Learning Through Problem Solving

A New Way of Thinking...

There has been a significant shift in recent years with the way math is run in the classroom.  Rather than the traditional teacher-centered approach math classes are taking a student centred approach. Students become active participants in the learning process and teachers take on the role of a facilitator.  Allowing students to take on this role and shifting the role of the teacher  occurs when teachers are able to teach through problem solving.  Rather than prescribing certain algorithms and methods of solving the problem, teachers probe, ask questions and organize student work in order to help the students consolidate, connect, learn new algorithms, concepts and strategies. While teachers have certain learning goals in mind they allow students the freedom to attack the problem anyway they wish and encourage them to reconsider their strategies to find better more efficient ones. Students also take much more of an active role. They are able to draw on previous knowledge, test out different strategies, teach each other, ask lots of questions and compare their work to enhance their learning. 

Problem-based learning goes well beyond these short-term instructional instances or simple questions. It encompasses a rethinking of the entire curriculum so that teachers design whole units around complex, "ill-structured" problematic scenarios that embody the major concepts to be mastered and understood. (Bellanca and Brandt 178)

The single most important principle for improving the teaching of mathematics is to allow the subject of mathematics to be problematic for the students. That is, students solve problems not ot paply mathematics, but to learn new mathematics. (Hiebert et al. cited by Van de Walle 11)