These learning activities lead the student in an exploration of linear, exponential and sine and cosine functions and provide them with experience using these functions to model actual data.
Type of Material:
Modeling and exploration
student tutorial, outside of class assignment
Requires one of: Mathcad, Maple, Mathematica, Matlab
Identify Major Learning Goals:
In one module, the successful student will learn how the slope of the line in the equation is related to the graph of the line and how b is related to the y-intercept. The student will be familiar with the graph of the line. In two modules, the student will discover the relationship between three different bases for exponential functions. The last two modules address the concepts of amplitude, period and translation of sine and cosine functions.
Target Student Population:
Students in PreCalculus
Prerequisite Knowledge or Skills:
Some familiarity with computer-assisted learning.
Evaluation and Observation
These activities contain both web-based lessons and worksheets to accompany them. These worksheets are created for each software package so that the users may select those appropriate for their available software. The activities are clearly stated and incorporate actual data that strongly fit the model. The accompanying worksheets allow the student to explore the data, equations, and the graphs. Each lesson includes an introduction, exploration, and a summary of the lesson with several thought-provoking questions. These assignments include a significant writing component that allows the student to express his/her observations and conclusions as they relate to the data and his/her knowledge of the application.
The modules are complete for Mathematica, Matlab and Maple. However, the users of Mathcad will find that the tutorial and Functions Defined by Data modules are not available. Since these two modules together describe the basic graphing functions for the software, the Mathcad user must be experienced with these capabilities. The Radioactive Decay module, a prerequisite for the Radioactive Waste module, is also absent for the Mathcad user.
Potential Effectiveness as a Teaching Tool
These activities are a wonderful tool to teach students how linear and exponential functions, sines, and cosines can be used to model data. The period, amplitude, and translation of the sine and cosine functions are introduced with these worksheets. A comparison of the bases b, 2 and e is made in the exponential modules. The linear applications use data to develop the concepts of slope and intercept in the equation of a line. The computer activities work as a critical thinking component of the pre-calculus course. Significant writing components are included in each module where students are asked to explain the concepts as they apply to the application.
None. The data provided is becoming dated (1992 and 1997). For the most part, the applications are interesting and this use of older data is not a concern.
Ease of Use for Both Students and Faculty
The activities described on the web notes are easy to follow. They include enumerated questions for the students to explore. The worksheets are easily downloadable. They begin with a fully worked out example and then provide all of the lines of code with a few parameters replaced by question marks for the students to fill in. There is a tutorial that explains the basics of functions and graphing.
The Helper Application Tutorial does not include how to work with data. Although some help is presented in the Functions Defined by Data, the Helper Application Tutorial would be an appropriate place to explain how to use the various software applications to enter and graph data. This would make the Helper Application Tutorial the only prerequisite to the rest of the modules