Mid-South Instructional Technology Conference
Teaching, Learning, & Technology
Transforming the Learning Environment
April 4-6, 2004
|
Dr. Dovie Kimmins |
Abstract
A variety of examples of the utility of computer software packages to visualize mathematical concepts and models in the areas of precalculus, geometry, probability, and calculus will be demonstrated. Technologies include Geometer's Sketchpad, Scientific Notebook, TI Interactive, Flash, and Camtasia. Examples will be presented in the context of research on visualization in mathematics and its relationship to deep learning. Time will be allowed for participants to discuss their use of technology to enhance deep learning via visualization.
Description
A variety of technological tools are available which can enhance students' visualization of mathematics. These include
* DYNAMIC GEOMETRY SOFTWARE such as Geometer's Sketchpad and Cabri which allow students to easily create a large amount of visual geometric data and examine it for patterns leading to the formulation of conjectures. Mathematical reasoning is enhanced as students construct their own geometric knowledge. In the same vein, TI-INTERACTIVE allows one to visualize the connections between the algebraic and graphical representations of functions and make conjectures concerning how changing parameters in the algebraic representation changes the graphical representation. Geometer's Sketchpad examples will be provided which will allow participants to visualize well-known and lesser-known geometric results. Examples of the ease of showing the connections of algebraic and graphical representations of functions via sliders in TI-Interactive will be demonstrated.
* COMPUTER ALGEBRA SYSTEMS such as Maple have 2- and 3- dimensional graphing capabilities which allow students to visualize and better analyze mathematical models which represent real world phenomena. The Maple kernel is embedded in Scientific Notebook. Examples of the analysis of mathematical models using the graphing capabilities of Scientific Notebook will be provided.
* ANIMATION PACKAGES such as Flash or Swish allow for the creation of movies using action script that captures the essence of certain mathematical phenoma. Examples of Flash movies showing exponential growth and decay at various rates and the nature of randomness will be shared.
* VIDEO PACKAGES such as Camtasia or Hypercam allow for the production of movies via screen capture. Used in conjunction with other resources including Geometer's Sketchpad, TI-Interactive or the Virtual Manipulatives website, instructors can easily create videos for distribution to their students on CD or on the web, allowing them to have ready access to the visualization experiences we want them to have. Examples of short videos produced by Camtasia in conjunction with Geometer's Sketchpad, TI-Interactive, and the Virtual Manipulatives website will be shared.
The above examples will be presented in the context of research on visualization in mathematics and its relationship to deep learning. Time will be allowed for participants to discuss their use of technology to enhance deep learning via visualization.