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“ A → E ” “ A pproaching…but not E qual to…” A Dynamic Visualization Tool for introducing the Concept of Limits to Pre-calculus Students Yunn Chyi Chao. y. 4. x. Given y = 4(1 – e -x ), When x gets larger, what is y?. “Infinity-ness” !!. y. 4. “Infinity-ness” !!. x.

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Presentation Transcript

A→E”

“Approaching…but not Equal to…”

A Dynamic Visualization Tool for introducing the Concept of Limits to Pre-calculus Students

Yunn Chyi Chao

4

x

Given y = 4(1 – e-x),

When x gets larger, what is y?

“Infinity-ness” !!

4

“Infinity-ness” !!

x

Learning Problem:

How to help students to understand the asymptotic property of “approaching…but not equal to….”

• Approach

• An interactive software tools “A→E”

• Using perspective 3D visualization

• Learning activities

• Using this tool as the media for exploration

Press run to start…

Numerical Data Panel

Press run to start…

Extend to infinity

Design Principles:

Perspective 3D Visual Display

Make explicit the experts’ experience!

Press run to start…

2.333

3.444.

5..66

10.44

0

0.1

0.2

0.3

0.4

Animation

Processing…

2.333

3.444.

3.666

3.777

3.8888

3.8899

0

0.1

0.2

0.3

0.4

2.4

344

Animation

Processing…

Processing…

0

2.333

3.444.

3.666

3.777

3.8888

3.8899

3.900

3.991

3.6777

234455

0

0.1

0.2

0.3

0.4

2.4

344

34

4455

E3e

234

y1

.

.

.

y1

.

.

.

.

.

.

X1

.

.

.

x1

Y = 4(1- e-x)

When x = x1,

Y = 4(1- e-x1)

Tracking and Details

y1

.

.

.

y1

.

.

.

.

.

.

X1

.

.

.

x1

Direct Manipulation

Grid – interval analysis

• Conclusion:

• A tool will not be useful if used without

• Meaningful learning activities

• Passionate teachers

• Right learning environment