Why Do Problem Solving?
- Problem solving places the focus on the student making sense of mathematical ideas. When solving problems students are exploring the mathematics within a probem context rather than as an abstract.
- Problem solving encourages students to believe in their ability to think mathematically. They will see that they can apply the maths that they are learning to find the solution to a problem.
- Problem solving provides ongoing assessment information that can help teachers make instructional decisions. The discussions and recording involved in problem solving provide a rich source of information about students' mathematical knowledge and understanding.
- Good problem solving activities provide an entry point that allows all students to be working on the same problem. The open-ended nature of problem solving allows high achieving students to extend the ideas involved to challenge their greater knowledge and understanding.
- Problem solving develops mathematical power. It gives students the tools to apply their mathematical knowledge to solve hypothetical and real world problems.
- Problem solving is enjoyable. It allows students to work at their own pace and make decisions about the way they explore the problem. Because the focus is not limited to a specific answer students at different ability levels can experience both challenges and sucesses on the same problem.
- Problem solving better represents the nature of mathematics. Research mathematicians apply this exact approach in their work on a daily basis.
There are several reasons why it is important to do problem solving or to take a problem solving approach to mathematics, especially with more able students. We discuss these under three headings below: to benefit the student, to better represent the subject and to benefit the teacher.