**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. |