Facilitating Problem Solving Math in the City/Akron

Incorporating Problem Solving into Instruction Teaching for problem solving – Often starts with learning the abstract concept and then moving to solving problems as a way to apply the learned skills. – Many textbooks follow this format. Teaching about problem solving – Involves teaching students how to problem solve, which can include teaching the process (e.g., Polya’s How to Solve It: understand, design a strategy, implement, look back) or strategies for solving a problem.

Incorporating Problem Solving into Instruction Teaching through problem solving – Students learn mathematics through real contexts, problems, situations, and models. – The contexts and models allow students to build meaning for the concepts so that they can move to abstract concepts. – Described as upside down from teaching for problem solving— with the problem(s) presented at the beginning of a lesson and skills emerging from working with the problem(s). Van de Walle. J.A., Karp, K.S., and Bay-Williams, J.M. (2010). Elementary and Middle School Mathematics: Teaching Developmentally (7 th ed.). Boston, MA: Allyn & Bacon.

Teaching Through Problem Solving Let Students do the Talking – Manage Conversations Walking the Fine Line – What to Tell and What Not to Tell Student Writing – Reflective, rehearsal for discussion, written record Metacognition – Promote the conscious monitoring and regulation of meanings and reasoning Disposition – Attitudes and beliefs about mathematics, doing mathematics, and abilities to do and understand the nature of mathematics