ABSTRACT
Nothing provides as concrete a model as using the students themselves for points on a plane. My students no longer ask why calculators don’t draw the expected graphs. After anticipating and then observing where one equation and then another will send their classmates, they can visualize clearly what certain operations do to graphs. Later, when we use the calculator, they can envision people marching around inside their calculator at their command. One of the biggest payoffs for me and for students is that we encounter the idea of analytic geometric transformations early in the year. Using graphing calculators later just fl avors the pot. Our analogies carry on for years of future math classes.
