce the learning burden of nursing students, so as to promote the improvement of learning enthusiasm and independent learning ability.

Blended teaching based on the O-AMAS effective teaching model is beneficial to improve the academic performance of nursing students. After teaching, the student’s average academic score was 78.38 ± 7.12 points, which was higher than the academic score of the previous students. More than 96% of students are generally satisfied with this course, and more than 80% believe it can stimulate their interest in learning, mobilize their learning initiative, and increase their learning investment. Moreover, the SDL ability of nursing students was higher than before class, with statistically significant differences ( p < 0.001). These results show that the O-AMAS effective teaching model helps to analyze and grasp students’ learning characteristics and cognitive mode, clarify multi-dimensional learning objectives, effectively and quickly activate the students’ learning behaviors and interests, and significantly improve students’ participation in class. The application of the online curriculum platform for teachers and students to communicate has provided more opportunities and diverse methods; while improving feedback efficiency, it can effectively promote the adjustment and improvement of teaching and learning methods. In this process, teachers’ pedagogy improved, and students effectively realized the enhancement of knowledge level and clinical ability. Both sides progress to complete the overall goal of the course and develop a harmonious relationship. Therefore, students achieved excellent academic performance and were given a higher teaching evaluation. In the post-epidemic era, Shen Bingzheng et al. based on the O-AMAS teaching model and flipped classroom, developed an online continuing training program, effectively improved community pharmacists’ SDL ability, professional competence online, and received a high evaluation of teaching satisfaction [ 23 ]; Luo PeiPei et al. adopted the results-oriented effective teaching mode (O-AMAS) to guide the clinical nursing teaching of undergraduates in cardiovascular internal medicine and improved the nursing students of theoretical scores, comprehensive skills test score, and evaluation of clinical teaching effect [ 37 ]. Wang Xiaojun et al. applied the O-AMAS effective teaching model in the health assessment course, which effectively improved the teaching effect, improved the teaching evaluation of teachers and students, and cultivated students’ independent learning ability [ 38 ]. Therefore, the O-AMAS effective teaching model is helpful in improving students’ self-learning ability, academic performance, and teaching satisfaction and is also suitable for nursing teaching in different settings.

This study further found that the self-directed learning instrument for nursing students of the three dimensions’ total scores (learning motivation, planning and implementation, self-management) were higher than before teaching, with statistically significant differences ( p < 0.05), which can be attributed to that the teaching model expand the cognition of learning from the starting point of teaching, let students get rid of the idea of learning for the sake of examination, and realize that the course of internal medicine nursing can help them master knowledge, improve their ability, and establish good professional ethics, to correct, activate and maintain the learning motivation of learners [ 39 ]; adhere to the student-centered from beginning to end, online and offline, and provides external learning conditions and resources that suitable for students’ learning paths, starting from the activation of existence, then using self-improvement as the intermediary, students to formulate and implement learning plans according to their own situation in the support of rich teaching resources and various teaching methods, finally promote individual self planning and implementation ability [ 40 ]. Besides, combining the online learning platforms of MOOC and the Chaoxing Learning platform to multi-dimensionally analyze, dynamically evaluate, and provide feedback improves students’ ability to actively think, explore, and build knowledge systems. Supervise and manage students’ online learning situations and include usual performances as process assessment data, which improves students’ self-management ability to a certain extent [ 41 , 42 , 43 , 44 ]. Compared with traditional face-to-face teaching and simple online teaching, the blended teaching mode that integrate online resources and clinical case has more positive effects on student’s academic performance [ 45 , 46 ], self-directed learning ability [ 47 , 48 ], learning interest [ 49 ], motivation [ 50 ], and satisfaction [ 51 , 52 ]. It is also worth noting that the interpersonal communication skills of nursing students improved compared with before teaching, but the result did not have statistical significance. In terms of interpersonal communication, when applying the O-AMAS effective teaching model in this course, the teaching process takes students as the main line and teachers as the guidance, but online learning mainly focuses on students’ independent learning, with fewer chapters on peer learning, team-based learning, and learning feedback between peers. Therefore, there is no noticeable improvement in students’ SDL ability in interpersonal communication. In the future, education must focus on cultivating students’ confidence to improve interpersonal communication.

The results of this study show that the design of blended teaching of internal medicine nursing based on the O-AMAS effective teaching model has an explicit level, rich content, a wide range of applications, more than 100 effective interactive methods, and a variety of teaching methods, teaching techniques, teaching organization and management complements each other, which can effectively improve students’ academic performance and SDL ability, further stimulating students’ enthusiasm for learning to encourage students to learn more actively and effectively. Students’ high satisfaction with the course also promotes the establishment of harmonious relationships between teachers and students and the realization of course objectives; the course objectives and teaching objectives are successfully realized and deeply penetrate the teaching process, the teaching objects are deeply involved, the teaching methods have rules to follow, and the teaching effect is visible and controllable. This study has limitations in the number of courses applied, class hours, and sample size, which need to be improved in future studies. Therefore, nursing teaching needs to innovate the classroom teaching mode and optimize the teaching process constantly to promote the development of students’ self-directed learning ability, improve students’ innovation capacity, and lay a talent foundation for the sustainable development of China’s health cause.

Data availability

The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request. The data are not available publicly due to privacy.

Abbreviations

Self-directed learning

Transient Ischemic Attacks

Lectured-based learning

Team-based learning

Problem-based learning

Case-based learning

Massive Open Online Courses

Small Private Online Course

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This work was supported by grants from the Teaching Reform research project of the Hunan Normal University School of Medicine.

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W.C. and A.Y.D. conceived the original idea and wrote the proposal. A.Y.D., W.C., and F.J. designed and applied the study. A.Y.D., F.J., L.L., Q.L., and W.C. organized the data collection and analyzed the data. All the authors contributed to revising the draft of the manuscript, and all the authors read and approved the final draft of the manuscript.

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ChatGPT-4o is a valuable resource for generating creative prompts. Teachers can use these prompts for storytelling, poetry, or essay assignments, encouraging students to explore their imagination. During class discussions, inputting keywords or themes into ChatGPT-4o can kickstart brainstorming sessions.

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With all of the exciting AI tools rolling out, this is a good time to stop and check in to make sure that they’re working for us and not hindering our ability to think critically.

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Set Expectations: From the outset, communicate that AI is a valuable resource, but it’s not a replacement for human intelligence. Encourage students to use AI as a tool to complement their thinking, not as a shortcut.

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Introduce AI Gradually: As students gain confidence, introduce AI tools. For instance, show them how to use AI for fact-checking or generating ideas. Gradually transition from teacher-led research to student-led AI exploration.

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Evaluate AI Responses: When students use AI, encourage them to critically assess the quality of the answers. Is the information accurate? Is it biased? Discuss these aspects in class.

Compare AI with Human Expertise: Have students compare AI-generated responses with those from human experts. Highlight the strengths and limitations of both approaches.

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Coding and Problem-Solving: Introduce students to AI-related coding tasks. For instance, they can create simple chatbots or analyze data using Python libraries.

7. Reflect on Ethical Implications

Discuss Bias and Fairness: Engage students in conversations about AI bias, privacy, and ethical considerations. Make them aware of the impact of biased training data on AI outcomes.

Explore AI in Context: When using AI, discuss its broader implications. How does it affect society, employment, and decision-making?

AI Tools Can Enhance Cognitive Development

As educators, we have a unique opportunity to shape how students interact with AI. By emphasizing critical thinking, independence, and responsible AI use, we can ensure that AI tools enhance—not hinder—their cognitive development.

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Teaching Problem Solving
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.
Teaching Problem Solving
Problem-Solving Fellows Program Undergraduate students who are currently or plan to be peer educators (e.g., UTAs, lab TAs, peer mentors, etc.) are encouraged to take the course, UNIV 1110: The Theory and Teaching of Problem Solving. Within this course, we focus on developing effective problem solvers through students' teaching practices.
Why Every Educator Needs to Teach Problem-Solving Skills
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.
Don't Just Tell Students to Solve Problems. Teach Them How
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 ...
Teaching problem solving: Let students get 'stuck' and 'unstuck'
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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 ...
Teaching Problem-Solving Skills
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 ...
Problem-Based Learning
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.
Problem Solving Lessons
3. 4. 5. TED-Ed lessons on the subject Problem Solving. TED-Ed celebrates the ideas of teachers and students around the world. Discover hundreds of animated lessons, create customized lessons, and share your big ideas.
Teaching Mathematics Through Problem Solving
Teaching about problem solving begins with suggested strategies to solve a problem. For example, "draw a picture," "make a table," etc. You may see posters in teachers' classrooms of the "Problem Solving Method" such as: 1) Read the problem, 2) Devise a plan, 3) Solve the problem, and 4) Check your work. There is little or no ...
6 Tips for Teaching Math Problem-Solving Skills
1. Link problem-solving to reading. When we can remind students that they already have many comprehension skills and strategies they can easily use in math problem-solving, it can ease the anxiety surrounding the math problem. For example, providing them with strategies to practice, such as visualizing, acting out the problem with math tools ...
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Here are the steps to problem-solving: . Identify the problem. Just stating the problem out loud can make a big difference for kids who are feeling stuck. Help your child state the problem, such as, "You don't have anyone to play with at recess," or "You aren't sure if you should take the advanced math class."
Problem Solving Resources
Problem-solving is the ability to identify and solve problems by applying appropriate skills systematically. Problem-solving is a process—an ongoing activity in which we take what we know to discover what we don't know. It involves overcoming obstacles by generating hypo-theses, testing those predictions, and arriving at satisfactory solutions.
Solve a Teaching Problem
How does it work? Step 1: Identify a PROBLEM you encounter in your teaching. Step 2: Identify possible REASONS for the problem Step 3: Explore STRATEGIES to address the problem. This site supplements our 1-on-1 teaching consultations. CONTACT US to talk with an Eberly colleague in person!
Full article: Understanding and explaining pedagogical problem solving
1. Introduction. The focus of this paper is on understanding and explaining pedagogical problem solving. This theoretical paper builds on two previous studies (Riordan, Citation 2020; and Riordan, Hardman and Cumbers, Citation 2021) by introducing an 'extended Pedagogy Analysis Framework' and a 'Pedagogical Problem Typology' illustrating both with examples from video-based analysis of ...
Teaching Problem Solving in Math
Then, I provided them with the "keys to success.". Step 1 - Understand the Problem. To help students understand the problem, I provided them with sample problems, and together we did five important things: read the problem carefully. restated the problem in our own words. crossed out unimportant information.
Problem Solving
(The term "problem solving" refers to mathematical tasks that have the potential to provide intellectual challenges for enhancing students' mathematical understanding and development.) Fortunately, a considerable amount of research on teaching and learning mathematical problem solving has been conducted during the past 40 years or so and, taken ...
(PDF) Principles for Teaching Problem Solving
structured problem solving. 7) Use inductive teaching strategies to encourage synthesis of mental models and for. moderately and ill-structured problem solving. 8) Within a problem exercise, help ...
Problem-Solving Method In Teaching
The problem-solving method is an effective teaching strategy that promotes critical thinking, creativity, and collaboration. It provides students with real-world problems that require them to apply their knowledge and skills to find solutions. By using the problem-solving method, teachers can help their students develop the skills they need to ...
Overview
Download. Teaching Through Problem-solving flows through four phases as students 1. Grasp the problem, 2. Try to solve the problem independently, 3. Present and discuss their work (selected strategies), and 4. Summarize and reflect. Click on the arrows below to find out what students and teachers do during each phase and to see video examples.
10 Best Problem-Solving Therapy Worksheets & Activities
Encourage the application of problem-solving skills across multiple domains and future stressful problems. Rapid problem-solving Teach clients how to apply problem-solving questions and guidelines quickly in any given situation. Success in PST depends on the effectiveness of its implementation; using the right approach is crucial (Dobson, 2011).
Teaching is Problem Solving
The site is always growing and changing. If you want to know when new material arrives, be sure to sign up to receive notifications of new content and resources. Come learn with us! Welcome to Teaching Is Problem Solving â€" a new site dedicated to sharing ideas about teaching with a focus on mathematics.
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Nine in ten educators believe that using a problem-solving approach to teaching math and science can be motivating for students, according to an EdWeek Research Center survey. But that doesn't ...
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Start with trust and end with speed. May 22, 2024. When it comes to solving complicated problems, the default for many organizational leaders is to take their time to work through the issues at hand.
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Exploring large language models as an integrated tool for learning
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Virtual Morning Report
Virtual Morning Report - May 31, 2024 Presenter: Kara LauCase Discussants: Rabih & CPS teamCase details & teaching points: Here
How To Use ChatGPT-4o In Your Classroom
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