Advanced Mathematical Explorations in GSP
Introduction
Geometer's Sketchpad uses dynamic geometry (DG) to allow students to explore the geometric world outside of 2-dimensions. The term dynamic geometry, originally coined by Nick Jackiw and Fileve Rasmussen, has quickly entered the literature as a generic term because of its aptness at characterizing the feature that distinguishes DG from other geometry software: the continuous real-time transformation often called 'dragging.'" (Goldenburg & Cuoco, ) This allows students to make alterations to the picture to observe what effects the movements have on the rest of the picture.
In this unit you will explore proofs and explore how dynamic geometry can be used in a mathematics classroom.
Unit Objectives
- Demonstrate an understanding of the capabilities of GSP in a mathematics classroom
- Create a proof of the Pythagorean Theorem using GSP
- Use a pre-designed program to explore solving algebraic equations for a variable
- Demonstrate an understanding of possible misconceptions students may have using GSP
Lesson Activities
Creating a proof for the Pythagorean Theorem
Now that we have gotten the basics down in GSP we want to explore how a teacher could design whole lessons are the program. Here we will design a Pythagorean Theorem proof that will allow students to drag the segment lengths to explore various sizes of triangles. Once the program is made it could be saved and used over and over to remind students about the theorem and where it comes from.
To begin click: File:Pythagorean.pdf
Think about what types of discussion topics this could bring about:
Since the Pythagorean Theorem is: 
. How can students explain how the equation uses the square of a, b, and c? This is an excellent way to discuss how "a squared" comes from creating a square.
For further exploration: Create triangles and half-circles on each side of the original triangle to explore if these still hold a similar relationship
REMEMBER: LEARN THROUGH EXPLORATION. TRY NEW THINGS AND EXPLORE THE TOOLS THAT THE PROGRAM GIVES YOU BEFORE YOU MOVE ON!
Using a pre-designed program for Mathematical exploration
Here we will use a program designed by Geoemeter's Sketchpad.
To download the program click : [1]
This download includes a .gsp program and a pdf with walkthrough guides.
Explore this program. Look for limitations, possible misconceptions that students may have, and how this may help students who are visual learners.
When finished post some ideas and thoughts to the class discussion board: Math&Tech Discussion Page.
References:
Goldenberg, E. P., & Cuoco, A. A. (1998). What is dynamic geometry? In R. Lehrer & C. Chazan (Eds.), Designing learning environments for developing understanding of geometry and space (pp. 351-367). Mahwah, NJ: Lawrence Erlbaum Associates.
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