Using a problem solving approach to teaching and learning maths is of value to all students and especially to those who are high achieving. Some of the reasons for using problem solving are summarised below.
- Problem solving places the focus on the student making sense of mathematical ideas. When solving problems students are exploring the mathematics within a problem 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 successes 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.
- Once students understand a problem solving approach to maths, a single well framed mathematical problem provides the potential for an extended period of exploration.