By Samuel Moy
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Extra resources for An introduction to the theory of field extensions
Where had the time gone—the bell was going to ring any minute. I told the students that for homework I wanted them to come up with a way to calculate the perimeter of the thirtieth train and any other train we could come up with. I thought that this would push us toward more formal ways of recording calculations and, ultimately, generalizations. 17 18 Using Cases to Enhance Learning Reflecting on Class Later That Day 29. The lesson was all I could have asked from the kids! They found the perimeters of the trains and were even making progress on finding generalizations.
In it, we offer suggestions on ways to connect the specific ideas investigated in “The Case of Catherine Evans and David Young” to a set of larger issues that can be explored in your own classroom. Building on your analysis of “The Case of Catherine Evans and David Young,” the activities presented in this section provide opportunities for focused reflection on issues that might be important to your own teaching of mathematics. • • In the “Analyzing the Case” section, you identified similarities and differences between Catherine Evans’s and David Young’s classrooms.
The following list identifies resources that contain problems that are considered to be “mathematically similar” to the task used in Catherine Evans’s and David Young’s classes. , & Williamson, J. (1999a). Middle grades math thematics: Book 1. Evanston, IL: McDougal Littell. Of particular interest is an exploration (pp. 6–7) in which students determine the generalization for two visual patterns made from square tiles. Education Development Center, Inc. (1998c). MathScape: Patterns in numbers and shapes: Using algebraic thinking (Student guide).
An introduction to the theory of field extensions by Samuel Moy