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Teaching: Investigating in the classroom

This information is for you as a teacher: some ideas for using these tours of discrete mathematics as a basis for teaching and learning through investigations in your classrooms.

We assume you have already investigated this material yourself in the role of tourist. We also assume that in working through the tours you have become familiar with the concepts of investigation that underlie the tours.

The suggestions below are meant for you to use as a guide for planning lessons that engage students in the activity of doing investigations. The suggestions are keyed to the information and activities accessible from each of the diamonds in the Navigation window.

Overall, the upper diamond focuses on a single problem. It maps out quite specifically one way that problem could be explored investigatively. This careful touring of a single, focused problem will help you and your students understand the activities of mathematical investigation—modeling, exploration, summary, etc. The Summary at the bottom of the diamond helps pose extension questions and problems that could be the focus of further investigation. With these questions in mind, you and your students can enter the bottom diamond and tour investigatively, switching back and forth among a variety of approaches.

In our suggestions, asterisks (*) mark areas that will require advance preparation of materials.

We suggest that you follow these steps in your teaching:

  1. Launch problem
  2. Model the problem
  3. Explore and conceptualize
  4. Summarize
  5. Generalize and abstract
  6. Critique
Click to continue the tour of teaching pages.

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