45 - Workshop Precalculus: Functions, Data, and Models

Summary

The Workshop Mathematics program [1], developed at Dickinson College, leads students to discover, explore, and apply fundamental concepts of introductory mathematics and statistics courses. Active learning is the distinguishing feature of the “workshop” pedagogical approach, which replaces lectures with activities through which students interact with each other, with technology, and with the instructor. This program has been extended from its beginnings in Calculus [2] and Statistics [3] to the precalculus level, supported by a grant from the National Science Foundation (#9952483). In this project, Nancy Baxter Hastings and I are developing materials for a course that integrates ideas of data analysis and mathematical modeling into the study of precalculus. The primary goal of the materials is to prepare students for calculus, primarily by helping them to develop a deep understanding of the crucial concept of function. A secondary goal, especially important considering that many precalculus students never go on to study calculus, is to develop skills of data analysis and mathematical modeling, which will be valuable for courses in other discliplines.

Some of the principles guiding the development of these materials are:

1. to focus on the concept of function as essential preparation for calculus;

2. to emphasize students' facility with multiple representations of functions (graphical, tabular, symbolic, verbal) throughout the course;

3. to integrate the study of data analysis and mathematical modeling with more standard precalculus topics;

4. to use genuine data and applications for motivating topics, activities, and exercises;

5. […]