Improving Mathematical Problem Solving

Based on extensive research, the Institute of Education Sciences (IES) has published a practice guide that provides five recommendations for improving students’ mathematical problem solving. This guide is geared toward teachers, math coaches, other educators, and curriculum developers who want to improve the mathematical problem solving of students.

The foundation for success in advanced mathematics is built on problem solving skills. Problem solving requires strong skills in reasoning, analysis, and argument construction, and the ability to apply innovative strategies to find a solution.

To help students become skilled problem solvers, teachers can:

• prepare problems to use in whole-class instruction
• provide explicit problem-solving instruction that teaches students to use visual representations, employ multiple strategies, and links mathematical concepts and notation to problems
• allow time to reflect and debrief on their strategies and solutions with classmates

While these skills should be taught at all levels, it's especially important to help students develop them as progress toward the more complex math concepts they will learn in high school.
Problem solving skills are essential for students as they progress through the entire mathematics curriculum. Students who develop proficiency in mathematical problem solving early are better prepared for advanced mathematics and other complex problem-solving tasks. Unfortunately, when compared with students in other countries, students in the U.S. are less prepared to solve mathematical problems.
Problem solving involves reasoning and analysis, argument construction, and the development of innovative strategies. These abilities are used not only in advanced mathematics topics — such as algebra, geometry and calculus—but also throughout the entire mathematics curriculum beginning in kindergarten, as well as in subjects such as science.
Pepper has released a new workshop focused on Improving Mathematical Problem Solving as part of it’s new Pepper Online Workshop (POW!) content. By taking this workshop you will explore strategies to help students become skilled problem solvers. Participants will be understand and take a deeper look at the three components involved in teaching problem solving to students.

You can check all of our new POW content by visiting the Courses and Workshops section on your dashboard.

Design Thinking: Improving Schools, Empowering Students

What is Design Thinking? Design Thinking for educators is a creative process that helps students and teachers design meaningful solutions in the classroom, at your school, and in your community. According to Thomas Riddle, Assistant Director of Roper Mtn. Science Center, “design thinking is a human-centered approach to problem solving that begins with developing empathy for those facing a particular challenge.” In a nutshell, design thinking is a problem solving framework that allows students and teachers to take action, make mistakes, and learn from those mistakes.

In his article, Improving Schools Through Design Thinking, Riddle describes five main stages of Design Thinking that have been used in the business community, but can also be easily transferred to the education world:

1. Empathize - This is the foundation of design thinking. Empathy allows us to see and understand the needs of others. It forces us to look away from ourselves - seeing other viewpoints and demonstrating understanding towards those often differing views.
2. Define - Listen carefully to the problem at hand. Get input from those directly affected. Riddle explains, “Clearly defining the problem gives you a better chance at creating a clear solution.”
3. Ideate - This means to form an idea; to imagine or conceive. Oftentimes we call this the “brainstorming” phase. Students can be particularly innovative and excel at “thinking outside the box”.
4. Prototype - Putting the idea into a preliminary model - knowing that it may go through several changes and adaptations.
5. Test - Test the prototype and make adjustments. Be flexible and open to change.

Design Thinking can be a powerful tool for both students and schools overall. As educators and administrators, we too can use the design thinking process for learning and making improvements within our schools and communities. Riddle has an excellent follow up article on Edutopia titled Empowering Students with Design Thinking. Here he gives concrete examples of how he’s using design thinking with students.
Susie Wise, Director of the K12 Lab Network at the Stanford d.school, also notes that the last few years have shown an “explosion of interest in design thinking”. The spread of design thinking is showing up in both professional development opportunities for teachers and as challenges for students. Design Thinking in Schools provides a directory of schools and programs that use design thinking in the curriculum for K12 students.
Design thinking is a mindset. Your Pepper Professional Development Courses and Workshops can help you create a more engaged and active classroom that includes Design Thinking strategies and processes. We’re adding new courses and workshops regularly, so be sure to check them out.