Have you noticed a diatribe in my posting? Here's the latest "gem" from an OCT colleague:
While not really a theory, for me one of the most influential ‘models’ in shaping my approach to teaching is of doing so through problem solving. “By learning to solve problems and by learning through problem solving, students are given numerous opportunities to connect mathematical ideas and to develop conceptual understanding” (Ontario Mathematics Curriculum, p 11). I find it surprising that many colleagues still struggle with this model, uncertain as to implementation and misunderstanding the “time factor” (“that would take waaaaay too much work to do – I don’t have time for that”).
As I learned to follow a problem solving approach to teaching and learning, what was impactful for me was the realization that, by teaching students mathematical concepts through problem solving, I can incorporate many critical skills while also providing opportunities for students to learn, connect, and apply concepts in meaningful and purposeful ways. “Students who engage in problem solving build a repertoire of reasoning skills and strategies…Students who work together to solve problems learn from one another as they demonstrate and communicate their mathematical understanding.“ (Guide to Effective Instruction K-6, Volume 1, p 27) Teaching through problem solving also provides a means to incorporate different strands of the curriculum as well as to integrate math into other curriculum areas. Too, it offers me a flexible framework in which to consider students’ needs, strengths, prior knowledge, and learning styles when planning, allowing me to differentiate based on their individual/common needs.
A problem solving approach also establishes a learning environment that values students’ thinking, communication, and participation, making students feel important, respected, and appreciated as a group member. It supports students in feeling accepted and valued for their different strategies, methods, and perspectives in solving problems, fostering confidence in themselves and their abilities to be successful in math.