What is Open-Ended Problem Solving?

What is Open-Ended Problem Solving? In open-ended problem solving, the problem will have multiple possible answers that can be derived by multiple solution methods. The focus is not on the answer to the problem, but on the methods for arriving at an answer. Genuine problem solving requires a problem that is just beyond the student’s skill level so that she will not automatically know which solution method to use. The problem should be nonroutine, in that the student perceives the problem as challenging and unfamiliar, yet not insurmountable (Becker & Shimada, 1997).
 

In open-ended problem solving, students are responsible for making many of the decisions that, in the past, have been the responsibility of teachers and textbooks. To decide which method, or procedure, to undertake to solve an open-ended problem, a student will draw on her previous knowledge and experience with related problems. She might construct her own procedure, trying this and that, before arriving at a solution. She will then reflect on and explain to others her problem-solving experience, tracing her thinking process and reviewing the strategies she attempted, determining why some worked and others didn't. This period of reflection deepens her understanding of the problem and helps to clarify her thinking about effective solution methods, and how the problem and methods she used relate to other problems or areas of mathematics.

One of the teacher’s key responsibilities is selecting and presenting “good” problem tasks. By choosing good problems, the teacher sets up optimal conditions for her students to be engaged in meaningful problem solving. This means that the problem will:

• Be open-ended, in that it presents multiple solution methods and answers
• Address important mathematics concepts
• Challenge and interest students
• Connect to students’ previous learning

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