As part of an N.S.F. funded project we have been developing software that uses the Harvard approach to reform calculus for teaching precollege algebra topics. The two fundamental principles of the reform calculus approach are:
The spreadsheet is the ideal environment for software that follows the Harvard approach. Spreadsheets naturally apply functions to tables of numbers and thus demonstrate numerical properties of functions. They also are designed to present numerical data graphically. Finally they also are quite effective at manipulating text strings thus allowing presentation and English descriptions of algebra. I have developed a package of spreadsheets that interactively present topics from the precalculus curriculum. For example, one of the spreadsheets demonstrates function addition subtraction and composition. Linear functions are presented both as slopes and intercepts and as tables. A keystroke generates a combination of two functions. A discussion of how to perform the combination is presented on the side of the screen. The spreadsheet presents the combination of slopes, followed by the tabulation of the combined function. At any time, the students can see the graph of the linear functions and their combination. Another enhancement to the precalculus curriculum is group projects in data modeling. Such projects force the students to understand data and use graphical, numeric and algebraic approaches to the data. The students develop linear quadratic and exponential models of a public domain data set for 3 projects. They performed algebraic manipulation in constructing the models, graphical manipulation when presenting the models and numerical analysis when measuring the error between their models and the actual data. Spreadsheets speed development of data models and avoid the tedious calculations involved in constructing them.