Subject: Question 1 Author: Richard Sisley Date: 7 March 2001
Dear Professor Zhang,
I have been personally involved in designing a new sequence of courses for college bound students in the United States. Geometry is present in each of the four courses. The presence begins in course one on the first day with an introduction to transformations of the plane. Transformational geometry provides a line to algebra in many ways. It can also play a strong role in the study of elementary functions. For example, the graphs of all quadratic functions can be linked to the graph of the basic y = x^2 function by simple transformations. As another example, all exponential functions can be transformed onto each other with a type of transformation called in our materials a horizontal scale change.
The transformational linkage of functions can be used for several purposes, including introducing the Chain Rule for Derivatives in calculus.
Transformations are very teachable today if the students and teachers have access to, and make use of technology including graphing calculators and classroom computer displays using software such as the Geometer's Sketchpad.
I can provide you with more detailed information if you would like.