Why mathematical problem solving matters

The term problem solving originated in the United States in the 1970s to shift mathematical skills from an emphasis on back-to-basics towards using them to solve non-routine practical problems. In the content-based curriculum of earlier decades, the teacher worked through examples of how to apply set routines and a prescribed algorithm to show students how to find solutions to narrowly defined problems. The students’ role was to follow the teacher’s lead rather than to think more broadly about the problem.

Yet problem solving is about solving problems that you don’t know how to approach so it’s not problem solving if someone has already shown you the solution process. With true problem solving, the student:

• starts with an unfamiliar problem where the solution is not obvious
• usually needs to formulate a pathway to understand the nature of the problem
• works through that pathway to reach one or more solutions
• has the freedom to check that those solutions work.

This approach shifts the emphasis from a teacher-centred dynamic to empowering students to take ownership of designing their own method and verifying their answers. It becomes a challenge that students actually enjoy! Once they have mastered the basic mathematical skills required to solve problems, it is the application of those skills to solve intriguing real-life problems that is critical in the holistic study of mathematics.

It is difficult for teachers to find good questions, activities and problems in a format that we can use in targeted problem-solving lessons. As part of my approach to differentiating the classroom curriculum, I aim to structure the tasks to include extension sections for my high achieving students who need extra challenge. For a programme I have developed that follows this approach, see my series Maths Problem Solving for Higher Achieving Students.

Ian Bull