Reys Ch. 6

What does it mean to teach math through problem solving? What "signposts" for teaching guide this approach?

Teaching math through problem solving is a teaching approach in which students are confronted with problems, supported in their attempts to solve the problem, and aided to discuss and incorporate the learning that results. The primary goal is to ensure that students make sense of and remember the math they are learning so as to use them appropriately in unfamiliar situations. There are three "signposts" for teaching that guide this approach. Signpost one says to allow math to be problematic for students. It is important for students to be presented with challenging problems and to struggle. This approach allows students to think of strategies and to examine those strategies in which they use. Students math abilities will grow from having a challenge. Signpost two suggest to focus on the methods used to solve problems. Students should be encouraged to communicate their methods to each other. Students deepen their understanding by thinking about approaches and which are easier, harder, or most appropriate for the problem. Signpost three advises the teacher to tell the right information at the right times. When teachers are using a problem solving approach to help their students learn, the teacher needs to know when to let the students figure some things out for themselves. This signpost is very similar to the first one, letting math be problematic. If the teacher explains thing completely and clearly in the beginning the students may not be challenged enough to grow in their understanding. This signpost also focuses on the importance of discussions in the classroom and to teach fundamentals. Fundamentals such as, math symbols and language need to be taught first because the students will not discover these things for themselves.