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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
slide1

“A→E”

“Approaching…but not Equal to…”

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

Yunn Chyi Chao

slide2

y

4

x

Given y = 4(1 – e-x),

When x gets larger, what is y?

“Infinity-ness” !!

slide3

y

4

“Infinity-ness” !!

x

Learning Problem:

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

slide4

Approach

  • An interactive software tools “A→E”
  • Using perspective 3D visualization
  • Learning activities
  • Using this tool as the media for exploration
slide5

Input Panel

Press run to start…

Numerical Data Panel

slide6

Perspective 3D Visual Display

Press run to start…

slide7

Focus (close inspection)

Extend to infinity

Design Principles:

Perspective 3D Visual Display

Make explicit the experts’ experience!

slide8

Animation

Press run to start…

slide9

0

2.333

3.444.

5..66

10.44

0

0.1

0.2

0.3

0.4

Animation

Processing…

slide10

0

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…

slide11

Animation

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

slide12

Tight - coupling

y1

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y1

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X1

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x1

slide13

Given the function

Y = 4(1- e-x)

When x = x1,

Y = 4(1- e-x1)

Tracking and Details

y1

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y1

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X1

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x1

slide14

Press run to start…

Direct Manipulation

slide15

Press run to start…

Grid – interval analysis

slide16

Conclusion:

  • A tool will not be useful if used without
  • Meaningful learning activities
  • Passionate teachers
  • Right learning environment
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