problem solving curriculum for students

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]

Published Date

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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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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Problem Solving in STEM

Solving problems is a key component of many science, math, and engineering classes. If a goal of a class is for students to emerge with the ability to solve new kinds of problems or to use new problem-solving techniques, then students need numerous opportunities to develop the skills necessary to approach and answer different types of problems. Problem solving during section or class allows students to develop their confidence in these skills under your guidance, better preparing them to succeed on their homework and exams. This page offers advice about strategies for facilitating problem solving during class.

How do I decide which problems to cover in section or class?

In-class problem solving should reinforce the major concepts from the class and provide the opportunity for theoretical concepts to become more concrete. If students have a problem set for homework, then in-class problem solving should prepare students for the types of problems that they will see on their homework. You may wish to include some simpler problems both in the interest of time and to help students gain confidence, but it is ideal if the complexity of at least some of the in-class problems mirrors the level of difficulty of the homework. You may also want to ask your students ahead of time which skills or concepts they find confusing, and include some problems that are directly targeted to their concerns.

You have given your students a problem to solve in class. What are some strategies to work through it?

Try to give your students a chance to grapple with the problems as much as possible. Offering them the chance to do the problem themselves allows them to learn from their mistakes in the presence of your expertise as their teacher. (If time is limited, they may not be able to get all the way through multi-step problems, in which case it can help to prioritize giving them a chance to tackle the most challenging steps.)
When you do want to teach by solving the problem yourself at the board, talk through the logic of how you choose to apply certain approaches to solve certain problems. This way you can externalize the type of thinking you hope your students internalize when they solve similar problems themselves.
Start by setting up the problem on the board (e.g you might write down key variables and equations; draw a figure illustrating the question). Ask students to start solving the problem, either independently or in small groups. As they are working on the problem, walk around to hear what they are saying and see what they are writing down. If several students seem stuck, it might be a good to collect the whole class again to clarify any confusion. After students have made progress, bring the everyone back together and have students guide you as to what to write on the board.
It can help to first ask students to work on the problem by themselves for a minute, and then get into small groups to work on the problem collaboratively.
If you have ample board space, have students work in small groups at the board while solving the problem. That way you can monitor their progress by standing back and watching what they put up on the board.
If you have several problems you would like to have the students practice, but not enough time for everyone to do all of them, you can assign different groups of students to work on different – but related - problems.

When do you want students to work in groups to solve problems?

Don’t ask students to work in groups for straightforward problems that most students could solve independently in a short amount of time.
Do have students work in groups for thought-provoking problems, where students will benefit from meaningful collaboration.
Even in cases where you plan to have students work in groups, it can be useful to give students some time to work on their own before collaborating with others. This ensures that every student engages with the problem and is ready to contribute to a discussion.

What are some benefits of having students work in groups?

Students bring different strengths, different knowledge, and different ideas for how to solve a problem; collaboration can help students work through problems that are more challenging than they might be able to tackle on their own.
In working in a group, students might consider multiple ways to approach a problem, thus enriching their repertoire of strategies.
Students who think they understand the material will gain a deeper understanding by explaining concepts to their peers.

What are some strategies for helping students to form groups?

Instruct students to work with the person (or people) sitting next to them.
Count off. (e.g. 1, 2, 3, 4; all the 1’s find each other and form a group, etc)
Hand out playing cards; students need to find the person with the same number card. (There are many variants to this. For example, you can print pictures of images that go together [rain and umbrella]; each person gets a card and needs to find their partner[s].)
Based on what you know about the students, assign groups in advance. List the groups on the board.
Note: Always have students take the time to introduce themselves to each other in a new group.

What should you do while your students are working on problems?

Walk around and talk to students. Observing their work gives you a sense of what people understand and what they are struggling with. Answer students’ questions, and ask them questions that lead in a productive direction if they are stuck.
If you discover that many people have the same question—or that someone has a misunderstanding that others might have—you might stop everyone and discuss a key idea with the entire class.

After students work on a problem during class, what are strategies to have them share their answers and their thinking?

Ask for volunteers to share answers. Depending on the nature of the problem, student might provide answers verbally or by writing on the board. As a variant, for questions where a variety of answers are relevant, ask for at least three volunteers before anyone shares their ideas.
Use online polling software for students to respond to a multiple-choice question anonymously.
If students are working in groups, assign reporters ahead of time. For example, the person with the next birthday could be responsible for sharing their group’s work with the class.
Cold call. To reduce student anxiety about cold calling, it can help to identify students who seem to have the correct answer as you were walking around the class and checking in on their progress solving the assigned problem. You may even want to warn the student ahead of time: "This is a great answer! Do you mind if I call on you when we come back together as a class?"
Have students write an answer on a notecard that they turn in to you. If your goal is to understand whether students in general solved a problem correctly, the notecards could be submitted anonymously; if you wish to assess individual students’ work, you would want to ask students to put their names on their notecard.
Use a jigsaw strategy, where you rearrange groups such that each new group is comprised of people who came from different initial groups and had solved different problems. Students now are responsible for teaching the other students in their new group how to solve their problem.
Have a representative from each group explain their problem to the class.
Have a representative from each group draw or write the answer on the board.

What happens if a student gives a wrong answer?

Ask for their reasoning so that you can understand where they went wrong.
Ask if anyone else has other ideas. You can also ask this sometimes when an answer is right.
Cultivate an environment where it’s okay to be wrong. Emphasize that you are all learning together, and that you learn through making mistakes.
Do make sure that you clarify what the correct answer is before moving on.
Once the correct answer is given, go through some answer-checking techniques that can distinguish between correct and incorrect answers. This can help prepare students to verify their future work.

How can you make your classroom inclusive?

The goal is that everyone is thinking, talking, and sharing their ideas, and that everyone feels valued and respected. Use a variety of teaching strategies (independent work and group work; allow students to talk to each other before they talk to the class). Create an environment where it is normal to struggle and make mistakes.
See Kimberly Tanner’s article on strategies to promoste student engagement and cultivate classroom equity.

A few final notes…

Make sure that you have worked all of the problems and also thought about alternative approaches to solving them.
Board work matters. You should have a plan beforehand of what you will write on the board, where, when, what needs to be added, and what can be erased when. If students are going to write their answers on the board, you need to also have a plan for making sure that everyone gets to the correct answer. Students will copy what is on the board and use it as their notes for later study, so correct and logical information must be written there.

For more information...

Tipsheet: Problem Solving in STEM Sections

Tanner, K. D. (2013). Structure matters: twenty-one teaching strategies to promote student engagement and cultivate classroom equity . CBE-Life Sciences Education, 12(3), 322-331.

Designing Your Course
A Teaching Timeline: From Pre-Term Planning to the Final Exam
The First Day of Class
Group Agreements
Classroom Debate
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Establishing Community Agreements and Classroom Norms
Sample group work rubric
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. 

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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Collaborative Problem Solving in Schools »

Collaborative Problem Solving in Schools

Collaborative Problem Solving ® (CPS) is an evidence-based, trauma-informed practice that helps students meet expectations, reduces concerning behavior, builds students’ skills, and strengthens their relationships with educators.

Collaborative Problem Solving is designed to meet the needs of all children, including those with social, emotional, and behavioral challenges. It promotes the understanding that students who have trouble meeting expectations or managing their behavior lack the skill—not the will—to do so. These students struggle with skills related to problem-solving, flexibility, and frustration tolerance. Collaborative Problem Solving has been shown to help build these skills.

Collaborative Problem Solving avoids using power, control, and motivational procedures. Instead, it focuses on collaborating with students to solve the problems leading to them not meeting expectations and displaying concerning behavior. This trauma-informed approach provides staff with actionable strategies for trauma-sensitive education and aims to mitigate implicit bias’s impact on school discipline . It integrates with MTSS frameworks, PBIS, restorative practices, and SEL approaches, such as RULER. Collaborative Problem Solving reduces challenging behavior and teacher stress while building future-ready skills and relationships between educators and students.

Transform School Discipline

Traditional school discipline is broken, it doesn’t result in improved behavior or improved relationships between educators and students. In addition, it has been shown to be disproportionately applied to students of color. The Collaborative Problem Solving approach is an equitable and effective form of relational discipline that reduces concerning behavior and teacher stress while building skills and relationships between educators and students. Learn more >>

A Client’s Story

Collaborative Problem Solving and SEL

Collaborative Problem Solving aligns with CASEL’s five core competencies by building relationships between teachers and students using everyday situations. Students develop the skills they need to prepare for the real world, including problem-solving, collaboration and communication, flexibility, perspective-taking, and empathy. Collaborative Problem Solving makes social-emotional learning actionable.

Collaborative Problem Solving and MTSS

The Collaborative Problem Solving approach integrates with Multi-Tiered Systems of Support (MTSS) in educational settings. CPS benefits all students and can be implemented across the three tiers of support within an MTSS framework to effectively identify and meet the diverse social emotional and behavioral needs of students in schools. Learn More >>

The Results

Our research has shown that the Collaborative Problem Solving approach helps kids and adults build crucial social-emotional skills and leads to dramatic decreases in behavior problems across various settings. Results in schools include remarkable reductions in time spent out of class, detentions, suspensions, injuries, teacher stress, and alternative placements as well as increases in emotional safety, attendance, academic growth, and family participation.

Educators, join us in this introductory course and develop your behavioral growth mindset!

This 2-hour, self-paced course introduces the principles of Collaborative Problem Solving ® while outlining how the approach is uniquely suited to the needs of today's educators and students. Tuition: $39 Enroll Now

Bring CPS to Your School

We can help you bring a more accurate, compassionate, and effective approach to working with children to your school or district.

What Our Clients Say

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Classroom Q&A

With larry ferlazzo.

In this EdWeek blog, an experiment in knowledge-gathering, Ferlazzo will address readers’ questions on classroom management, ELL instruction, lesson planning, and other issues facing teachers. Send your questions to [email protected]. Read more from this blog.

Eight Instructional Strategies for Promoting Critical Thinking

(This is the first post in a three-part series.)

The new question-of-the-week is:

What is critical thinking and how can we integrate it into the classroom?

This three-part series will explore what critical thinking is, if it can be specifically taught and, if so, how can teachers do so in their classrooms.

Today’s guests are Dara Laws Savage, Patrick Brown, Meg Riordan, Ph.D., and Dr. PJ Caposey. Dara, Patrick, and Meg were also guests on my 10-minute BAM! Radio Show . You can also find a list of, and links to, previous shows here.

You might also be interested in The Best Resources On Teaching & Learning Critical Thinking In The Classroom .

Current Events

Dara Laws Savage is an English teacher at the Early College High School at Delaware State University, where she serves as a teacher and instructional coach and lead mentor. Dara has been teaching for 25 years (career preparation, English, photography, yearbook, newspaper, and graphic design) and has presented nationally on project-based learning and technology integration:

There is so much going on right now and there is an overload of information for us to process. Did you ever stop to think how our students are processing current events? They see news feeds, hear news reports, and scan photos and posts, but are they truly thinking about what they are hearing and seeing?

I tell my students that my job is not to give them answers but to teach them how to think about what they read and hear. So what is critical thinking and how can we integrate it into the classroom? There are just as many definitions of critical thinking as there are people trying to define it. However, the Critical Think Consortium focuses on the tools to create a thinking-based classroom rather than a definition: “Shape the climate to support thinking, create opportunities for thinking, build capacity to think, provide guidance to inform thinking.” Using these four criteria and pairing them with current events, teachers easily create learning spaces that thrive on thinking and keep students engaged.

One successful technique I use is the FIRE Write. Students are given a quote, a paragraph, an excerpt, or a photo from the headlines. Students are asked to F ocus and respond to the selection for three minutes. Next, students are asked to I dentify a phrase or section of the photo and write for two minutes. Third, students are asked to R eframe their response around a specific word, phrase, or section within their previous selection. Finally, students E xchange their thoughts with a classmate. Within the exchange, students also talk about how the selection connects to what we are covering in class.

There was a controversial Pepsi ad in 2017 involving Kylie Jenner and a protest with a police presence. The imagery in the photo was strikingly similar to a photo that went viral with a young lady standing opposite a police line. Using that image from a current event engaged my students and gave them the opportunity to critically think about events of the time.

Here are the two photos and a student response:

F - Focus on both photos and respond for three minutes

In the first picture, you see a strong and courageous black female, bravely standing in front of two officers in protest. She is risking her life to do so. Iesha Evans is simply proving to the world she does NOT mean less because she is black … and yet officers are there to stop her. She did not step down. In the picture below, you see Kendall Jenner handing a police officer a Pepsi. Maybe this wouldn’t be a big deal, except this was Pepsi’s weak, pathetic, and outrageous excuse of a commercial that belittles the whole movement of people fighting for their lives.

I - Identify a word or phrase, underline it, then write about it for two minutes

A white, privileged female in place of a fighting black woman was asking for trouble. A struggle we are continuously fighting every day, and they make a mockery of it. “I know what will work! Here Mr. Police Officer! Drink some Pepsi!” As if. Pepsi made a fool of themselves, and now their already dwindling fan base continues to ever shrink smaller.

R - Reframe your thoughts by choosing a different word, then write about that for one minute

You don’t know privilege until it’s gone. You don’t know privilege while it’s there—but you can and will be made accountable and aware. Don’t use it for evil. You are not stupid. Use it to do something. Kendall could’ve NOT done the commercial. Kendall could’ve released another commercial standing behind a black woman. Anything!

Exchange - Remember to discuss how this connects to our school song project and our previous discussions?

This connects two ways - 1) We want to convey a strong message. Be powerful. Show who we are. And Pepsi definitely tried. … Which leads to the second connection. 2) Not mess up and offend anyone, as had the one alma mater had been linked to black minstrels. We want to be amazing, but we have to be smart and careful and make sure we include everyone who goes to our school and everyone who may go to our school.

As a final step, students read and annotate the full article and compare it to their initial response.

Using current events and critical-thinking strategies like FIRE writing helps create a learning space where thinking is the goal rather than a score on a multiple-choice assessment. Critical-thinking skills can cross over to any of students’ other courses and into life outside the classroom. After all, we as teachers want to help the whole student be successful, and critical thinking is an important part of navigating life after they leave our classrooms.

‘Before-Explore-Explain’

Patrick Brown is the executive director of STEM and CTE for the Fort Zumwalt school district in Missouri and an experienced educator and author :

Planning for critical thinking focuses on teaching the most crucial science concepts, practices, and logical-thinking skills as well as the best use of instructional time. One way to ensure that lessons maintain a focus on critical thinking is to focus on the instructional sequence used to teach.

Explore-before-explain teaching is all about promoting critical thinking for learners to better prepare students for the reality of their world. What having an explore-before-explain mindset means is that in our planning, we prioritize giving students firsthand experiences with data, allow students to construct evidence-based claims that focus on conceptual understanding, and challenge students to discuss and think about the why behind phenomena.

Just think of the critical thinking that has to occur for students to construct a scientific claim. 1) They need the opportunity to collect data, analyze it, and determine how to make sense of what the data may mean. 2) With data in hand, students can begin thinking about the validity and reliability of their experience and information collected. 3) They can consider what differences, if any, they might have if they completed the investigation again. 4) They can scrutinize outlying data points for they may be an artifact of a true difference that merits further exploration of a misstep in the procedure, measuring device, or measurement. All of these intellectual activities help them form more robust understanding and are evidence of their critical thinking.

In explore-before-explain teaching, all of these hard critical-thinking tasks come before teacher explanations of content. Whether we use discovery experiences, problem-based learning, and or inquiry-based activities, strategies that are geared toward helping students construct understanding promote critical thinking because students learn content by doing the practices valued in the field to generate knowledge.

An Issue of Equity

Meg Riordan, Ph.D., is the chief learning officer at The Possible Project, an out-of-school program that collaborates with youth to build entrepreneurial skills and mindsets and provides pathways to careers and long-term economic prosperity. She has been in the field of education for over 25 years as a middle and high school teacher, school coach, college professor, regional director of N.Y.C. Outward Bound Schools, and director of external research with EL Education:

Although critical thinking often defies straightforward definition, most in the education field agree it consists of several components: reasoning, problem-solving, and decisionmaking, plus analysis and evaluation of information, such that multiple sides of an issue can be explored. It also includes dispositions and “the willingness to apply critical-thinking principles, rather than fall back on existing unexamined beliefs, or simply believe what you’re told by authority figures.”

Despite variation in definitions, critical thinking is nonetheless promoted as an essential outcome of students’ learning—we want to see students and adults demonstrate it across all fields, professions, and in their personal lives. Yet there is simultaneously a rationing of opportunities in schools for students of color, students from under-resourced communities, and other historically marginalized groups to deeply learn and practice critical thinking.

For example, many of our most underserved students often spend class time filling out worksheets, promoting high compliance but low engagement, inquiry, critical thinking, or creation of new ideas. At a time in our world when college and careers are critical for participation in society and the global, knowledge-based economy, far too many students struggle within classrooms and schools that reinforce low-expectations and inequity.

If educators aim to prepare all students for an ever-evolving marketplace and develop skills that will be valued no matter what tomorrow’s jobs are, then we must move critical thinking to the forefront of classroom experiences. And educators must design learning to cultivate it.

So, what does that really look like?

Unpack and define critical thinking

To understand critical thinking, educators need to first unpack and define its components. What exactly are we looking for when we speak about reasoning or exploring multiple perspectives on an issue? How does problem-solving show up in English, math, science, art, or other disciplines—and how is it assessed? At Two Rivers, an EL Education school, the faculty identified five constructs of critical thinking, defined each, and created rubrics to generate a shared picture of quality for teachers and students. The rubrics were then adapted across grade levels to indicate students’ learning progressions.

At Avenues World School, critical thinking is one of the Avenues World Elements and is an enduring outcome embedded in students’ early experiences through 12th grade. For instance, a kindergarten student may be expected to “identify cause and effect in familiar contexts,” while an 8th grader should demonstrate the ability to “seek out sufficient evidence before accepting a claim as true,” “identify bias in claims and evidence,” and “reconsider strongly held points of view in light of new evidence.”

When faculty and students embrace a common vision of what critical thinking looks and sounds like and how it is assessed, educators can then explicitly design learning experiences that call for students to employ critical-thinking skills. This kind of work must occur across all schools and programs, especially those serving large numbers of students of color. As Linda Darling-Hammond asserts , “Schools that serve large numbers of students of color are least likely to offer the kind of curriculum needed to ... help students attain the [critical-thinking] skills needed in a knowledge work economy. ”

So, what can it look like to create those kinds of learning experiences?

Designing experiences for critical thinking

After defining a shared understanding of “what” critical thinking is and “how” it shows up across multiple disciplines and grade levels, it is essential to create learning experiences that impel students to cultivate, practice, and apply these skills. There are several levers that offer pathways for teachers to promote critical thinking in lessons:

1.Choose Compelling Topics: Keep it relevant

A key Common Core State Standard asks for students to “write arguments to support claims in an analysis of substantive topics or texts using valid reasoning and relevant and sufficient evidence.” That might not sound exciting or culturally relevant. But a learning experience designed for a 12th grade humanities class engaged learners in a compelling topic— policing in America —to analyze and evaluate multiple texts (including primary sources) and share the reasoning for their perspectives through discussion and writing. Students grappled with ideas and their beliefs and employed deep critical-thinking skills to develop arguments for their claims. Embedding critical-thinking skills in curriculum that students care about and connect with can ignite powerful learning experiences.

2. Make Local Connections: Keep it real

At The Possible Project , an out-of-school-time program designed to promote entrepreneurial skills and mindsets, students in a recent summer online program (modified from in-person due to COVID-19) explored the impact of COVID-19 on their communities and local BIPOC-owned businesses. They learned interviewing skills through a partnership with Everyday Boston , conducted virtual interviews with entrepreneurs, evaluated information from their interviews and local data, and examined their previously held beliefs. They created blog posts and videos to reflect on their learning and consider how their mindsets had changed as a result of the experience. In this way, we can design powerful community-based learning and invite students into productive struggle with multiple perspectives.

3. Create Authentic Projects: Keep it rigorous

At Big Picture Learning schools, students engage in internship-based learning experiences as a central part of their schooling. Their school-based adviser and internship-based mentor support them in developing real-world projects that promote deeper learning and critical-thinking skills. Such authentic experiences teach “young people to be thinkers, to be curious, to get from curiosity to creation … and it helps students design a learning experience that answers their questions, [providing an] opportunity to communicate it to a larger audience—a major indicator of postsecondary success.” Even in a remote environment, we can design projects that ask more of students than rote memorization and that spark critical thinking.

Our call to action is this: As educators, we need to make opportunities for critical thinking available not only to the affluent or those fortunate enough to be placed in advanced courses. The tools are available, let’s use them. Let’s interrogate our current curriculum and design learning experiences that engage all students in real, relevant, and rigorous experiences that require critical thinking and prepare them for promising postsecondary pathways.

Critical Thinking & Student Engagement

Dr. PJ Caposey is an award-winning educator, keynote speaker, consultant, and author of seven books who currently serves as the superintendent of schools for the award-winning Meridian CUSD 223 in northwest Illinois. You can find PJ on most social-media platforms as MCUSDSupe:

When I start my keynote on student engagement, I invite two people up on stage and give them each five paper balls to shoot at a garbage can also conveniently placed on stage. Contestant One shoots their shot, and the audience gives approval. Four out of 5 is a heckuva score. Then just before Contestant Two shoots, I blindfold them and start moving the garbage can back and forth. I usually try to ensure that they can at least make one of their shots. Nobody is successful in this unfair environment.

I thank them and send them back to their seats and then explain that this little activity was akin to student engagement. While we all know we want student engagement, we are shooting at different targets. More importantly, for teachers, it is near impossible for them to hit a target that is moving and that they cannot see.

Within the world of education and particularly as educational leaders, we have failed to simplify what student engagement looks like, and it is impossible to define or articulate what student engagement looks like if we cannot clearly articulate what critical thinking is and looks like in a classroom. Because, simply, without critical thought, there is no engagement.

The good news here is that critical thought has been defined and placed into taxonomies for decades already. This is not something new and not something that needs to be redefined. I am a Bloom’s person, but there is nothing wrong with DOK or some of the other taxonomies, either. To be precise, I am a huge fan of Daggett’s Rigor and Relevance Framework. I have used that as a core element of my practice for years, and it has shaped who I am as an instructional leader.

So, in order to explain critical thought, a teacher or a leader must familiarize themselves with these tried and true taxonomies. Easy, right? Yes, sort of. The issue is not understanding what critical thought is; it is the ability to integrate it into the classrooms. In order to do so, there are a four key steps every educator must take.

Integrating critical thought/rigor into a lesson does not happen by chance, it happens by design. Planning for critical thought and engagement is much different from planning for a traditional lesson. In order to plan for kids to think critically, you have to provide a base of knowledge and excellent prompts to allow them to explore their own thinking in order to analyze, evaluate, or synthesize information.
SIDE NOTE – Bloom’s verbs are a great way to start when writing objectives, but true planning will take you deeper than this.

QUESTIONING

If the questions and prompts given in a classroom have correct answers or if the teacher ends up answering their own questions, the lesson will lack critical thought and rigor.
Script five questions forcing higher-order thought prior to every lesson. Experienced teachers may not feel they need this, but it helps to create an effective habit.
If lessons are rigorous and assessments are not, students will do well on their assessments, and that may not be an accurate representation of the knowledge and skills they have mastered. If lessons are easy and assessments are rigorous, the exact opposite will happen. When deciding to increase critical thought, it must happen in all three phases of the game: planning, instruction, and assessment.

TALK TIME / CONTROL

To increase rigor, the teacher must DO LESS. This feels counterintuitive but is accurate. Rigorous lessons involving tons of critical thought must allow for students to work on their own, collaborate with peers, and connect their ideas. This cannot happen in a silent room except for the teacher talking. In order to increase rigor, decrease talk time and become comfortable with less control. Asking questions and giving prompts that lead to no true correct answer also means less control. This is a tough ask for some teachers. Explained differently, if you assign one assignment and get 30 very similar products, you have most likely assigned a low-rigor recipe. If you assign one assignment and get multiple varied products, then the students have had a chance to think deeply, and you have successfully integrated critical thought into your classroom.

Thanks to Dara, Patrick, Meg, and PJ for their contributions!

Please feel free to leave a comment with your reactions to the topic or directly to anything that has been said in this post.

Consider contributing a question to be answered in a future post. You can send one to me at [email protected] . When you send it in, let me know if I can use your real name if it’s selected or if you’d prefer remaining anonymous and have a pseudonym in mind.

You can also contact me on Twitter at @Larryferlazzo .

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Problem-Solving in Elementary School

Elementary students practice problem-solving and self-questioning techniques to improve reading and social and emotional learning skills.

Three elementary students reading together in a library

In a school district in New Jersey, beginning in kindergarten each child is seen as a future problem solver with creative ideas that can help the world. Vince Caputo, superintendent of the Metuchen School District, explained that what drew him to the position was “a shared value for whole child education.”

Caputo’s first hire as superintendent was Rick Cohen, who works as both the district’s K–12 director of curriculum and principal of Moss Elementary School . Cohen is committed to integrating social and emotional learning (SEL) into academic curriculum and instruction by linking cognitive processes and guided self-talk.

Cohen’s first focus was kindergarten students. “I recommended Moss teachers teach just one problem-solving process to our 6-year-olds across all academic content areas and challenge students to use the same process for social problem-solving,” he explained.

Reading and Social Problem-Solving

Moss Elementary classrooms use a specific process to develop problem-solving skills focused on tending to social and interpersonal relationships. The process also concentrates on building reading skills—specifically, decoding and comprehension.

Stop, Look, and Think. Students define the problem. As they read, they look at the pictures and text for clues, searching for information and asking, “What is important and what is not?” Social problem-solving aspect: Students look for signs of feelings in others’ faces, postures, and tone of voice.

Gather Information . Next, students explore what feelings they’re having and what feelings others may be having. As they read, they look at the beginning sound of a word and ask, “What else sounds like this?” Social problem-solving aspect: Students reflect on questions such as, “What word or words describe the feeling you see or hear in others? What word describes your feeling? How do you know, and how sure are you?”

Brainstorming . Then students seek different solutions. As they read, they wonder, “Does it sound right? Does it make sense? How else could it sound to make more sense? What other sounds do those letters make?” Social problem-solving aspect: Students reflect on questions such as, “How can you solve the problem or make the situation better? What else can you think of? What else can you try? What other ideas do you have?”

Pick the Best One. Next, students evaluate the solution. While reading, they scan for smaller words they know within larger, more difficult words. They read the difficult words the way they think they sound while asking, “Will it make sense to other people?” Social problem-solving aspect: Students reflect on prompts such as, “Pick the solution that you think will be best to solve the problem. Ask yourself, ‘What will happen if I do this—for me, and for others involved?’”

Go . In the next step, students make a plan and act. They do this by rereading the text. Social problem-solving aspect: Students are asked to try out what they will say and how they will say it. They’re asked to pick a good time to do this, when they’re willing to try it.

Check . Finally, students reflect and revise. After they have read, they ponder what exactly was challenging about what they read and, based on this, decide what to do next. Social problem-solving aspect: Students reflect on questions such as, “How did it work out? Did you solve the problem? How did others feel about what happened? What did you learn? What would you do if the same thing happened again?”

You can watch the Moss Elementary Problem Solvers video and see aspects of this process in action.

The Process of Self-Questioning

Moss Elementary students and other students in the district are also taught structured self-questioning. Cohen notes, “We realized that many of our elementary students would struggle to generalize the same steps and thinking skills they previously used to figure out an unknown word in a text or resolve social conflicts to think through complex inquiries and research projects.” The solution? Teach students how to self-question, knowing they can also apply this effective strategy across contexts. The self-questioning process students use looks like this:

Stop and Think. “What’s the question?”

Gather Information. “How do I gather information? What are different sides of the issue?”

Brainstorm and Choose. “How do I select, organize, and choose the information? What are some ways to solve the problem? What’s the best choice?”

Plan and Try. “What does the plan look like? When and how can it happen? Who needs to be involved?”

Check & Revise. “How can I present the information? What did I do well? How can I improve?”

The Benefits

Since using the problem-solving and self-questioning processes, the students at Moss Elementary have had growth in their scores for the last two years on the fifth-grade English language arts PARCC tests . However, as Cohen shares, “More important than preparing our students for the tests on state standards, there is evidence that we are also preparing them for the tests of life.”

New Designs for School 5 Steps to Teaching Students a Problem-Solving Routine

Jeff Heyck-Williams (He, His, Him) Director of the Two Rivers Learning Institute in Washington, DC

We’ve all had the experience of truly purposeful, authentic learning and know how valuable it is. Educators are taking the best of what we know about learning, student support, effective instruction, and interpersonal skill-building to completely reimagine schools so that students experience that kind of purposeful learning all day, every day.

Students can use the 5 steps in this simple routine to solve problems across the curriculum and throughout their lives.

When I visited a fifth-grade class recently, the students were tackling the following problem:

If there are nine people in a room and every person shakes hands exactly once with each of the other people, how many handshakes will there be? How can you prove your answer is correct using a model or numerical explanation?

There were students on the rug modeling people with Unifix cubes. There were kids at one table vigorously shaking each other’s hand. There were kids at another table writing out a diagram with numbers. At yet another table, students were working on creating a numeric expression. What was common across this class was that all of the students were productively grappling around the problem.

On a different day, I was out at recess with a group of kindergarteners who got into an argument over a vigorous game of tag. Several kids were arguing about who should be “it.” Many of them insisted that they hadn’t been tagged. They all agreed that they had a problem. With the assistance of the teacher they walked through a process of identifying what they knew about the problem and how best to solve it. They grappled with this very real problem to come to a solution that all could agree upon.

Then just last week, I had the pleasure of watching a culminating showcase of learning for our 8th graders. They presented to their families about their project exploring the role that genetics plays in our society. Tackling the problem of how we should or should not regulate gene research and editing in the human population, students explored both the history and scientific concerns about genetics and the ethics of gene editing. Each student developed arguments about how we as a country should proceed in the burgeoning field of human genetics which they took to Capitol Hill to share with legislators. Through the process students read complex text to build their knowledge, identified the underlying issues and questions, and developed unique solutions to this very real problem.

Problem-solving is at the heart of each of these scenarios, and an essential set of skills our students need to develop. They need the abilities to think critically and solve challenging problems without a roadmap to solutions. At Two Rivers Public Charter School in Washington, D.C., we have found that one of the most powerful ways to build these skills in students is through the use of a common set of steps for problem-solving. These steps, when used regularly, become a flexible cognitive routine for students to apply to problems across the curriculum and their lives.

The Problem-Solving Routine

At Two Rivers, we use a fairly simple routine for problem solving that has five basic steps. The power of this structure is that it becomes a routine that students are able to use regularly across multiple contexts. The first three steps are implemented before problem-solving. Students use one step during problem-solving. Finally, they finish with a reflective step after problem-solving.

Problem Solving from Two Rivers Public Charter School

Before Problem-Solving: The KWI

The three steps before problem solving: we call them the K-W-I.

The “K” stands for “know” and requires students to identify what they already know about a problem. The goal in this step of the routine is two-fold. First, the student needs to analyze the problem and identify what is happening within the context of the problem. For example, in the math problem above students identify that they know there are nine people and each person must shake hands with each other person. Second, the student needs to activate their background knowledge about that context or other similar problems. In the case of the handshake problem, students may recognize that this seems like a situation in which they will need to add or multiply.

The “W” stands for “what” a student needs to find out to solve the problem. At this point in the routine the student always must identify the core question that is being asked in a problem or task. However, it may also include other questions that help a student access and understand a problem more deeply. For example, in addition to identifying that they need to determine how many handshakes in the math problem, students may also identify that they need to determine how many handshakes each individual person has or how to organize their work to make sure that they count the handshakes correctly.

The “I” stands for “ideas” and refers to ideas that a student brings to the table to solve a problem effectively. In this portion of the routine, students list the strategies that they will use to solve a problem. In the example from the math class, this step involved all of the different ways that students tackled the problem from Unifix cubes to creating mathematical expressions.

This KWI routine before problem solving sets students up to actively engage in solving problems by ensuring they understand the problem and have some ideas about where to start in solving the problem. Two remaining steps are equally important during and after problem solving.

The power of teaching students to use this routine is that they develop a habit of mind to analyze and tackle problems wherever they find them.

During Problem-Solving: The Metacognitive Moment

The step that occurs during problem solving is a metacognitive moment. We ask students to deliberately pause in their problem-solving and answer the following questions: “Is the path I’m on to solve the problem working?” and “What might I do to either stay on a productive path or readjust my approach to get on a productive path?” At this point in the process, students may hear from other students that have had a breakthrough or they may go back to their KWI to determine if they need to reconsider what they know about the problem. By naming explicitly to students that part of problem-solving is monitoring our thinking and process, we help them become more thoughtful problem solvers.

After Problem-Solving: Evaluating Solutions

As a final step, after students solve the problem, they evaluate both their solutions and the process that they used to arrive at those solutions. They look back to determine if their solution accurately solved the problem, and when time permits they also consider if their path to a solution was efficient and how it compares to other students’ solutions.

The power of teaching students to use this routine is that they develop a habit of mind to analyze and tackle problems wherever they find them. This empowers students to be the problem solvers that we know they can become.

Jeff Heyck-Williams (He, His, Him)

Director of the two rivers learning institute.

Jeff Heyck-Williams is the director of the Two Rivers Learning Institute and a founder of Two Rivers Public Charter School. He has led work around creating school-wide cultures of mathematics, developing assessments of critical thinking and problem-solving, and supporting project-based learning.

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Developing Problem-Solving Skills for Kids | Strategies & Tips

We've made teaching problem-solving skills for kids a whole lot easier! Keep reading and comment below with any other tips you have for your classroom!

Problem-Solving Skills for Kids: The Real Deal

Picture this: You've carefully created an assignment for your class. The step-by-step instructions are crystal clear. During class time, you walk through all the directions, and the response is awesome. Your students are ready! It's finally time for them to start working individually and then... 8 hands shoot up with questions. You hear one student mumble in the distance, "Wait, I don't get this" followed by the dreaded, "What are we supposed to be doing again?"

When I was a new computer science teacher, I would have this exact situation happen. As a result, I would end up scrambling to help each individual student with their problems until half the class period was eaten up. I assumed that in order for my students to learn best, I needed to be there to help answer questions immediately so they could move forward and complete the assignment.

Here's what I wish I had known when I started teaching coding to elementary students - the process of grappling with an assignment's content can be more important than completing the assignment's product. That said, not every student knows how to grapple, or struggle, in order to get to the "aha!" moment and solve a problem independently. The good news is, the ability to creatively solve problems is not a fixed skill. It can be learned by students, nurtured by teachers, and practiced by everyone!

Your students are absolutely capable of navigating and solving problems on their own. Here are some strategies, tips, and resources that can help:

Problem-Solving Skills for Kids: Student Strategies

These are strategies your students can use during independent work time to become creative problem solvers.

1. Go Step-By-Step Through The Problem-Solving Sequence

Post problem-solving anchor charts and references on your classroom wall or pin them to your Google Classroom - anything to make them accessible to students. When they ask for help, invite them to reference the charts first.

Problem-solving skills for kids made easy using the problem solving sequence.

2. Revisit Past Problems

If a student gets stuck, they should ask themself, "Have I ever seen a problem like this before? If so, how did I solve it?" Chances are, your students have tackled something similar already and can recycle the same strategies they used before to solve the problem this time around.

3. Document What Doesn’t Work

Sometimes finding the answer to a problem requires the process of elimination. Have your students attempt to solve a problem at least two different ways before reaching out to you for help. Even better, encourage them write down their "Not-The-Answers" so you can see their thought process when you do step in to support. Cool thing is, you likely won't need to! By attempting to solve a problem in multiple different ways, students will often come across the answer on their own.

4. "3 Before Me"

Let's say your students have gone through the Problem Solving Process, revisited past problems, and documented what doesn't work. Now, they know it's time to ask someone for help. Great! But before you jump into save the day, practice "3 Before Me". This means students need to ask 3 other classmates their question before asking the teacher. By doing this, students practice helpful 21st century skills like collaboration and communication, and can usually find the info they're looking for on the way.

Problem-Solving Skills for Kids: Teacher Tips

These are tips that you, the teacher, can use to support students in developing creative problem-solving skills for kids.

1. Ask Open Ended Questions

When a student asks for help, it can be tempting to give them the answer they're looking for so you can both move on. But what this actually does is prevent the student from developing the skills needed to solve the problem on their own. Instead of giving answers, try using open-ended questions and prompts. Here are some examples:

2. Encourage Grappling

Grappling is everything a student might do when faced with a problem that does not have a clear solution. As explained in this article from Edutopia , this doesn't just mean perseverance! Grappling is more than that - it includes critical thinking, asking questions, observing evidence, asking more questions, forming hypotheses, and constructing a deep understanding of an issue.

There are lots of ways to provide opportunities for grappling. Anything that includes the Engineering Design Process is a good one! Examples include:

Engineering or Art Projects
Design-thinking challenges
Computer science projects
Science experiments

3. Emphasize Process Over Product

For elementary students, reflecting on the process of solving a problem helps them develop a growth mindset . Getting an answer "wrong" doesn't need to be a bad thing! What matters most are the steps they took to get there and how they might change their approach next time. As a teacher, you can support students in learning this reflection process.

4. Model The Strategies Yourself!

As creative problem-solving skills for kids are being learned, there will likely be moments where they are frustrated or unsure. Here are some easy ways you can model what creative problem-solving looks and sounds like.

Ask clarifying questions if you don't understand something
Admit when don't know the correct answer
Talk through multiple possible outcomes for different situations
Verbalize how you’re feeling when you find a problem

Practicing these strategies with your students will help create a learning environment where grappling, failing, and growing is celebrated!

Problem-Solving Skill for Kids

Did we miss any of your favorites? Comment and share them below!

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I Can Problem Solve

Get info and pricing on the provider’s website.

I Can Problem Solve provides a lesson-based approach to SEL. It includes programming for grades PreK-5 and demonstrates evidence of effectiveness at grade 1. Translated materials for the preschool & kindergarten levels as well as the parent program are available in Spanish.

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Evidence of effectiveness

Results from a randomized control trial (RCT) conducted in the 1997-1998 school year (published in 2002) supported the effectiveness of I Can Problem Solve for early elementary school students. This evaluation included 578 grade 1 students enrolled in multiple rural schools in the US West region (87% white; sample was largely middle class). Students who participated in the program had greater growth in teacher-reported self-regulation (i.e., decreases in impulsivity, hyperactivity, aggressive, disruptive behaviors) and in student-reported school bonding (i.e., engagement and student-teacher relationship quality) compared to students in the control group (9 months after baseline, analyses controlled for outcome pretest).

Not Specified
Improved academic performance
Reduced emotional distress
Improved identity development and agency
Reduced problem behaviors
Improved school climate
Improved school connectedness
Improved social behaviors
Improved teaching practices
Improved other SEL skills and attitudes

How does I Can Problem Solve support SEL implementation across multiple settings?

“The I Can Problem Solve (ICPS) program teaches students to recognize that when there is a problem, there is a process they can call upon to solve it. With support materials across settings, the ICPS problem solving approach creates consistent communication between adults and youth by engaging students as active participants, not passive recipients. ”

Accepted by CASEL

Kumpfer, K. L., Alvarado, R., Tait, C., & Turner, C. (2002). Effectiveness of school-based family and children’s skills training for substance abuse prevention among 6-8-year-old rural children. Psychology of Addictive Behaviors, 16 (4S), S65-S71.

Other references

Boyle, D., & Hassett-Walker, C. (2008). Reducing Overt and Relational Aggression Among Young Children: The Results from a Two-Year Outcome Study. Journal of School Violence, 7 (1), 27-42.

Feis, C. L., & Simons, C. (1985). Training Preschool Children in Interpersonal Cognitive Problem-Solving Skills: A Replication. Prevention in Human Services, 3 (4), 59-70.

Gaete, J., Nejaz, L., Otegui, M., & Perry, R. (2019). Mental Health Prevention in Preschool Children: study protocol for a feasibility and acceptability randomised controlled trial of a culturally adapted version of I Can Problem Solve (ICPS) program in Chile. Poster presented at the annual meeting of the Society for Prevention Research, San Francisco, CA. Trials, 20, 158.

Shure, M. B., & Spivack, G. (1982). Interpersonal problem-solving in young children: A cognitive approach to prevention. American Journal of Community Psychology, 10 (3), 341-356.

Shure, M. B., & Spivack, G. (1980). Interpersonal problem solving as a mediator of behavioral adjustment in preschool and kindergarten children. Journal of Applied Developmental Psychology, 1 (1), 29-44.

Shure, M. B., & Spivack, G. (1979). Interpersonal cognitive problem solving and primary prevention: Programming for preschool and kindergarten children. Journal of Clinical Child Psychology, 8 (2), 89-94.

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Strategies to develop problem-solving skills in students.

November 14, 2023

OWIS Nanyang | Secondary Students in Maths Lesson | Problem-Solving Skills | International School in Singapore

Students need the freedom to brainstorm, develop solutions and make mistakes — this is truly the only way to prepare them for life outside the classroom. When students are immersed in a learning environment that only offers them step-by-step guides and encourages them to focus solely on memorisation, they are not gaining the skills necessary to help them navigate in the complex, interconnected environment of the real world.

Choosing a school that emphasises the importance of future-focussed skills will ensure your child has the abilities they need to survive and thrive anywhere in the world. What are future-focussed skills? Students who are prepared for the future need to possess highly developed communication skills, self-management skills, research skills, thinking skills, social skills and problem-solving skills. In this blog, I would like to focus on problem-solving skills.

What Are Problem-Solving Skills?

The Forage defines problem-solving skills as those that allow an individual to identify a problem, come up with solutions, analyse the options and collaborate to find the best solution for the issue.

Importance of Problem-Solving in the Classroom Setting

Learning how to solve problems effectively and positively is a crucial part of child development. When children are allowed to solve problems in a classroom setting, they can test those skills in a safe and nurturing environment. Generally, when they face age-appropriate issues, they can begin building those skills in a healthy and positive manner.

Without exposure to challenging situations and scenarios, children will not be equipped with the foundational problem-solving skills needed to tackle complex issues in the real world. Experts predict that problem-solving skills will eventually be more sought after in job applicants than hard skills related to that specific profession. Students must be given opportunities in school to resolve conflicts, address complex problems and come up with their own solutions in order to develop these skills.

Benefits of Problem-Solving Skills for Students

Learning how to solve problems offers students many advantages, such as:

Improving Academic Results

When students have a well-developed set of problem-solving skills, they are often better critical and analytical thinkers as well. They are able to effectively use these 21st-century skills when completing their coursework, allowing them to become more successful in all academic areas. By prioritising problem-solving strategies in the classroom, teachers often find that academic performance improves.

Developing Confidence

Giving students the freedom to solve problems and create their own solutions is essentially permitting them to make their own choices. This sense of independence — and the natural resilience that comes with it — allows students to become confident learners who aren’t intimidated by new or challenging situations. Ultimately, this prepares them to take on more complex challenges in the future, both on a professional and social level.

Preparing Students for Real-World Challenges

The challenges we are facing today are only growing more complex, and by the time students have graduated, they are going to be facing issues that we may not even have imagined. By arming them with real-world problem-solving experience, they will not feel intimidated or stifled by those challenges; they will be excited and ready to address them. They will know how to discuss their ideas with others, respect various perspectives and collaborate to develop a solution that best benefits everyone involved.

The Best Problem-Solving Strategies for Students

No single approach or strategy will instil a set of problem-solving skills in students. Every child is different, so educators should rely on a variety of strategies to develop this core competency in their students. It is best if these skills are developed naturally.

These are some of the best strategies to support students problem-solving skills:

Project-Based Learning

By providing students with project-based learning experiences and allowing plenty of time for discussion, educators can watch students put their problem-solving skills into action inside their classrooms. This strategy is one of the most effective ways to fine-tune problem-solving skills in students. During project-based learning, teachers may take notes on how the students approach a problem and then offer feedback to students for future development. Teachers can address their observations of interactions during project-based learning at the group level or they can work with students on an individual basis to help them become more effective problem-solvers.

Encourage Discussion and Collaboration in the Classroom Setting

Another strategy to encourage the development of problem-solving skills in students is to allow for plenty of discussion and collaboration in the classroom setting. When students interact with one another, they are naturally developing problem solving skills. Rather than the teacher delivering information and requiring the students to passively receive information, students can share thoughts and ideas with one another. Getting students to generate their own discussion and communication requires thinking skills.

Utilising an Inquiry-Based approach to Learning

Students should be presented with situations in which their curiosity is sparked and they are motivated to inquire further. Teachers should ask open-ended questions and encourage students to develop responses which require problem-solving. By providing students with complex questions for which a variety of answers may be correct, teachers get students to consider different perspectives and deal with potential disagreement, which requires problem-solving skills to resolve.

Model Appropriate Problem-Solving Skills

One of the simplest ways to instil effective problem-solving skills in students is to model appropriate and respectful strategies and behaviour when resolving a conflict or addressing an issue. Teachers can showcase their problem-solving skills by:

Identifying a problem when they come across one for the class to see
Brainstorming possible solutions with students
Collaborating with students to decide on the best solution
Testing that solution and examining the results with the students
Adapting as necessary to improve results or achieve the desired goal

Prioritise Student Agency in Learning

Recent research shows that self-directed learning is one of the most effective ways to nurture 21st-century competency development in young learners. Learning experiences that encourage student agency often require problem-solving skills. When creativity and innovation are needed, students often encounter unexpected problems along the way that must be solved. Through self-directed learning, students experience challenges in a natural situation and can fine-tune their problem-solving skills along the way. Self-directed learning provides them with a foundation in problem-solving that they can build upon in the future, allowing them to eventually develop more advanced and impactful problem-solving skills for real life.

21st-Century Skill Development at OWIS Singapore

Problem-solving has been identified as one of the core competencies that young learners must develop to be prepared to meet the dynamic needs of a global environment. At OWIS Singapore, we have implemented an inquiry-driven, skills-based curriculum that allows students to organically develop critical future-ready skills — including problem-solving. Our hands-on approach to education enables students to collaborate, explore, innovate, face-challenges, make mistakes and adapt as necessary. As such, they learn problem-solving skills in an authentic manner.

For more information about 21st-century skill development, schedule a campus tour today.

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65+ Real-World Project-Based Learning Ideas for All Ages and Interests

Find and implement solutions to real-world problems.

Collage of project based learning ideas, including a school garden and volunteering with seniors

Project-based learning is a hot topic in many schools these days, as educators work to make learning more meaningful for students. As students conduct hands-on projects addressing real-world issues, they dig deeper and make personal connections to the knowledge and skills they’re gaining. But not just any project fits into this concept. Learn more about strong project-based learning ideas, and find examples for any age or passion.

What is project-based learning?

Project-based learning (PBL) uses real-world projects and student-directed activities to build knowledge and skills. Kids choose a real-world topic that’s meaningful to them (some people call these “passion projects”), so they’re engaged in the process from the beginning. These projects are long-term, taking weeks, months, or even a full semester or school year. Students may complete them independently or working in small groups. Learn much more about project-based learning here.

What makes a good PBL project?

Chart showing the difference between traditional projects and project based learning

In many ways, PBL is more like the work adults do in their daily jobs, especially because student efforts have potential real-world effects. A strong PBL project:

Addresses a real-world issue or problem
Requires sustained and independent inquiry, in and out of the classroom
Allows students voice and choice throughout the project
Combines elements of many disciplines
Includes collaboration with public partners, such as universities, community organizations, or businesses
Produces a public product that is seen by those outside the school community
Covers a complete process, including activities like research, design, production, marketing or public awareness, and enlisting supporters or investors

Outdoor Project-Based Learning Ideas

Children holding produce standing in a garden they've grown themselves

Create a new local park, or improve an existing one by adding new features or providing needed maintenance.
Plant a community garden to provide food for a soup kitchen, food pantry, or other organization.
Design and create a butterfly, pollinator, or other wildlife garden to support the local ecosystem.
Build a new walking or biking trail that’s safe for people of all ages to use.
Devise and implement a way to reduce litter in your community.
Set up and manage a school or community compost pile, and distribute the resulting soil to those who need it most.
Find and help the public use a new way to grow food that requires less soil, water, or fertilizers, which are in short supply in some parts of the world.
Design, build, and install a completely unique piece of playground equipment that serves a specific purpose or need.

School Community Project-Based Learning Ideas

Students and adults reading student-produced newspaper (Project Based Learning Ideas)

Start a comprehensive recycling program at school, or substantially improve participation in an existing one.
Add collaborative artwork like murals or other displays to school hallways, bathrooms, or grounds.
Determine a location or program at your school that needs improvement, then make a plan, raise the funds, and implement your ideas.
Come up with ways to celebrate your school’s diversity and improve relationships between all students.
Start and run a school store , including inventory, financial plans, and marketing.
Write a school handbook for new students, with tips and tricks for helping them feel at home.
Figure out how to offer healthier, better-tasting meals and snacks in the school cafeteria.
Implement a mentoring program for older students to help younger students, with planned activities and appropriate training for older students.
Design and propose a new style of grading system that ensures equity.
Find ways to improve the indoor recess experience at your school.
Set up and run a new school newspaper, magazine, podcast, video channel, etc.

Greater Community Project-Based Learning Ideas

Children and senior citizens working on an art project together

Coordinate a community art project in a central location to celebrate local culture or artists.
Set up a program for schoolkids to socialize with senior citizens in nursing homes, hospitals, or retirement communities.
Create a program to offer free translation services for ESL families in the community.
Help a local animal shelter improve its facilities, or find new ways to match homeless pets with their forever families.
Build and maintain Little Free Libraries around your community, especially in underserved areas.
Help local businesses become more environmentally conscious, increasing sustainability and decreasing waste.
Create and lead a walking tour of your community, highlighting its culture, history, landmarks, and more.
Find a way to record and celebrate local voices in your community’s history.
Come up with ideas for welcoming immigrants and other newcomers to your community.
Set up a series of events that will encourage the community to mix and experience each others’ foods, cultures, and more.
Create and implement a new program to inspire a love of books and reading in preschool students.
Set up and help run a new charitable organization your community needs.

Social Issues Project-Based Learning Ideas

Poster with question: "How can we as students create a space where people feel like they belong and are safe in order to impact students at Asbury?"

Start an awareness campaign on a topic that’s important to you, like anti-bullying, healthy living, protecting the environment, civil rights, equality and equity, etc.
Come up with and implement ways to increase voter turnout in your community, especially among younger voters.
Write, record, and share with a wider audience your own TED Talk–style video on an issue that hasn’t been covered yet or on which you have a unique perspective.
Devise and implement ways for unheard voices to be amplified in your school or community.
Write and publicly perform a play that highlights a social issue that’s important to you.
Look for areas in your community that present challenges to those with disabilities, and help to improve them to overcome those challenges.
Research, write, and publicly present and defend a position paper on an issue that’s important to your community.
Choose a real court case, then research the law and work with legal experts to prepare and present your own case as you would in a courtroom.
Write, edit, seek, and incorporate real-world feedback, and publish or publicly present your own book, poem, or song on an issue that’s important to you.
Start a program to teach a specific group (e.g., preschoolers, senior citizens, business owners) to care for and protect the environment.
Plan and hold a fundraiser to support an issue you care about.
Choose a law you feel is unjust, and write, research, and publicly present and defend a position paper about your desired change.

STEM Project-Based Learning Ideas

Two students holding a large model rocket built as part of project based learning

Create an app that meets a specific purpose for a specific audience.
Invent something new that the world needs, and then fund, create, and sell your product in the community.
Design a game to help students learn important STEM concepts.
Find a simple way to improve an existing product, especially if it cuts costs or improves environmental sustainability.
Explore ways to reduce the amount of waste we produce, especially plastic and other landfill-bound items.
Write a book or graphic novel that’s entertaining but also teaches kids about science or math.
Devise new ways to provide clean drinking water to communities where water is scarce.
Build an effective solar oven people can use to cook during extended power outages, or in areas where electricity isn’t available.
Work with a university or STEM organization to gather, analyze, and present real-world scientific data.
Design a building to fit a specific purpose or need, including researching the requirements and zoning laws, accurately drafting a plan, determining the costs, and presenting the plan to the proposed client.
Create an interactive hands-on exhibit to teach people about STEM concepts.
Determine a type of website you believe is missing, then research, build, and publish the site you envision.

Creative Arts Project-Based Learning Ideas

Student and parent standing by artwork at an art show

Organize an art show for the community, seeking out those who ordinarily might not have a chance to display their work.
Create and teach an art class in your area of expertise to children, the elderly, or another segment of the population.
Design a mural for an area in your community that needs beautification, and seek funding or other assistance from community members to install it.
Write a play about a topic that’s meaningful to you or your community. Work with the community to stage a performance for all to attend.
Invite local dancers to perform at a school or community Festival of Dance, highlighting a variety of cultures and dance styles.
Start a regular writer’s workshop where community writers can come together to share and seek feedback. Invite local authors or publishing experts to speak as guests.
Collect stories, poems, and essays from local authors, and put them together into a book. Sell the book to raise money for a cause that’s important to local writers.
Gather singers or instrumentalists from your community into a choir or band. Put on a concert to raise money for a special cause, or take your choir on tour to local retirement homes, hospitals, etc.
Write a song about a person or cause that’s important to you. Produce and record the song, then find a way to share it with others.
Make a short film about a local hero, community event, or local place. Invite others to do the same, and organize a local film festival.

What are some your favorite project-based learning ideas? Come share your thoughts in the We Are Teachers HELPLINE group on Facebook !

Plus, meaningful service learning projects for kids and teens ..

These project-based learning ideas are real-world applicable and student-directed, requiring outside collaboration and public results.

What is Project Based Learning? #buzzwordsexplained

What Is Project-Based Learning and How Can I Use It With My Students?

There's a difference between regular projects and true-project based learning. Continue Reading

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As our world and educators are confronted with a range of unprecedented challenges, Future Problem Solving helps students keep pace. Our standard-based and skill-based programs meaningfully engage young people in all the places and spaces they learn. With Future Problem Solving, students learn how to think, not what to think, and gain lifelong learning skills.

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Future Problem Solving Students – A Five Year Study

A comparison of reading and mathematics performance between students participating in a future problem solving program and nonparticipants.

Data from the The Minnesota Comprehensive Assessment (MCA) was collected by Grandview Middle School and provided to Scholastic Testing Service, Inc. for statistical analysis.

Findings reported by Scholastic Testing Service, Inc. Performance data on the MCA was collected from 2010-2014 for students in grade 6 at Grandview Middle School in Mound, MN (Westonka Public School District). Students were identified as either FPS: students participating in a Future Problem Solving program, or Non-FPS: students not participating in the program. Summary statistics using Reading and Mathematics Scaled Scores were developed for each group of students by year and across years. To determine if the mean scores across the years were significantly different, t-tests were used. A Cohen’s d test was then performed to measure the effect of the size of the found differences.

In all cases, students participating in the Future Problem Solving Program performed significantly higher on the MCA in both areas of Mathematics and Reading.

Effects of Group Training in Problem-Solving Style on Future Problem-Solving Performance

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Seventy-five participants from one suburban high school formed 21 teams with 3–4 members each for Future Problem Solving (FPS). Students were selected to participate in either the regular FPS or an enhanced FPS, where multiple group training activities grounded in problem-solving style were incorporated into a 9-week treatment period.

An ANCOVA procedure was used to examine the difference in team responses to a creative problem-solving scenario for members of each group, after accounting for initial differences in creative problem-solving performance, years of experience in FPS, and creative thinking related to fluency, flexibility, and originality. The ANCOVA resulted in a significant difference in problem-solving performance in favor of students in the treatment group (F(1, 57) = 8.21, p = .006, partial eta squared = .126, medium), while there were no significant differences in years of experience or creativity scores. This result led researchers to conclude that students in both groups had equivalent creative ability and that participation in the group activities emphasizing problem-solving style significantly contributed to creative performance.

In the comparison group, a total of 47% had scores that qualified for entry to the state competition. In contrast, 89% of the students in the treatment group had scores that qualified them for the state bowl. None of the teams from the comparison group qualified for the international competition, while two teams from the treatment group were selected, with one earning sixth place.

The results of this study suggest that problem-solving performance by team members can be improved through direct instruction in problem-solving style, particularly when there is a focus on group dynamics.

Future Problem Solving Program International—Second Generation Study

“how important was future problem solving in the development of your following skill sets”.

In 2011, a team of researchers from the University of Virginia submitted a report titled “Future Problem Solving Program International—Second Generation Study.” (Callahan, Alimin, & Uguz, 2012). The study, based on a survey, collected data from over 150 Future Problem Solving alumni to understand the impact of their participation in Future Problem Solving as students or volunteers.

Percentage of Alumni Rating Important and Extremely Important in Developing Skill Sets

96% Look at the “Big Picture”
93% Critical Thinking
93% Teamwork and Collaboration
93% Identify and Solve Problems
93% Time Management
90% Researching
90% Evaluation and Decision Making
86% Creativity and Innovation
86% Written Communication

The report captured alumni’s positive experiences as students in Future Problem Solving and documented that the alumni continued to utilize the FPS-structured approach to solving problems in their adult lives.

Executive Director

A seasoned educator, April Michele has served as the Executive Director since 2018 and been with Future Problem Solving more than a decade. Her background in advanced curriculum strategies and highly engaging learning techniques translates well in the development of materials, publications, training, and marketing for the organization and its global network. April’s expertise includes pedagogy and strategies for critical and creative thinking and providing quality educational services for students and adults worldwide.

Prior to joining Future Problem Solving, April taught elementary and middle grades, spending most of her classroom career in gifted education. She earned the National Board certification (NBPTS) as a Middle Childhood/Generalist and later served as a National Board assessor for the certification of others. In addition, April facilitated the Theory and Development of Creativity course for the state of Florida’s certification of teachers. She has also collaborated on a variety of special projects through the Department of Education. Beyond her U.S. education credentials, she has been trained for the International Baccalaureate Middle Years Programme (MYP) in Humanities.

A graduate of the University of Central Florida with a bachelor’s in Elementary Education and the University of South Florida with a master’s in Gifted Education, April’s passion is providing a challenging curriculum for 21st century students so they are equipped with the problem-solving and ethical leadership skills they need to thrive in the future. As a board member in her local Rotary Club, she facilitates problem solving in leadership at the Rotary Youth Leadership Awards (RYLA). She is also a certified Project Management Professional (PMP) from the Project Management Institute and earned her certificate in Nonprofit Management from the Edyth Bush Institute at Rollins College.

Explained: Importance of critical thinking, problem-solving skills in curriculum

F uture careers are no longer about domain expertise or technical skills. Rather, critical thinking and problem-solving skills in employees are on the wish list of every big organization today. Even curriculums and pedagogies across the globe and within India are now requiring skilled workers who are able to think critically and are analytical.

The reason for this shift in perspective is very simple.

These skills provide a staunch foundation for comprehensive learning that extends beyond books or the four walls of the classroom. In a nutshell, critical thinking and problem-solving skills are a part of '21st Century Skills' that can help unlock valuable learning for life.

Over the years, the education system has been moving away from the system of rote and other conventional teaching and learning parameters.

They are aligning their curriculums to the changing scenario which is becoming more tech-driven and demands a fusion of critical skills, life skills, values, and domain expertise. There's no set formula for success.

Rather, there's a defined need for humans to be more creative, innovative, adaptive, agile, risk-taking, and have a problem-solving mindset.

In today's scenario, critical thinking and problem-solving skills have become more important because they open the human mind to multiple possibilities, solutions, and a mindset that is interdisciplinary in nature.

Therefore, many schools and educational institutions are deploying AI and immersive learning experiences via gaming, and AR-VR technologies to give a more realistic and hands-on learning experience to their students that hone these abilities and help them overcome any doubt or fear.

ADVANTAGES OF CRITICAL THINKING AND PROBLEM-SOLVING IN CURRICULUM

Ability to relate to the real world: Instead of theoretical knowledge, critical thinking, and problem-solving skills encourage students to look at their immediate and extended environment through a spirit of questioning, curiosity, and learning. When the curriculum presents students with real-world problems, the learning is immense.

Confidence, agility & collaboration : Critical thinking and problem-solving skills boost self-belief and confidence as students examine, re-examine, and sometimes fail or succeed while attempting to do something.

They are able to understand where they may have gone wrong, attempt new approaches, ask their peers for feedback and even seek their opinion, work together as a team, and learn to face any challenge by responding to it.

Willingness to try new things: When problem-solving skills and critical thinking are encouraged by teachers, they set a robust foundation for young learners to experiment, think out of the box, and be more innovative and creative besides looking for new ways to upskill.

It's important to understand that merely introducing these skills into the curriculum is not enough. Schools and educational institutions must have upskilling workshops and conduct special training for teachers so as to ensure that they are skilled and familiarized with new teaching and learning techniques and new-age concepts that can be used in the classrooms via assignments and projects.

Critical thinking and problem-solving skills are two of the most sought-after skills. Hence, schools should emphasise the upskilling of students as a part of the academic curriculum.

The article is authored by Dr Tassos Anastasiades, Principal- IB, Genesis Global School, Noida.

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Explained: Importance of critical thinking, problem-solving skills in curriculum

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Google Circle to Search can now solve maths problems for students: Here's how the feature works

Google's circle to search focuses on educational support by aiding students in understanding problem-solving techniques, with plans to expand to more complex equations using ai model learnlm..

Tech giant Google has unveiled a significant update to its Circle to Search feature during the annual developer conference, Google I/O. This enhancement aims to empower students by providing assistance with math and physics problems directly from their Android smartphones or tablets.

The revamped Circle to Search now offers a specialized tool tailored to guide students through solving homework problems in mathematics and physics. Unlike merely providing answers, Google emphasizes that the feature is designed to foster a deeper understanding of problem-solving techniques, aiding students in learning how to tackle challenges independently.

Through Circle to Search, students can activate AI-driven assistance for mathematical word problems, which systematically breaks down the problem and provides step-by-step instructions for finding the correct solution. Google underscores that the feature is intended as a supportive educational tool, rather than a shortcut for completing assignments.

This announcement comes amidst ongoing discussions surrounding the integration of AI tools in education, with concerns raised about potential misuse by students seeking to expedite their homework. Google addresses these concerns by positioning Circle to Search as a resource focused on facilitating learning and skill development.

Looking ahead, Google revealed plans to further expand the capabilities of Circle to Search. Soon, the functionality will be upgraded to tackle more intricate mathematical equations, encompassing symbolic formulas, diagrams, and graphs, suggests the American company.

Google will utilize LearnLM , its most recent AI model optimized explicitly for educational tasks, to drive these advanced capabilities.

In a blog post announcing the update, Google stated, "Starting today, Circle to Search can now help students with homework, giving them a deeper understanding, not just an answer — directly from their phones and tablets. When students circle a prompt they’re stuck on, they’ll get step-by-step instructions to solve a range of physics and math word problems without leaving their digital info sheet or syllabus. Later this year, Circle to Search will be able to help solve even more complex problems involving symbolic formulas, diagrams, graphs, and more. This is all possible due to our LearnLM effort to enhance our models and products for learning."

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Open access
Published: 11 May 2024

Nursing students’ stressors and coping strategies during their first clinical training: a qualitative study in the United Arab Emirates

Jacqueline Maria Dias 1 ,
Muhammad Arsyad Subu 1 ,
Nabeel Al-Yateem 1 ,
Fatma Refaat Ahmed 1 ,
Syed Azizur Rahman 1 , 2 ,
Mini Sara Abraham 1 ,
Sareh Mirza Forootan 1 ,
Farzaneh Ahmad Sarkhosh 1 &
Fatemeh Javanbakh 1

BMC Nursing volume 23 , Article number: 322 ( 2024 ) Cite this article

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Metrics details

Understanding the stressors and coping strategies of nursing students in their first clinical training is important for improving student performance, helping students develop a professional identity and problem-solving skills, and improving the clinical teaching aspects of the curriculum in nursing programmes. While previous research have examined nurses’ sources of stress and coping styles in the Arab region, there is limited understanding of these stressors and coping strategies of nursing students within the UAE context thereby, highlighting the novelty and significance of the study.

A qualitative study was conducted using semi-structured interviews. Overall 30 students who were undergoing their first clinical placement in Year 2 at the University of Sharjah between May and June 2022 were recruited. All interviews were recorded and transcribed verbatim and analyzed for themes.

During their first clinical training, nursing students are exposed to stress from different sources, including the clinical environment, unfriendly clinical tutors, feelings of disconnection, multiple expectations of clinical staff and patients, and gaps between the curriculum of theory classes and labatories skills and students’ clinical experiences. We extracted three main themes that described students’ stress and use of coping strategies during clinical training: (1) managing expectations; (2) theory-practice gap; and (3) learning to cope. Learning to cope, included two subthemes: positive coping strategies and negative coping strategies.

Conclusions

This qualitative study sheds light from the students viewpoint about the intricate interplay between managing expectations, theory practice gap and learning to cope. Therefore, it is imperative for nursing faculty, clinical agencies and curriculum planners to ensure maximum learning in the clinical by recognizing the significance of the stressors encountered and help students develop positive coping strategies to manage the clinical stressors encountered. Further research is required look at the perspective of clinical stressors from clinical tutors who supervise students during their first clinical practicum.

Peer Review reports

Nursing education programmes aim to provide students with high-quality clinical learning experiences to ensure that nurses can provide safe, direct care to patients [ 1 ]. The nursing baccalaureate programme at the University of Sharjah is a four year program with 137 credits. The programmes has both theoretical and clinical components withs nine clinical courses spread over the four years The first clinical practicum which forms the basis of the study takes place in year 2 semester 2.

Clinical practice experience is an indispensable component of nursing education and links what students learn in the classroom and in skills laboratories to real-life clinical settings [ 2 , 3 , 4 ]. However, a gap exists between theory and practice as the curriculum in the classroom differs from nursing students’ experiences in the clinical nursing practicum [ 5 ]. Clinical nursing training places (or practicums, as they are commonly referred to), provide students with the necessary experiences to ensure that they become proficient in the delivery of patient care [ 6 ]. The clinical practicum takes place in an environment that combines numerous structural, psychological, emotional and organizational elements that influence student learning [ 7 ] and may affect the development of professional nursing competencies, such as compassion, communication and professional identity [ 8 ]. While clinical training is a major component of nursing education curricula, stress related to clinical training is common among students [ 9 ]. Furthermore, the nursing literature indicates that the first exposure to clinical learning is one of the most stressful experiences during undergraduate studies [ 8 , 10 ]. Thus, the clinical component of nursing education is considered more stressful than the theoretical component. Students often view clinical learning, where most learning takes place, as an unsupportive environment [ 11 ]. In addition, they note strained relationships between themselves and clinical preceptors and perceive that the negative attitudes of clinical staff produce stress [ 12 ].

The effects of stress on nursing students often involve a sense of uncertainty, uneasiness, or anxiety. The literature is replete with evidence that nursing students experience a variety of stressors during their clinical practicum, beginning with the first clinical rotation. Nursing is a complex profession that requires continuous interaction with a variety of individuals in a high-stress environment. Stress during clinical learning can have multiple negative consequences, including low academic achievement, elevated levels of burnout, and diminished personal well-being [ 13 , 14 ]. In addition, both theoretical and practical research has demonstrated that increased, continual exposure to stress leads to cognitive deficits, inability to concentrate, lack of memory or recall, misinterpretation of speech, and decreased learning capacity [ 15 ]. Furthermore, stress has been identified as a cause of attrition among nursing students [ 16 ].

Most sources of stress have been categorized as academic, clinical or personal. Each person copes with stress differently [ 17 ], and utilizes deliberate, planned, and psychological efforts to manage stressful demands [ 18 ]. Coping mechanisms are commonly termed adaptation strategies or coping skills. Labrague et al. [ 19 ] noted that students used critical coping strategies to handle stress and suggested that problem solving was the most common coping or adaptation mechanism used by nursing students. Nursing students’ coping strategies affect their physical and psychological well-being and the quality of nursing care they offer. Therefore, identifying the coping strategies that students use to manage stressors is important for early intervention [ 20 ].

Studies on nursing students’ coping strategies have been conducted in various countries. For example, Israeli nursing students were found to adopt a range of coping mechanisms, including talking to friends, engaging in sports, avoiding stress and sadness/misery, and consuming alcohol [ 21 ]. Other studies have examined stress levels among medical students in the Arab region. Chaabane et al. [ 15 ], conducted a systematic review of sudies in Arab countries, including Saudi Arabia, Egypt, Jordan, Iraq, Pakistan, Oman, Palestine and Bahrain, and reported that stress during clinical practicums was prevalent, although it could not be determined whether this was limited to the initial clinical course or occurred throughout clinical training. Stressors highlighted during the clinical period in the systematic review included assignments and workload during clinical practice, a feeling that the requirements of clinical practice exceeded students’ physical and emotional endurance and that their involvement in patient care was limited due to lack of experience. Furthermore, stress can have a direct effect on clinical performance, leading to mental disorders. Tung et al. [ 22 ], reported that the prevalence of depression among nursing students in Arab countries is 28%, which is almost six times greater than the rest of the world [ 22 ]. On the other hand, Saifan et al. [ 5 ], explored the theory-practice gap in the United Arab Emirates and found that clinical stressors could be decreased by preparing students better for clinical education with qualified clinical faculty and supportive preceptors.

The purpose of this study was to identify the stressors experienced by undergraduate nursing students in the United Arab Emirates during their first clinical training and the basic adaptation approaches or coping strategies they used. Recognizing or understanding different coping processes can inform the implementation of corrective measures when students experience clinical stress. The findings of this study may provide valuable information for nursing programmes, nurse educators, and clinical administrators to establish adaptive strategies to reduce stress among students going clinical practicums, particularly stressors from their first clinical training in different healthcare settings.

A qualitative approach was adopted to understand clinical stressors and coping strategies from the perspective of nurses’ lived experience. Qualitative content analysis was employed to obtain rich and detailed information from our qualitative data. Qualitative approaches seek to understand the phenomenon under study from the perspectives of individuals with lived experience [ 23 ]. Qualitative content analysis is an interpretive technique that examines the similarities and differences between and within different areas of text while focusing on the subject [ 24 ]. It is used to examine communication patterns in a repeatable and systematic way [ 25 ] and yields rich and detailed information on the topic under investigation [ 23 ]. It is a method of systematically coding and categorizing information and comprises a process of comprehending, interpreting, and conceptualizing the key meanings from qualitative data [ 26 ].

Setting and participants

This study was conducted after the clinical rotations ended in April 2022, between May and June in the nursing programme at the College of Health Sciences, University of Sharjah, in the United Arab Emirates. The study population comprised undergraduate nursing students who were undergoing their first clinical training and were recruited using purposive sampling. The inclusion criteria for this study were second-year nursing students in the first semester of clinical training who could speak English, were willing to participate in this research, and had no previous clinical work experience. The final sample consisted of 30 students.

Research instrument

The research instrument was a semi structured interview guide. The interview questions were based on an in-depth review of related literature. An intensive search included key words in Google Scholar, PubMed like the terms “nursing clinical stressors”, “nursing students”, and “coping mechanisms”. Once the questions were created, they were validated by two other faculty members who had relevant experience in mental health. A pilot test was conducted with five students and based on their feedback the following research questions, which were addressed in the study.

How would you describe your clinical experiences during your first clinical rotations?

In what ways did you find the first clinical rotation to be stressful?

What factors hindered your clinical training?

How did you cope with the stressors you encountered in clinical training?

Which strategies helped you cope with the clinical stressors you encountered?

Data collection

Semi-structured interviews were chosen as the method for data collection. Semi structured interviews are a well-established approach for gathering data in qualitative research and allow participants to discuss their views, experiences, attitudes, and beliefs in a positive environment [ 27 ]. This approach allows for flexibility in questioning thereby ensuring that key topics related to clinical learning stressors and coping strategies would be explored. Participants were given the opportunity to express their views, experiences, attitudes, and beliefs in a positive environment, encouraging open communication. These semi structured interviews were conducted by one member of the research team (MAS) who had a mental health background, and another member of the research team who attended the interviews as an observer (JMD). Neither of these researchers were involved in teaching the students during their clinical practicum, which helped to minimize bias. The interviews took place at the University of Sharjah, specifically in building M23, providing a familiar and comfortable environment for the participant. Before the interviews were all students who agreed to participate were provided with an explanation of the study’s purpose. The time and location of each interview were arranged. Before the interviews were conducted, all students who provided consent to participate received an explanation of the purpose of the study, and the time and place of each interview were arranged to accommodate the participants’ schedules and preferences. The interviews were conducted after the clinical rotation had ended in April, and after the final grades had been submitted to the coordinator. The timings of the interviews included the month of May and June which ensured that participants have completed their practicum experience and could reflect on the stressors more comprehensively. The interviews were audio-recorded with the participants’ consent, and each interview lasted 25–40 min. The data were collected until saturation was reached for 30 students. Memos and field notes were also recorded as part of the data collection process. These additional data allowed for triangulation to improve the credibility of the interpretations of the data [ 28 ]. Memos included the interviewers’ thoughts and interpretations about the interviews, the research process (including questions and gaps), and the analytic progress used for the research. Field notes were used to record the interviewers’ observations and reflections on the data. These additional data collection methods were important to guide the researchers in the interpretation of the data on the participants’ feelings, perspectives, experiences, attitudes, and beliefs. Finally, member checking was performed to ensure conformability.

Data analysis

The study used the content analysis method proposed by Graneheim and Lundman [ 24 ]. According to Graneheim and Lundman [ 24 ], content analysis is an interpretive technique that examines the similarities and differences between distinct parts of a text. This method allows researchers to determine exact theoretical and operational definitions of words, phrases, and symbols by elucidating their constituent properties [ 29 ]. First, we read the interview transcripts several times to reach an overall understanding of the data. All verbatim transcripts were read several times and discussed among all authors. We merged and used line-by-line coding of words, sentences, and paragraphs relevant to each other in terms of both the content and context of stressors and coping mechanisms. Next, we used data reduction to assess the relationships among themes using tables and diagrams to indicate conceptual patterns. Content related to stress encountered by students was extracted from the transcripts. In a separate document, we integrated and categorized all words and sentences that were related to each other in terms of both content and context. We analyzed all codes and units of meaning and compared them for similarities and differences in the context of this study. Furthermore, the emerging findings were discussed with other members of the researcher team. The final abstractions of meaningful subthemes into themes were discussed and agreed upon by the entire research team. This process resulted in the extraction of three main themes in addition to two subthemes related to stress and coping strategies.

Ethical considerations

The University of Sharjah Research Ethics Committee provided approval to conduct this study (Reference Number: REC 19-12-03-01-S). Before each interview, the goal and study procedures were explained to each participant, and written informed consent was obtained. The participants were informed that participation in the study was voluntary and that they could withdraw from the study at any time. In the event they wanted to withdraw from the study, all information related to the participant would be removed. No participant withdrew from the study. Furthermore, they were informed that their clinical practicum grade would not be affected by their participation in this study. We chose interview locations in Building M23that were private and quiet to ensure that the participants felt at ease and confident in verbalizing their opinions. No participant was paid directly for involvement in this study. In addition, participants were assured that their data would remain anonymous and confidential. Confidentiality means that the information provided by participants was kept private with restrictions on how and when data can be shared with others. The participants were informed that their information would not be duplicated or disseminated without their permission. Anonymity refers to the act of keeping people anonymous with respect to their participation in a research endeavor. No personal identifiers were used in this study, and each participant was assigned a random alpha-numeric code (e.g., P1 for participant 1). All digitally recorded interviews were downloaded to a secure computer protected by the principal investigator with a password. The researchers were the only people with access to the interview material (recordings and transcripts). All sensitive information and materials were kept secure in the principal researcher’s office at the University of Sharjah. The data will be maintained for five years after the study is completed, after which the material will be destroyed (the transcripts will be shredded, and the tapes will be demagnetized).

In total, 30 nursing students who were enrolled in the nursing programme at the Department of Nursing, College of Health Sciences, University of Sharjah, and who were undergoing their first clinical practicum participated in the study. Demographically, 80% ( n = 24) were females and 20% ( n = 6) were male participants. The majority (83%) of study participants ranged in age from 18 to 22 years. 20% ( n = 6) were UAE nationals, 53% ( n = 16) were from Gulf Cooperation Council countries, while 20% ( n = 6) hailed from Africa and 7% ( n = 2) were of South Asian descent. 67% of the respondents lived with their families while 33% lived in the hostel. (Table 1 )

Following the content analysis, we identified three main themes: (1) managing expectations, (2) theory-practice gap and 3)learning to cope. Learning to cope had two subthemes: positive coping strategies and negative coping strategies. An account of each theme is presented along with supporting excerpts for the identified themes. The identified themes provide valuable insight into the stressors encountered by students during their first clinical practicum. These themes will lead to targeted interventions and supportive mechanisms that can be built into the clinical training curriculum to support students during clinical practice.

Theme 1: managing expectations

In our examination of the stressors experienced by nursing students during their first clinical practicum and the coping strategies they employed, we identified the first theme as managing expectations.

The students encountered expectations from various parties, such as clinical staff, patients and patients’ relatives which they had to navigate. They attempted to fulfil their expectations as they progressed through training, which presented a source of stress. The students noted that the hospital staff and patients expected them to know how to perform a variety of tasks upon request, which made the students feel stressed and out of place if they did not know how to perform these tasks. Some participants noted that other nurses in the clinical unit did not allow them to participate in nursing procedures, which was considered an enormous impediment to clinical learning, as noted in the excerpt below:

“…Sometimes the nurses… They will not allow us to do some procedures or things during clinical. And sometimes the patients themselves don’t allow us to do procedures” (P5).

Some of the students noted that they felt they did not belong and felt like foreigners in the clinical unit. Excerpts from the students are presented in the following quotes;

“The clinical environment is so stressful. I don’t feel like I belong. There is too little time to build a rapport with hospital staff or the patient” (P22).

“… you ask the hospital staff for some guidance or the location of equipment, and they tell us to ask our clinical tutor …but she is not around … what should I do? It appears like we do not belong, and the sooner the shift is over, the better” (P18).

“The staff are unfriendly and expect too much from us students… I feel like I don’t belong, or I am wasting their (the hospital staff’s) time. I want to ask questions, but they have loads to do” (P26).

Other students were concerned about potential failure when working with patients during clinical training, which impacted their confidence. They were particularly afraid of failure when performing any clinical procedures.

“At the beginning, I was afraid to do procedures. I thought that maybe the patient would be hurt and that I would not be successful in doing it. I have low self-confidence in doing procedures” (P13).

The call bell rings, and I am told to answer Room No. XXX. The patient wants help to go to the toilet, but she has two IV lines. I don’t know how to transport the patient… should I take her on the wheelchair? My eyes glance around the room for a wheelchair. I am so confused …I tell the patient I will inform the sister at the nursing station. The relative in the room glares at me angrily … “you better hurry up”…Oh, I feel like I don’t belong, as I am not able to help the patient… how will I face the same patient again?” (P12).

Another major stressor mentioned in the narratives was related to communication and interactions with patients who spoke another language, so it was difficult to communicate.

“There was a challenge with my communication with the patients. Sometimes I have communication barriers because they (the patients) are of other nationalities. I had an experience with a patient [who was] Indian, and he couldn’t speak my language. I did not understand his language” (P9).

Thus, a variety of expectations from patients, relatives, hospital staff, and preceptors acted as sources of stress for students during their clinical training.

Theme 2: theory-practice gap

Theory-practice gaps have been identified in previous studies. In our study, there was complete dissonance between theory and actual clinical practice. The clinical procedures or practices nursing students were expected to perform differed from the theory they had covered in their university classes and skills lab. This was described as a theory–practice gap and often resulted in stress and confusion.

“For example …the procedures in the hospital are different. They are different from what we learned or from theory on campus. Or… the preceptors have different techniques than what we learned on campus. So, I was stress[ed] and confused about it” (P11).

Furthermore, some students reported that they did not feel that they received adequate briefing before going to clinical training. A related source of stress was overload because of the volume of clinical coursework and assignments in addition to clinical expectations. Additionally, the students reported that a lack of time and time management were major sources of stress in their first clinical training and impacted their ability to complete the required paperwork and assignments:

“…There is not enough time…also, time management at the hospital…for example, we start at seven a.m., and the handover takes 1 hour to finish. They (the nurses at the hospital) are very slow…They start with bed making and morning care like at 9.45 a.m. Then, we must fill [out] our assessment tool and the NCP (nursing care plan) at 10 a.m. So, 15 only minutes before going to our break. We (the students) cannot manage this time. This condition makes me and my friends very stressed out. -I cannot do my paperwork or assignments; no time, right?” (P10).

“Stressful. There is a lot of work to do in clinical. My experiences are not really good with this course. We have a lot of things to do, so many assignments and clinical procedures to complete” (P16).

The participants noted that the amount of required coursework and number of assignments also presented a challenge during their first clinical training and especially affected their opportunity to learn.

“I need to read the file, know about my patient’s condition and pathophysiology and the rationale for the medications the patient is receiving…These are big stressors for my learning. I think about assignments often. Like, we are just focusing on so many assignments and papers. We need to submit assessments and care plans for clinical cases. We focus our time to complete and finish the papers rather than doing the real clinical procedures, so we lose [the] chance to learn” (P25).

Another participant commented in a similar vein that there was not enough time to perform tasks related to clinical requirements during clinical placement.

“…there is a challenge because we do not have enough time. Always no time for us to submit papers, to complete assessment tools, and some nurses, they don’t help us. I think we need more time to get more experiences and do more procedures, reduce the paperwork that we have to submit. These are challenges …” (P14).

There were expectations that the students should be able to carry out their nursing duties without becoming ill or adversely affected. In addition, many students reported that the clinical environment was completely different from the skills laboratory at the college. Exposure to the clinical setting added to the theory-practice gap, and in some instances, the students fell ill.

One student made the following comment:

“I was assisting a doctor with a dressing, and the sight and smell from the oozing wound was too much for me. I was nauseated. As soon as the dressing was done, I ran to the bathroom and threw up. I asked myself… how will I survive the next 3 years of nursing?” (P14).

Theme 3: learning to cope

The study participants indicated that they used coping mechanisms (both positive and negative) to adapt to and manage the stressors in their first clinical practicum. Important strategies that were reportedly used to cope with stress were time management, good preparation for clinical practice, and positive thinking as well as engaging in physical activity and self-motivation.

“Time management. Yes, it is important. I was encouraging myself. I used time management and prepared myself before going to the clinical site. Also, eating good food like cereal…it helps me very much in the clinic” (P28).

“Oh yeah, for sure positive thinking. In the hospital, I always think positively. Then, after coming home, I get [to] rest and think about positive things that I can do. So, I will think something good [about] these things, and then I will be relieved of stress” (P21).

Other strategies commonly reported by the participants were managing their breathing (e.g., taking deep breaths, breathing slowly), taking breaks to relax, and talking with friends about the problems they encountered.

“I prefer to take deep breaths and breathe slowly and to have a cup of coffee and to talk to my friends about the case or the clinical preceptor and what made me sad so I will feel more relaxed” (P16).

“Maybe I will take my break so I feel relaxed and feel better. After clinical training, I go directly home and take a long shower, going over the day. I will not think about anything bad that happened that day. I just try to think about good things so that I forget the stress” (P27).

“Yes, my first clinical training was not easy. It was difficult and made me stressed out…. I felt that it was a very difficult time for me. I thought about leaving nursing” (P7).

I was not able to offer my prayers. For me, this was distressing because as a Muslim, I pray regularly. Now, my prayer time is pushed to the end of the shift” (P11).

“When I feel stress, I talk to my friends about the case and what made me stressed. Then I will feel more relaxed” (P26).

Self-support or self-motivation through positive self-talk was also used by the students to cope with stress.

“Yes, it is difficult in the first clinical training. When I am stress[ed], I go to the bathroom and stand in the front of the mirror; I talk to myself, and I say, “You can do it,” “you are a great student.” I motivate myself: “You can do it”… Then, I just take breaths slowly several times. This is better than shouting or crying because it makes me tired” (P11).

Other participants used physical activity to manage their stress.

“How do I cope with my stress? Actually, when I get stressed, I will go for a walk on campus” (P4).

“At home, I will go to my room and close the door and start doing my exercises. After that, I feel the negative energy goes out, then I start to calm down… and begin my clinical assignments” (P21).

Both positive and negative coping strategies were utilized by the students. Some participants described using negative coping strategies when they encountered stress during their clinical practice. These negative coping strategies included becoming irritable and angry, eating too much food, drinking too much coffee, and smoking cigarettes.

“…Negative adaptation? Maybe coping. If I am stressed, I get so angry easily. I am irritable all day also…It is negative energy, right? Then, at home, I am also angry. After that, it is good to be alone to think about my problems” (P12).

“Yeah, if I…feel stress or depressed, I will eat a lot of food. Yeah, ineffective, like I will be eating a lot, drinking coffee. Like I said, effective, like I will prepare myself and do breathing, ineffective, I will eat a lot of snacks in between my free time. This is the bad side” (P16).

“…During the first clinical practice? Yes, it was a difficult experience for us…not only me. When stressed, during a break at the hospital, I will drink two or three cups of coffee… Also, I smoke cigarettes… A lot. I can drink six cups [of coffee] a day when I am stressed. After drinking coffee, I feel more relaxed, I finish everything (food) in the refrigerator or whatever I have in the pantry, like chocolates, chips, etc” (P23).

These supporting excerpts for each theme and the analysis offers valuable insights into the specific stressors faced by nursing students during their first clinical practicum. These insights will form the basis for the development of targeted interventions and supportive mechanisms within the clinical training curriculum to better support students’ adjustment and well-being during clinical practice.

Our study identified the stressors students encounter in their first clinical practicum and the coping strategies, both positive and negative, that they employed. Although this study emphasizes the importance of clinical training to prepare nursing students to practice as nurses, it also demonstrates the correlation between stressors and coping strategies.The content analysis of the first theme, managing expectations, paves the way for clinical agencies to realize that the students of today will be the nurses of tomorrow. It is important to provide a welcoming environment where students can develop their identities and learn effectively. Additionally, clinical staff should foster an environment of individualized learning while also assisting students in gaining confidence and competence in their repertoire of nursing skills, including critical thinking, problem solving and communication skills [ 8 , 15 , 19 , 30 ]. Another challenge encountered by the students in our study was that they were prevented from participating in clinical procedures by some nurses or patients. This finding is consistent with previous studies reporting that key challenges for students in clinical learning include a lack of clinical support and poor attitudes among clinical staff and instructors [ 31 ]. Clinical staff with positive attitudes have a positive impact on students’ learning in clinical settings [ 32 ]. The presence, supervision, and guidance of clinical instructors and the assistance of clinical staff are essential motivating components in the clinical learning process and offer positive reinforcement [ 30 , 33 , 34 ]. Conversely, an unsupportive learning environment combined with unwelcoming clinical staff and a lack of sense of belonging negatively impact students’ clinical learning [ 35 ].

The sources of stress identified in this study were consistent with common sources of stress in clinical training reported in previous studies, including the attitudes of some staff, students’ status in their clinical placement and educational factors. Nursing students’ inexperience in the clinical setting and lack of social and emotional experience also resulted in stress and psychological difficulties [ 36 ]. Bhurtun et al. [ 33 ] noted that nursing staff are a major source of stress for students because the students feel like they are constantly being watched and evaluated.

We also found that students were concerned about potential failure when working with patients during their clinical training. Their fear of failure when performing clinical procedures may be attributable to low self-confidence. Previous studies have noted that students were concerned about injuring patients, being blamed or chastised, and failing examinations [ 37 , 38 ]. This was described as feeling “powerless” in a previous study [ 7 , 12 ]. In addition, patients’ attitudes towards “rejecting” nursing students or patients’ refusal of their help were sources of stress among the students in our study and affected their self-confidence. Self-confidence and a sense of belonging are important for nurses’ personal and professional identity, and low self-confidence is a problem for nursing students in clinical learning [ 8 , 39 , 40 ]. Our findings are consistent with a previous study that reported that a lack of self-confidence was a primary source of worry and anxiety for nursing students and affected their communication and intention to leave nursing [ 41 ].

In the second theme, our study suggests that students encounter a theory-practice gap in clinical settings, which creates confusion and presents an additional stressors. Theoretical and clinical training are complementary elements of nursing education [ 40 ], and this combination enables students to gain the knowledge, skills, and attitudes necessary to provide nursing care. This is consistent with the findings of a previous study that reported that inconsistencies between theoretical knowledge and practical experience presented a primary obstacle to the learning process in the clinical context [ 42 ], causing students to lose confidence and become anxious [ 43 ]. Additionally, the second theme, the theory-practice gap, authenticates Safian et al.’s [ 5 ] study of the theory-practice gap that exists United Arab Emirates among nursing students as well as the need for more supportive clinical faculty and the extension of clinical hours. The need for better time availability and time management to complete clinical tasks were also reported by the students in the study. Students indicated that they had insufficient time to complete clinical activities because of the volume of coursework and assignments. Our findings support those of Chaabane et al. [ 15 ]. A study conducted in Saudi Arabia [ 44 ] found that assignments and workload were among the greatest sources of stress for students in clinical settings. Effective time management skills have been linked to academic achievement, stress reduction, increased creativity [ 45 ], and student satisfaction [ 46 ]. Our findings are also consistent with previous studies that reported that a common source of stress among first-year students was the increased classroom workload [ 19 , 47 ]. As clinical assignments and workloads are major stressors for nursing students, it is important to promote activities to help them manage these assignments [ 48 ].

Another major challenge reported by the participants was related to communicating and interacting with other nurses and patients. The UAE nursing workforce and population are largely expatriate and diverse and have different cultural and linguistic backgrounds. Therefore, student nurses encounter difficulty in communication [ 49 ]. This cultural diversity that students encounter in communication with patients during clinical training needs to be addressed by curriculum planners through the offering of language courses and courses on cultural diversity [ 50 ].

Regarding the third and final theme, nursing students in clinical training are unable to avoid stressors and must learn to cope with or adapt to them. Previous research has reported a link between stressors and the coping mechanisms used by nursing students [ 51 , 52 , 53 ]. In particular, the inability to manage stress influences nurses’ performance, physical and mental health, attitude, and role satisfaction [ 54 ]. One such study suggested that nursing students commonly use problem-focused (dealing with the problem), emotion-focused (regulating emotion), and dysfunctional (e.g., venting emotions) stress coping mechanisms to alleviate stress during clinical training [ 15 ]. Labrague et al. [ 51 ] highlighted that nursing students use both active and passive coping techniques to manage stress. The pattern of clinical stress has been observed in several countries worldwide. The current study found that first-year students experienced stress during their first clinical training [ 35 , 41 , 55 ]. The stressors they encountered impacted their overall health and disrupted their clinical learning. Chaabane et al. [ 15 ] reported moderate and high stress levels among nursing students in Bahrain, Egypt, Iraq, Jordan, Oman, Pakistan, Palestine, Saudi Arabia, and Sudan. Another study from Bahrain reported that all nursing students experienced moderate to severe stress in their first clinical placement [ 56 ]. Similarly, nursing students in Spain experienced a moderate level of stress, and this stress was significantly correlated with anxiety [ 30 ]. Therefore, it is imperative that pastoral systems at the university address students’ stress and mental health so that it does not affect their clinical performance. Faculty need to utilize evidence-based interventions to support students so that anxiety-producing situations and attrition are minimized.

In our study, students reported a variety of positive and negative coping mechanisms and strategies they used when they experienced stress during their clinical practice. Positive coping strategies included time management, positive thinking, self-support/motivation, breathing, taking breaks, talking with friends, and physical activity. These findings are consistent with those of a previous study in which healthy coping mechanisms used by students included effective time management, social support, positive reappraisal, and participation in leisure activities [ 57 ]. Our study found that relaxing and talking with friends were stress management strategies commonly used by students. Communication with friends to cope with stress may be considered social support. A previous study also reported that people seek social support to cope with stress [ 58 ]. Some students in our study used physical activity to cope with stress, consistent with the findings of previous research. Stretching exercises can be used to counteract the poor posture and positioning associated with stress and to assist in reducing physical tension. Promoting such exercise among nursing students may assist them in coping with stress in their clinical training [ 59 ].

Our study also showed that when students felt stressed, some adopted negative coping strategies, such as showing anger/irritability, engaging in unhealthy eating habits (e.g., consumption of too much food or coffee), or smoking cigarettes. Previous studies have reported that high levels of perceived stress affect eating habits [ 60 ] and are linked to poor diet quality, increased snacking, and low fruit intake [ 61 ]. Stress in clinical settings has also been linked to sleep problems, substance misuse, and high-risk behaviors’ and plays a major role in student’s decision to continue in their programme.

Implications of the study

The implications of the study results can be grouped at multiple levels including; clinical, educational, and organizational level. A comprehensive approach to addressing the stressors encountered by nursing students during their clinical practicum can be overcome by offering some practical strategies to address the stressors faced by nursing students during their clinical practicum. By integrating study findings into curriculum planning, mentorship programs, and organizational support structures, a supportive and nurturing environment that enhances students’ learning, resilience, and overall success can be envisioned.

Clinical level

Introducing simulation in the skills lab with standardized patients and the use of moulage to demonstrate wounds, ostomies, and purulent dressings enhances students’ practical skills and prepares them for real-world clinical scenarios. Organizing orientation days at clinical facilities helps familiarize students with the clinical environment, identify potential stressors, and introduce interventions to enhance professionalism, social skills, and coping abilities Furthermore, creating a WhatsApp group facilitates communication and collaboration among hospital staff, clinical tutors, nursing faculty, and students, enabling immediate support and problem-solving for clinical situations as they arise, Moreover, involving chief nursing officers of clinical facilities in the Nursing Advisory Group at the Department of Nursing promotes collaboration between academia and clinical practice, ensuring alignment between educational objectives and the needs of the clinical setting [ 62 ].

Educational level

Sharing study findings at conferences (we presented the results of this study at Sigma Theta Tau International in July 2023 in Abu Dhabi, UAE) and journal clubs disseminates knowledge and best practices among educators and clinicians, promoting awareness and implementation of measures to improve students’ learning experiences. Additionally we hold mentorship training sessions annually in January and so we shared with the clinical mentors and preceptors the findings of this study so that they proactively they are equipped with strategies to support students’ coping with stressors during clinical placements.

Organizational level

At the organizational we relooked at the available student support structures, including counseling, faculty advising, and career advice, throughout the nursing program emphasizing the importance of holistic support for students’ well-being and academic success as well as retention in the nursing program. Also, offering language courses as electives recognizes the value of communication skills in nursing practice and provides opportunities for personal and professional development.

For first-year nursing students, clinical stressors are inevitable and must be given proper attention. Recognizing nursing students’ perspectives on the challenges and stressors experienced in clinical training is the first step in overcoming these challenges. In nursing schools, providing an optimal clinical environment as well as increasing supervision and evaluation of students’ practices should be emphasized. Our findings demonstrate that first-year nursing students are exposed to a variety of different stressors. Identifying the stressors, pressures, and obstacles that first-year students encounter in the clinical setting can assist nursing educators in resolving these issues and can contribute to students’ professional development and survival to allow them to remain in the profession. To overcome stressors, students frequently employ problem-solving approaches or coping mechanisms. The majority of nursing students report stress at different levels and use a variety of positive and negative coping techniques to manage stress.

The present results may not be generalizable to other nursing institutions because this study used a purposive sample along with a qualitative approach and was limited to one university in the Middle East. Furthermore, the students self-reported their stress and its causes, which may have introduced reporting bias. The students may also have over or underreported stress or coping mechanisms because of fear of repercussions or personal reasons, even though the confidentiality of their data was ensured. Further studies are needed to evaluate student stressors and coping now that measures have been introduced to support students. Time will tell if these strategies are being used effectively by both students and clinical personnel or if they need to be readdressed. Finally, we need to explore the perceptions of clinical faculty towards supervising students in their first clinical practicum so that clinical stressors can be handled effectively.

Data availability

The data sets are available with the corresponding author upon reasonable request.

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Jacqueline Maria Dias, Muhammad Arsyad Subu, Nabeel Al-Yateem, Fatma Refaat Ahmed, Syed Azizur Rahman, Mini Sara Abraham, Sareh Mirza Forootan, Farzaneh Ahmad Sarkhosh & Fatemeh Javanbakh

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JMD conceptualized the idea and designed the methodology, formal analysis, writing original draft and project supervision and mentoring. MAS prepared the methodology and conducted the qualitative interviews and analyzed the methodology and writing of original draft and project supervision. NY, FRA, SAR, MSA writing review and revising the draft. SMF, FAS, FJ worked with MAS on the formal analysis and prepared the first draft.All authors reviewed the final manuscipt of the article.

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Dias, J.M., Subu, M.A., Al-Yateem, N. et al. Nursing students’ stressors and coping strategies during their first clinical training: a qualitative study in the United Arab Emirates. BMC Nurs 23 , 322 (2024). https://doi.org/10.1186/s12912-024-01962-5

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Teens come up with trigonometry proof for Pythagorean Theorem, a problem that stumped math world for centuries

By Bill Whitaker

May 5, 2024 / 7:00 PM EDT / CBS News

As the school year ends, many students will be only too happy to see math classes in their rearview mirrors. It may seem to some of us non-mathematicians that geometry and trigonometry were created by the Greeks as a form of torture, so imagine our amazement when we heard two high school seniors had proved a mathematical puzzle that was thought to be impossible for 2,000 years.

We met Calcea Johnson and Ne'Kiya Jackson at their all-girls Catholic high school in New Orleans. We expected to find two mathematical prodigies.

Instead, we found at St. Mary's Academy , all students are told their possibilities are boundless.

Come Mardi Gras season, New Orleans is alive with colorful parades, replete with floats, and beads, and high school marching bands.

In a city where uniqueness is celebrated, St. Mary's stands out – with young African American women playing trombones and tubas, twirling batons and dancing - doing it all, which defines St. Mary's, students told us.

Junior Christina Blazio says the school instills in them they have the ability to accomplish anything.

Christina Blazio: That is kinda a standard here. So we aim very high - like, our aim is excellence for all students.

The private Catholic elementary and high school sits behind the Sisters of the Holy Family Convent in New Orleans East. The academy was started by an African American nun for young Black women just after the Civil War. The church still supports the school with the help of alumni.

In December 2022, seniors Ne'Kiya Jackson and Calcea Johnson were working on a school-wide math contest that came with a cash prize.

Ne'Kiya Jackson: I was motivated because there was a monetary incentive.

Calcea Johnson: 'Cause I was like, "$500 is a lot of money. So I-- I would like to at least try."

Both were staring down the thorny bonus question.

Bill Whitaker: So tell me, what was this bonus question?

Calcea Johnson: It was to create a new proof of the Pythagorean Theorem. And it kind of gave you a few guidelines on how would you start a proof.

The seniors were familiar with the Pythagorean Theorem, a fundamental principle of geometry. You may remember it from high school: a² + b² = c². In plain English, when you know the length of two sides of a right triangle, you can figure out the length of the third.

Both had studied geometry and some trigonometry, and both told us math was not easy. What no one told them was there had been more than 300 documented proofs of the Pythagorean Theorem using algebra and geometry, but for 2,000 years a proof using trigonometry was thought to be impossible, … and that was the bonus question facing them.

Bill Whitaker: When you looked at the question did you think, "Boy, this is hard"?

Ne'Kiya Jackson: Yeah.

Bill Whitaker: What motivated you to say, "Well, I'm going to try this"?

Calcea Johnson: I think I was like, "I started something. I need to finish it."

Bill Whitaker: So you just kept on going.

Calcea Johnson: Yeah.

For two months that winter, they spent almost all their free time working on the proof.

CeCe Johnson: She was like, "Mom, this is a little bit too much."

CeCe and Cal Johnson are Calcea's parents.

CeCe Johnson: So then I started looking at what she really was doing. And it was pages and pages and pages of, like, over 20 or 30 pages for this one problem.

Cal Johnson: Yeah, the garbage can was full of papers, which she would, you know, work out the problems and-- if that didn't work she would ball it up, throw it in the trash.

Bill Whitaker: Did you look at the problem?

Neliska Jackson is Ne'Kiya's mother.

Neliska Jackson: Personally I did not. 'Cause most of the time I don't understand what she's doing (laughter).

Michelle Blouin Williams: What if we did this, what if I write this? Does this help? ax² plus ….

Their math teacher, Michelle Blouin Williams, initiated the math contest.

Bill Whitaker: And did you think anyone would solve it?

Michelle Blouin Williams: Well, I wasn't necessarily looking for a solve. So, no, I didn't—

Bill Whitaker: What were you looking for?

Michelle Blouin Williams: I was just looking for some ingenuity, you know—

Calcea and Ne'Kiya delivered on that! They tried to explain their groundbreaking work to 60 Minutes. Calcea's proof is appropriately titled the Waffle Cone.

Calcea Johnson: So to start the proof, we start with just a regular right triangle where the angle in the corner is 90°. And the two angles are alpha and beta.

Bill Whitaker: Uh-huh

Calcea Johnson: So then what we do next is we draw a second congruent, which means they're equal in size. But then we start creating similar but smaller right triangles going in a pattern like this. And then it continues for infinity. And eventually it creates this larger waffle cone shape.

Calcea Johnson: Am I going a little too—

Bill Whitaker: You've been beyond me since the beginning. (laughter)

Bill Whitaker: So how did you figure out the proof?

Ne'Kiya Jackson: Okay. So you have a right triangle, 90° angle, alpha and beta.

Bill Whitaker: Then what did you do?

Bill Whitaker with Calcea Johnson and Ne'Kiya Jackson

Ne'Kiya Jackson: Okay, I have a right triangle inside of the circle. And I have a perpendicular bisector at OP to divide the triangle to make that small right triangle. And that's basically what I used for the proof. That's the proof.

Bill Whitaker: That's what I call amazing.

Ne'Kiya Jackson: Well, thank you.

There had been one other documented proof of the theorem using trigonometry by mathematician Jason Zimba in 2009 – one in 2,000 years. Now it seems Ne'Kiya and Calcea have joined perhaps the most exclusive club in mathematics.

Bill Whitaker: So you both independently came up with proof that only used trigonometry.

Ne'Kiya Jackson: Yes.

Bill Whitaker: So are you math geniuses?

Calcea Johnson: I think that's a stretch.

Bill Whitaker: If not genius, you're really smart at math.

Ne'Kiya Jackson: Not at all. (laugh)

To document Calcea and Ne'Kiya's work, math teachers at St. Mary's submitted their proofs to an American Mathematical Society conference in Atlanta in March 2023.

Ne'Kiya Jackson: Well, our teacher approached us and was like, "Hey, you might be able to actually present this," I was like, "Are you joking?" But she wasn't. So we went. I got up there. We presented and it went well, and it blew up.

Bill Whitaker: It blew up.

Calcea Johnson: Yeah.

Ne'Kiya Jackson: It blew up.

Bill Whitaker: Yeah. What was the blowup like?

Calcea Johnson: Insane, unexpected, crazy, honestly.

It took millenia to prove, but just a minute for word of their accomplishment to go around the world. They got a write-up in South Korea and a shout-out from former first lady Michelle Obama, a commendation from the governor and keys to the city of New Orleans.

Bill Whitaker: Why do you think so many people found what you did to be so impressive?

Ne'Kiya Jackson: Probably because we're African American, one. And we're also women. So I think-- oh, and our age. Of course our ages probably played a big part.

Bill Whitaker: So you think people were surprised that young African American women, could do such a thing?

Calcea Johnson: Yeah, definitely.

Ne'Kiya Jackson: I'd like to actually be celebrated for what it is. Like, it's a great mathematical achievement.

Achievement, that's a word you hear often around St. Mary's academy. Calcea and Ne'Kiya follow a long line of barrier-breaking graduates.

The late queen of Creole cooking, Leah Chase , was an alum. so was the first African-American female New Orleans police chief, Michelle Woodfork …

And judge for the Fifth Circuit Court of Appeals, Dana Douglas. Math teacher Michelle Blouin Williams told us Calcea and Ne'Kiya are typical St. Mary's students.

Bill Whitaker: They're not unicorns.

Michelle Blouin Williams: Oh, no no. If they are unicorns, then every single lady that has matriculated through this school is a beautiful, Black unicorn.

Pamela Rogers: You're good?

Pamela Rogers, St. Mary's president and interim principal, told us the students hear that message from the moment they walk in the door.

St. Mary's Academy president and interim principal Pamela Rogers

Pamela Rogers: We believe all students can succeed, all students can learn. It does not matter the environment that you live in.

Bill Whitaker: So when word went out that two of your students had solved this almost impossible math problem, were they universally applauded?

Pamela Rogers: In this community, they were greatly applauded. Across the country, there were many naysayers.

Bill Whitaker: What were they saying?

Pamela Rogers: They were saying, "Oh, they could not have done it. African Americans don't have the brains to do it." Of course, we sheltered our girls from that. But we absolutely did not expect it to come in the volume that it came.

Bill Whitaker: And after such a wonderful achievement.

Pamela Rogers: People-- have a vision of who can be successful. And-- to some people, it is not always an African American female. And to us, it's always an African American female.

Gloria Ladson-Billings: What we know is when teachers lay out some expectations that say, "You can do this," kids will work as hard as they can to do it.

Gloria Ladson-Billings, professor emeritus at the University of Wisconsin, has studied how best to teach African American students. She told us an encouraging teacher can change a life.

Bill Whitaker: And what's the difference, say, between having a teacher like that and a whole school dedicated to the excellence of these students?

Gloria Ladson-Billings: So a whole school is almost like being in Heaven.

Bill Whitaker: What do you mean by that?

Bill Whitaker and Gloria Ladson-Billings

Gloria Ladson-Billings: Many of our young people have their ceilings lowered, that somewhere around fourth or fifth grade, their thoughts are, "I'm not going to be anything special." What I think is probably happening at St. Mary's is young women come in as, perhaps, ninth graders and are told, "Here's what we expect to happen. And here's how we're going to help you get there."

At St. Mary's, half the students get scholarships, subsidized by fundraising to defray the $8,000 a year tuition. Here, there's no test to get in, but expectations are high and rules are strict: no cellphones, modest skirts, hair must be its natural color.

Students Rayah Siddiq, Summer Forde, Carissa Washington, Tatum Williams and Christina Blazio told us they appreciate the rules and rigor.

Rayah Siddiq: Especially the standards that they set for us. They're very high. And I don't think that's ever going to change.

Bill Whitaker: So is there a heart, a philosophy, an essence to St. Mary's?

Summer Forde: The sisterhood—

Carissa Washington: Sisterhood.

Tatum Williams: Sisterhood.

Bill Whitaker: The sisterhood?

Voices: Yes.

Bill Whitaker: And you don't mean the nuns. You mean-- (laughter)

Christina Blazio: I mean, yeah. The community—

Bill Whitaker: So when you're here, there's just no question that you're going to go on to college.

Rayah Siddiq: College is all they talk about. (laughter)

Pamela Rogers: … and Arizona State University (Cheering)

Principal Rogers announces to her 615 students the colleges where every senior has been accepted.

Bill Whitaker: So for 17 years, you've had a 100% graduation rate—

Pamela Rogers: Yes.

Bill Whitaker: --and a 100% college acceptance rate?

Pamela Rogers: That's correct.

Last year when Ne'Kiya and Calcea graduated, all their classmates went to college and got scholarships. Ne'Kiya got a full ride to the pharmacy school at Xavier University in New Orleans. Calcea, the class valedictorian, is studying environmental engineering at Louisiana State University.

Bill Whitaker: So wait a minute. Neither one of you is going to pursue a career in math?

Both: No. (laugh)

Calcea Johnson: I may take up a minor in math. But I don't want that to be my job job.

Ne'Kiya Jackson: Yeah. People might expect too much out of me if (laugh) I become a mathematician. (laugh)

But math is not completely in their rear-view mirrors. This spring they submitted their high school proofs for final peer review and publication … and are still working on further proofs of the Pythagorean Theorem. Since their first two …

Calcea Johnson: We found five. And then we found a general format that could potentially produce at least five additional proofs.

Bill Whitaker: And you're not math geniuses?

Bill Whitaker: I'm not buying it. (laughs)

Produced by Sara Kuzmarov. Associate producer, Mariah B. Campbell. Edited by Daniel J. Glucksman.

Bill Whitaker is an award-winning journalist and 60 Minutes correspondent who has covered major news stories, domestically and across the globe, for more than four decades with CBS News.

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