Teaching Strategies
Structured problems solving
The general form of lessons I will use in this unit will be centered on structured problem solving. This is different from a typical gradual release lesson format where students are taught a strategy explicitly, practice the strategy with heavy teacher guidance, and then eventually apply it through independent practice. In a problem-based format, students are presented a problem to be first worked on independently. Here students will apply their own mathematical knowledge in an effort to develop strategies to reach a solution. Once students have had time to work independently, their different strategies and solutions are shared and discussed in groups or as a class. During this time, students will be able to see multiple approaches, discuss misconceptions, and come to new conclusions about the material. The discussion must be carefully facilitated in order to reach the desired outcomes for the lesson. If all student ideas have been exhausted and the strategies or understandings the lesson set out to achieve have still not been reached, a different task must be presented. Finally, the students are given a set of additional problems to apply and practice what they learned from the problem solving and the discussion. The key idea behind a structured problem solving approach is that students are first given the opportunity to reason and construct their own concepts and strategies, which leads to a deeper understanding of the content covered in a given lesson. In the pursuit of nurturing new ways for students to think about large numbers, this approach will be fundamental.
Structured problem solving is laid out in Akihiko Takahashi’s paper titled, “Characteristics of Japanese Mathematics Lessons”. Takahashi stresses that in addition to the attention devoted to extensive discussion, the selection of problems and activities needs to be carefully considered as well. (Takahashi 2006) The progression of problems in this unit is designed to bring out concepts and strategies that cohesively build on each other. In general, each lesson will present a new problem context for students to solve. The problems are designed to have a question of high interest or a compelling visual to build student investment in the task. After the structured problem-solving process has taken place, students will be given some decontextualized examples to focus more in on the number concepts. These exercises will give students the opportunity to process, apply, and generalize the previously discussed strategies and understandings.
Some of the tasks I will use in each lesson are detailed in the following section.
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