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

  1. More information about ClassPad  300, ClassPad Manager, eActivities can be found at http://classpad.net or http://classpad.org.
  2. The Free 30 days Trial of ClassPad Manager Professional Version 3 software can be downloaded at http://edu.casio.com.
  3. ClassPad 101 course contents can be viewed at www.classpad101.com.
  4. 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

e1

v1

2

Inv_Functions

Inverse Trig and Exponential Functions

e2

v2

3

Trig_Shifting1

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

e3

v3

4

Trig_Shifting2

Expansion, Compression and Shifting Techniques for Trig. Functions

e4

v4

5

Max_Triangle

Maximum Area of a Triangle

e5

v5

6

Slope_Tangent

Slope of the Tangent Line at a point

e6

v6

7

Derivative_sine_tan

About Derivatives of Sin(x) and Tan(x)

e7

v7

8

Limits

Limits (Piecewise-Defined Functions and Squeeze Principle)

e8

v8

9

Limit2

Finding Limits Using Geometric Approaches

e9

v9

10

Shrinking_Circle

A Shrinking Circle: A Limit problem

e10

v10

11

Epsilon_Delta

Epsilon and Delta Concept

e11

v11

12

Shortest_Dist1

Shortest distance between a point and a curve

e12

v12

13

Shortest_Dist2

Minimum Distance Between Two Curves

e13

v13

14

Ladder

A Ladder Problem

e14

v14

15

Rope

A Calculus Problem

e15

v15

16

Max_Rectangle

Maximum area of a rectangle under a curve

e16

v16

17

Max_Parallel

Maximum Parallelogram Bounded by Curves

e17

v17

18

Exp_Diff

Exponential Differentiation

e18

v18

19

Imp_Diff

Implicit Differentiation

e19

v19

20

Polar_Diff

Polar Differentiation

e20

v20

21

MVT

Mean Value Theorem (A Geometric Proof)

e21

v21

22

CMVT

Cauchy Mean Value Theorem (A Geometric Proof)

e22

v22

23

Riemann_Sum

Riemann Sum

e23

v23

24

Area_TwoCurves

Riemann Sum and Area Between Curves

e24

v24