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Using Programming to Teach Mathematical Generalization

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Making generalizations and writing general expressions is an essential skill in mathematics. Developing this skill and making it a "habit of mind" for the learner is an elusive goal for math educators, yet this skill is vital, not only in the classroom, but in society. There are several meanings attached to generalization in the literature. It can be seen as a process, going from naming a member of the group to describing all members of the group. For example, going from naming an odd integer as 1, 3, or 5 to describing all odd integers as 2k+1, where k is any integer. The expectation is that generalization skills will develop in the mathematics classroom. However, explicit methods for teaching generalization are rare. The CPR2 project examines the effectiveness of an explicit instructional strategy using computer programming to teach participants to write general expressions. The participants are in-service middle and high school teachers (and their students) participating in professional development sessions to improve mathematical reasoning.