**Integrating Dynamic Geometry with
Computer Algebra System **

-with the help of Casio ClassPad-

**Introduction**

When I first saw the ClassPad (CP) demonstrated by Hideshi Fukaya and Diane Whitfield in 2002, I was impressed by how much it can offer in Dynamic Geometry (DG) and Computer Algebra System (CAS). I had to admit that it took me a while to learn how to use the CP and later incorporate it into my regular teaching. One of the best ways to learn how to use software or a hand-held device is to see what other people have done. This is precisely why we are launching this project by providing a soft copy of each eActivity, which learners can modify to suit their needs using the ClassPad Manager software or the trial version. In the mean time, we are also including a brief video clip for each corresponding eActivity.

In this project, you will find 24 eActivities and corresponding video clips. It is a fact that evolving technological tools have prompted us to rethink the way we teach and learn mathematics. The eActivities cover topics from Pre-Calculus to Advanced Calculus. Each demonstrates how CP can help us learn traditional contents with ease and allow us to experiment and explore more mathematics along the way.

We often find ourselves lacking the time needed to apply why we learn Calculus. In this project, you will find many applications on optimization, finding limits and etc. For my general approach, I use graphical and geometrical animations to bring out the natural conjectures from a learner and later prove or disprove conjectures analytically with the help of CAS. It is natural to use graphical representations to make mathematics more accessible to more learners, which in turn gives motivation to solve a problem analytically. Once learners capture the essence of solving a problem, complicated manipulations can be done with the help of CAS.

I am fortunate to have Professor Jonathan Lewin giving me advice on this project and helping with the creation of some of the sound tracks. I would also like to sincerely thank CASIO staffs from MRD in Portland, USA and Tokyo, Japan for much assistance. Please excuse my not so perfect spoken English (in the video clips) and some errors you might find in the contents. I claim to not be an expert using CP here; my main goal of this project is to share how much a technological tool like CP has helped us in teaching and learning.

Wei-Chi Yang, Ph.D.

http://www.radford.edu/wyang

Professor of Mathematics

Radford University

Founder of the Electronic Journal of Mathematics

And Technology (eJMT, https://php.radford.edu/~ejmt/).

Founder of the Asian Technology Conference

In Mathematics (ATCM, http://atcm.mathandtech.org)

Notes

- More information about ClassPad 300, ClassPad Manager, eActivities can be found at http://classpad.net or http://classpad.org.
- The Free 30 days Trial of ClassPad Manager Professional Version 3 software can be downloaded at http://edu.casio.com.
- ClassPad 101 course contents can be viewed at www.classpad101.com.
- Before downloading and viewing the following video clips, be sure to turn down the volume level from your computer to avoid distributing your neighbor.

No. |
Folder Name |
Title |
eActivity |
Video Clips |

1 |
Unitcircle |
The Unit Circle and
Trigonometric Functions |
||

2 |
Inv_Functions |
Inverse Trig and Exponential
Functions |
||

3 |
Trig_Shifting1 |
About the graphs of a*sin(x), a*cos(x), sin(a*x) and cos (a*x)
and circles |
||

4 |
Trig_Shifting2 |
Expansion, Compression and
Shifting Techniques for Trig. Functions |
||

5 |
Max_Triangle |
Maximum Area of a Triangle |
||

6 |
Slope_Tangent |
Slope of the Tangent Line at a
point |
||

7 |
Derivative_sine_tan |
About Derivatives of Sin(x) and
Tan(x) |
||

8 |
Limits |
Limits (Piecewise-Defined
Functions and Squeeze Principle) |
||

9 |
Limit2 |
Finding Limits Using Geometric
Approaches |
||

10 |
Shrinking_Circle |
A Shrinking Circle: A Limit
problem |
||

11 |
Epsilon_Delta |
Epsilon and Delta Concept |
||

12 |
Shortest_Dist1 |
Shortest distance between a
point and a curve |
||

13 |
Shortest_Dist2 |
Minimum Distance Between Two
Curves |
||

14 |
Ladder |
A Ladder Problem |
||

15 |
Rope |
A Calculus Problem |
||

16 |
Max_Rectangle |
Maximum area of a rectangle
under a curve |
||

17 |
Max_Parallel |
Maximum Parallelogram Bounded by
Curves |
||

18 |
Exp_Diff |
Exponential Differentiation |
||

19 |
Imp_Diff |
Implicit Differentiation |
||

20 |
Polar_Diff |
Polar Differentiation |
||

21 |
MVT |
Mean Value Theorem (A Geometric
Proof) |
||

22 |
CMVT |
Cauchy Mean Value Theorem (A
Geometric Proof) |
||

23 |
Riemann_Sum |
Riemann Sum |
||

24 |
Area_TwoCurves |
Riemann Sum and Area Between
Curves |