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September 2007, Volume 101, Issue 2

FEATURES

Where Have All the Flowers Gone?
Janet Walker
An activity for secondary mathematics students using digital imaging on The Geometer's Sketchpad to model polar functions of flowers. Students import images of flowers into GSP and use its capabilities to find a best fit polar equation.

Using Technology to Optimize and Generalize: The Least-Squares Line
Maurice Burke, Ted Hodgson
With the help of technology and a basic high school algebra method for finding the vertex of a quadratic polynomial, students can develop and prove the formula for least-squares lines. Students are exposed to the power of a computer algebra system to generalize processes they understand and to see deeper patterns in those processes.

The Inverse Name Game
Christine Benson, Margaret Buerman
The importance of emphasizing the concept of inverse. It addresses the different names we use for inverses and suggests ways to help students see the big picture. The author ties together the use of inverses in functions, arithmetic operations, reciprocal relationships, and makes a case for instruction of the inverse as a coherent whole.

Some Interesting and Thought-Provoking Geometric Fallacies
Alan Sultan
Some interesting geometric fallacies that were used in a problem-solving course for preservice high school mathematics teachers. Errors in logic and false assumptions lead to misleading conclusions. The authors demonstrate that incorrect sketches lead us to wrong conclusions. The use of Geometers Sketchpad is one strategy that will benefits students.

Purchasing a Used Car Using Multiple Criteria Decision Making
Thomas Edwards, Kenneth Chelst
A Multiple Criteria Decision Making process (MCDM) in which students assign a numerical value to each alternative in a situation, and compute the highest value in order to quantify the optimum choice. MCDM can be used in making decisions such as choosing the best car or right college. This lesson can be used across the mathematics curriculum.

Critical Juncture Ahead! Proceed with Caution to Introduce the Concept of Function
Gregorio Ponce
Algebra teachers find themselves overwhelmed by the sheer volume of information that they have to teach their students. One way to address this issue is to have teachers teach for understanding by focusing on concepts. The author shares how language can help uncover the core ideas that define the concept of function and provides activities that have been successfully used with students to introduce the core ideas and illustrate the usefulness of a function outside the classroom. Teaching functions is the vehicle for this process.

Teaching Preservice Secondary Teachers How to Teach Elementary Mathematics Concepts
Robin Kalder
A course in elementary mathematics concepts that was specially designed for preservice teachers who plan to teach at the secondary level. The article suggests concrete methods for teaching basic number facts for understanding at the secondary level.