Manipulatives are things which are held and moved and represent or model mathematical ideas. With them, one can "hold" ideas in one's hands making the abstract more concrete.

Go see Graphing w/Manipulatives NOW to see what I'm talking about! Or if you are more sedate, read: Exploring Functions, the abstract and handout.

These manipulatives are an elegantly simple way of thinking about ideas usually discussed in algebra I, algebra II, precalculus and calculus. The manipulatives provide the tools. The book Exploring Functions through The Use of Manipulatives tells you how to use them and contains a set of masters.

•Exploring Functions through the Use of Manipulatives, written by Agnes Azzolino, is a collection of activities and a set of masters for exploring functions in a hands-on approach. Communication and introduction to functions, translation, reflection, and dilation of functions, solution of equations and systems, slope, and the composition of functions are explored at length. An appendix containing a function library and masters of the Graphing With Manipulatives are included. ISBN: 0-9623593-3-5, 100 pg., 1994

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