In Saskatchewan our provincial curricula are built around one central core…inquiry. Inquiry is a philosophical approach to teaching and learning that empowers students to explore and discover. Through inquiry students are active participants in the creation of understanding and knowledge. They are asked to be curious, to wonder, to question, to reflect, to share and to think
In Mathematics inquiry is often seen through problem solving. By collaboratively solving and creating mathematical problems students construct and deepen their understandings of concepts, strengthen their strategic competence, and develop their logical reasoning skills. As students engage in problem solving they need to attend to 4 important stages in the inquiry/problem solving process:
Stage 1: Understand the Problem- This very important stage is often overlooked in the classroom. It is often assume that students understand the problem in front of them but this assumption can by costly. Without a solid understanding of what they are being asked to do, students are often stumped before they start. Time spent carefully dissecting a problem and ensuring understanding can be critical to success.
Stage 2: Make a Plan- Just like the construction of a building, the construction of a mathematical solution requires forethought and a plan. Having a carefully considered plan of attack can help students construct their solution successfully. Problem Solving plans or strategies can include:
- Acting it out
- Using a model
- Drawing a picture
- Guessing and testing
- Looking for a pattern
- Making a chart or a graph
- Working backwards
- Making an organized list
- Using logical reasoning
Stage 3: Carry out the Plan -In the words of Nike - Just Do It!
Stage 4: Look Back - This stage involves careful reflection, checking to see if your answer makes sense, and considering the solutions of others. Considering the solutions of others and comparing them to your own provides an opportunity for understanding and learning to be collaboratively constructed in the mathematics classroom.
For more information on Problem Solving in Mathematics check out these great resources:
Introduction to Problem Solving by Susan O`Connell