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August 2008, Volume 102, Issue 1

FEATURES

Generating Problems from Problems and Solutions from Solutions
Abraham Arcavi, Zippora Resnick
A geometric solution to a problem that is usually solved analytically as an example of how alternative solutions may enrich the teaching and learning of mathematics. The problem discussed is the "Reaper Problem."  This problem could be posed to students to solve algebraically or geometrically, or to be used to show the connection between the two subjects.

A, E, I, O, U and Always Y: A Simple Technique for Improving Communication and Assessment in the Mathematics Classroom
Lorna Vazquez
A technique for structuring and assessing student work that, when applied appropriately, can improve students' ability to communicate their mathematical thinking and the teacher's ability to assess understanding. Includes a framework for the technique and a rubric for assessing student responses. See the difference in two students' responses before and after learning this method of showing their thinking.

Designer Functions: Power Tools for Teaching Mathematics
Marcia Weinhold
An activity for exploring polynomials. In this activity teacher candidates apply technology to explore mathematics that they will teach but that they have not studied since high school. Included are examples of graphs created by students and questions about the graphs that could be used to motivate a more in-depth understanding of polynomial functions.

Learning about Students' Mathematical Literacy from PISA 2003
Sharon McCrone, John Dossey, Ross Turner, Mary Lindquist
The need for mathematical literacy in our world today and shares results from the 2003 PISA assessment of mathematical literacy. Includes ideas for incorporating similar problems in the classroom. Several examples of PISA problems are included, as well an internet address where other released PISA test items can be found.

Read how you can use this article as part of a Professional Development Experience.

Applied Algebra: The Modeling Technique of Least Squares
Jeremy Zelkowski, Robert Mayes
Engaging students in algebra through modeling real-world problems. Least squares is explored, encouraging students to develop a deeper understanding of the method. Includes several labs and an activity sheet that can be used in a lesson on the least squares method.

A Song for 8-8-08
Lawrence Lesser
A song about mathematical properties of the number eight, and places the number occurs in the natural world. Written to a familiar tune, teachers could use this song in their classroom to get their students excited about numbers.