Problem Solving Activities for Students

To build strong problem solving skills, students need to challenge themselves. While instruction and guidance are highly valuable resources, it’s necessary to combine them with hands-on projects and activities — in both individual and group contexts — that push students to discover strategies and solutions that work for them. 

Below, we discuss the importance of problem solving skills for high school students, provide resources for finding different types of problem solving activities, break down the skills developed through solving complex problems, and even talk about common frustrations that students may experience and how to push through them for sustained growth.

Why Problem Solving Skills Matter

Individual and collaborative problem solving skills build academic resilience and intellectual adaptability, strengthen career readiness, and enhance students’ self-confidence levels. Being able to effectively frame, approach, understand, and work on a problem from multiple angles is a crucial soft skill for growth in both classroom learning and hands-on research contexts. According to Stanford professor Carol Dweck, students who lack these skills tend to believe their intellectual abilities are fixed, and as a result, tend to shy away from tough problems. Developing and maintaining a growth mindset — that is, viewing problems as opportunities to learn rather than as obstacles to progress — enables students to process errors more deeply and correct more quickly compared to students with fixed mindsets. This cognitive resilience and flexibility empowers students to set and achieve significant goals, resolve conflicts, and tackle increasingly complex problems in academics as well as in their future professional careers.

Types of Problem Solving Activities

One of the most effective strategies for building problem solving skills is to practice Project-Based Learning (PBL). PBL teaches students to identify and understand complex problems, hypothesize potential solution paths, and iterate based on outcomes and feedback. In addition to PBL, students can engage in targeted problem solving activities that challenge them to practice critical skills and build new techniques quickly.

Logic challenges push students to think critically and practice logical reasoning, which is the foundation for professional fields such as computer science, law, medicine, and engineering. The International Logic Olympiad (ILO) offers logical reasoning resources and useful practice tests that students can use to build problem solving skills over time. The Introduction to Logic course at Stanford also has open resources and sample problems. For even more logic challenges, visit the website of Philip S. Thomas, Associate Professor and Co-Director of the Autonomous Learning Lab at the University of Massachusetts, Amherst.

Design problems require students to engage in “design thinking”, a term that continues to expand in meaning throughout technological practice but which generally refers to an iterative and non-linear approach to understanding people and processes. Researchers have described design problems as “underdetermined problems” because although they are partly determined by unalterable need, they are, in a sense, “open” — which means that they don't have a singular correct answer. In design contexts, problem solving “involves the seeking of opportunities, and of building up expectations,” according to Kees Dorst, Professor of Transdisciplinary Innovation at the University of Technology Sydney. One way for students to gain hands-on experience working on design projects is by prototyping solutions to problems in their own daily environments. This could take the form of a physical design, an app, or even an artistic design.

Collaborative tasks can greatly enhance students’ problem solving skills. As mentioned above, there are two main categories of problem solving skills: individual and collaborative. Collaborative problem solving means working with a group to collectively address a challenge. This type of problem solving is much more complex and can be a powerful tool for businesses, organizations, and researchers. Collaborative problem solving requires training additional soft skills including:

• Communicating through verbal and written systems

• Identifying and utilizing individual strengths within a team

• Providing and receiving constructive criticism

To build collaborative problem solving skills, students should work together in small groups of 2-3 peers to practice completing logic and design problems as a team.

Skills Developed Through Problem Solving

Problem solving activities strengthen multiple soft skills such as:

• Creativity

• Strategic thinking

• Collaboration

According to Harvard Business School, creative problem solving involves the following key principles:

• Balancing divergent thinking (i.e. generating ideas or brainstorming) and convergent thinking (narrowing options down to shortlist of ranked solutions)

• Framing problems as questions

• Deferring judgment of ideas until they’ve been explored and tested

• Favoring "Yes, and" Instead of "No, but" though processes to encourage innovation

In addition to building creativity, solving complex problems help students build strategic thinking skills. These skills empower students to:

• Ask strategic questions (e.g. “How can I best position myself for success when facing new challenges?”)

• Observe and reflect (e.g. gathering as much data and information as possible to ensure evidence-based approaches)

• Consider opposing ideas (e.g. playing devil’s advocate with their own ideas and assumptions)

Finally, engaging in collaborative problem solving activities helps students learn to communicate effectively. Communication skills include listening, speaking, reading, and writing. Working on solving problems in groups teaches students to practice what McKinsey & Company terms “contributive dissent”. In other words, through these challenges, students learn to equip themselves with the communication skills necessary to express disagreement in a way that moves the conversation forward, driving innovation while maintaining group cohesion.

Common Student Frustrations

When working on problem solving activities, many high school students face common frustrations. For example, as discussed above, many open-ended design problems have no singular, clear solution. This lack of clarity can present a challenge to many high school students who are accustomed to “closed” challenges such as mathematical problems, to which there is often only one correct answer. For students who struggle to stay focused when working on open-ended problems, it can be useful to borrow a technique from PBL, and ask yourself the following questions:

• What information do you already have about the problem?

• What information do you need to solve the problem?

• What strategies are available to you to employ when solving the problem?

• What are the criteria for a complete solution to the problem?

Keeping in mind the answers to the above questions can help students build and maintain positive momentum.

Limited feedback is another source of student frustration. High school students are often accustomed to receiving direct and individual feedback from teachers throughout the process of working on a problem. In situations where access to feedback and support is more limited, many students can feel a) stuck, b) directionless, c) unmotivated, or d) a combination of some or all of the above. In this case, it can be highly rewarding to work with an experienced mentor who can help students push through difficult stages.

Fear of failure is another tricky challenge that students often face when working on complex problems. The New York Times suggests the following helpful steps for students struggling with fear of failure:

1. Put your failure into context. When you make a mistake, try reframing it as a necessary and meaningful life experience. This strategy can prevent panic and generate personal growth.

2. Learn how to pivot. Instead of viewing setbacks as dead-ends, practice imagining possibilities and changing directions on the fly.

3. If you fail, share about your experience. We can all learn from one another’s mistakes, and learning to open up about failure is a part of being fully honest and vulnerable.

How Projects Strengthen Problem Solving

Projects are essential for supporting the development of problem solving skills. High school students who engage in projects with logic-based components build critical and logical reasoning skills that set them up for success in careers ranging from law to computer science. Through iteration and experimentation, students who work on design projects continuously build intellectual curiosity, resilience, and adaptability, as well as nonlinear thinking skills that will benefit them in future research and business contexts.

Another important reason for students to work on projects is that they get to completely own the outcomes and results. Hands-on independent projects can feel more directly rewarding than classroom-based learning or theoretical assignments.

Conclusion

Problem solving improves continuously with practice, leading to stronger skills that enable students to solve increasingly complex challenges. Polygence is a unique space for highly curious students to build hands-on problem-solving skills through independent and mentored Project-Based Learning.

Our Research Mentorship Program connects high school students with experienced, PhD-level mentors for guided projects based on students’ own academic passions. Each participant gets ten individual sessions with their research program mentor, as well as access to writing support and showcasing support to help them show off their successful projects in competitions, publications, presentations, and future applications.

Additionally, our Work Lab program places advanced high school students within cutting-edge startup companies for rigorous projects focused on gaining industry experience. Participants work alongside founders on a real-world project leading to impacts in areas such as tech, healthcare, sustainability, and more.

For students seeking to gain foundational knowledge and learn about research skills and methodologies, we developed Polygence Pods. These fast-paced courses group students with a small group of like-minded peers united by a shared passion for a cutting topic. Recent Pods topics have ranged from AI in STEM to Venture Capital.

Apply now to start solving challenging problems with support from Polygence!