1 / 16

Introducing Limits: A Dynamic Visualization Tool for Pre-Calculus Students

This article presents “A→E”, an interactive visualization tool designed to help pre-calculus students grasp the concept of limits. Utilizing 3D perspective visualization, the tool illustrates the asymptotic property of "approaching but not equal to". Students can explore the function y = 4(1 - e^(-x)) as x approaches infinity, enhancing their understanding through engaging learning activities. The article emphasizes the importance of facilitating meaningful explorations with passionate teachers in the right learning environment to maximize effectiveness.

wynne-grimes
Télécharger la présentation

Introducing Limits: A Dynamic Visualization Tool for Pre-Calculus Students

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. “A→E” “Approaching…but not Equal to…” A Dynamic Visualization Tool for introducing the Concept of Limits to Pre-calculus Students Yunn Chyi Chao

  2. y 4 x Given y = 4(1 – e-x), When x gets larger, what is y? “Infinity-ness” !!

  3. y 4 “Infinity-ness” !! x Learning Problem: How to help students to understand the asymptotic property of “approaching…but not equal to….”

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

  5. Input Panel Press run to start… Numerical Data Panel

  6. Perspective 3D Visual Display Press run to start…

  7. Focus (close inspection) Extend to infinity Design Principles: Perspective 3D Visual Display Make explicit the experts’ experience!

  8. Animation Press run to start…

  9. 0 2.333 3.444. 5..66 10.44 0 0.1 0.2 0.3 0.4 Animation Processing…

  10. 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…

  11. 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

  12. Tight - coupling y1 . . . y1 . . . . . . X1 . . . x1

  13. Given the function Y = 4(1- e-x) When x = x1, Y = 4(1- e-x1) Tracking and Details y1 . . . y1 . . . . . . X1 . . . x1

  14. Press run to start… Direct Manipulation

  15. Press run to start… Grid – interval analysis

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

More Related