This is the summary of a presentation given at the Joint Mathematics Meetings, January 10-13, 1996, Orlando, Florida.
Patterns, Functions, and Recursion for the Middle School Teacher
A "guess my rule" approach to functions dominates the elementary grades. Many functions which can be constructed with manipulatives are recursive in nature and the closed form of the function may not be easily determined. However, the recursive function expression reflects directly the representation of the concrete manipulatives. Elementary students should be exposed to recursive function expressions as well as the closed form, certainly by the middle school grades. Discrete mathematics uses recursion in its approach to functions. Spreadsheets and the graphing calculator, which build terms of the functions from an initial value and a sequencing pattern, offer effective means with which to explore functions. The opportunity to move quickly between the recursive form, seed and sequence in a table, and the graph of table values exhibit multiple representations of the function and often lead to a discovery of the closed form. A recursive approach also fosters exploration of different types of functions which otherwise would be postponed for study to a secondary mathematics class. This session will present functions for the middle school from a recursive viewpoint using manipulatives and the Tl-82 graphing calculator.
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