Teaching THROUGH Problem Solving?

What does teaching through problem solving really mean?

Before diving into conversations about teaching math through problem solving, let’s get a good understanding of what is meant by teaching math via this approach. Small (2008) suggests that “to teach through problem solving, the teacher provides a context or reason for the learning by beginning the lesson with a problem to be solved and later drawing out any necessary procedures” (p.38). Van de Walle and Lovin (2006) states that as students work on and engage in well-chosen problems and focus on the methods to finding a solution (and not solely on getting the correct answer), the result is a new understanding of the mathematics that is embedded in the task. As students ‘problem solve’ to find the solution, they look for relationships among numbers, patterns, testing out different methods, inventing their own methods, justifying their results, evaluating other’s work and most importantly, they are necessarily and optimally engaged in reflective thought about the ideas that are involved. Van de Walle and Lovin (2006) states that “students solve problems to not only apply mathematics, but to learn new mathematics” (p. 11). Small (2008) notes that teaching math in this way allows students to apply and adapt their new skills to different situations due to the fact that students get more opportunity to “mathematize real life situations” (p.38).