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# Visualizing Mathematical Ideas With Technologies (page 4)

By Pearson Allyn Bacon Prentice Hall
Updated on Jul 20, 2010

### Fathom Dynamic Statistics Software (by Fran Arbaugh)

Like TinkerPlots for elementary and middle grade students, Fathom Dynamic Statistics Software (Finzer, Erickson, & Binker, 2001) allows high school students access to powerful tools for making sense of large data sets.

### Visual Geometry With Geometric Supposer

One of the best-known visualization tools is Geometric Supposer (http://cet.ac.il/ math-international/software5.htm), a tool for making and testing conjectures in geometry through the process of constructing and manipulating geometric objects and exploring the relationships within and between these objects (Schwartz & Yerushalmy, 1987). Geometric Supposer allows students to choose a primitive shape, such as a triangle, and construct it by defining points, segments, parallels or perpendiculars, bisectors, or angles (Yerushalmy & Houde, 1986). The program plots and remembers each manipulation and can apply it to similar figures. For example, if the students conjecture that “a median drawn from the vertex of any triangle to the opposite side bisects the angle,” they can test it easily by asking Geometric Supposer to measure the angles or by applying the relationship to several other triangles. The students will learn immediately that the conjecture is not true. Constructing these test examples manually would require more effort than students are likely to generate, but the computational power of the computer makes this testing very easy.

Geometry instruction is traditionally based on the application of theorems to prove that certain relationships exist among objects. This top-down approach requires analytic reasoning, which a majority of students find difficult. Geometric Supposer supports the learning of geometry by enabling the student to inductively prove these relationships by manipulating the components of geometric objects and observing the results. Rather than having the student apply someone else’s logic, Geometric Supposer makes explicit the relationships between visual properties and the numerical properties of the objects (Yerushalmy, 1990). Rather than using the computer to provide conclusive results, the computer calculates the results of students’ experiments. The research results with Geometric Supposer have been consistently positive.

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