This sketch is the product of some ideas I had been mulling over after a Discussion Group at ICME 12, which I have had the pleasure to attend. The group is led by Scott Steketee of KCP Technologies, and the topic involves the early study of functions using geometric transformations in the dynamic geometry environment.

In the discussion, two minor points caught my attention. Many students find it difficult to discuss the function x*y. Many students have difficulty working with a broad notion of function - is eye-color a function? The dynamic geometry environment provides a neat way to explore other types of functions that reach beyond those with real variable domain and real variable range.

This sketch strays a bit from the basic transformations, but it does use the dynamic geometry advantage of being tactile and potentially unconcerned with numerical processing on the part of the user. That is, a student can grapple with the nature of a concept without performing calculations in the usual sense. In this sketch, the input or independent variable of the function is a point in the x-y plane. The output or dependent variable is the color of a circle. The color changes according to the product x*y.

Download (GSP 5 file): color_function_of_xy.gsp

Download GSP 4 file

In the discussion, two minor points caught my attention. Many students find it difficult to discuss the function x*y. Many students have difficulty working with a broad notion of function - is eye-color a function? The dynamic geometry environment provides a neat way to explore other types of functions that reach beyond those with real variable domain and real variable range.

This sketch strays a bit from the basic transformations, but it does use the dynamic geometry advantage of being tactile and potentially unconcerned with numerical processing on the part of the user. That is, a student can grapple with the nature of a concept without performing calculations in the usual sense. In this sketch, the input or independent variable of the function is a point in the x-y plane. The output or dependent variable is the color of a circle. The color changes according to the product x*y.

Download (GSP 5 file): color_function_of_xy.gsp

Download GSP 4 file

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