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January 2007, Volume 12, Issue 5

FEATURES

Math Roots: The Beginnings of the Metric System
Art Johnson, Kit Norris
The history of the metric system, from a proposal of a sixteenth-century mathematician to its implementation in Revolutionary France some 200 years later. Recent developments in the metric system are discussed, along with where the United States stands on officially adopting the metric system.

It's the Thought That Counts: Reflecting on Problem Solving
Sally Roberts, Carla Tayeh
How metacognitive skills contribute to the teaching and learning of problem solving in mathematics. Teacher candidates kept metacognitive journals while solving math problems. Excerpts from the journals are used to show how the teacher candidates improved problem solving skills by becoming aware of their problem solving strengths and weaknesses.

Using Error Analysis to Teach Equation Solving
Kathy Hawes
How to use error analysis to expand student's mathematically reasoning skills. Four error analysis activities are described based on the topic of solving equations, but the activities can be used for a wide range of topics.

Using Alice in Wonderland to Teach Multiplication of Fractions
Susan Taber
How the story of Alice in Wonderland helps students understand the operation of multiplying by a rational number less than 1 and related aspects of ratio and proportion. Activity sheets are included as well as guidelines on how to use the novel as a cross curricular activity.

Engaging Contexts for the Game of Nim
Charles Reeves, Rosemarie Reeves Gleichowski
Various versions of the traditional game of Nim and demonstrations of how working backward can be used to find a winning strategy. The link is then made between working backward and using inverse operation to solve equations. Other problems are presented in which students can use their developed skills of working backwards.

Not Just for Computation: Basic Calculators Can Advance the Process Standards
Laura Moss, Barbara Grover
Using two real-world situations, this article describes in detail how the use of basic calculators can be the basis for an instructional strategy. Student worksheets are provided that require student to first estimate, then record the calculator key strokes used to arrive at their answer. By completing this activity, students will explore the fraction, decimal, percent relationships as well as explore the meaning of the remainder in division. Additional real-world situations are provided.

Finding Areas on Dot Paper
David Pagni
Investigative activities to assist students in constructing area formulas by partitioning geometric shapes on dot paper. Formulas are found in square units and triangular units (on isometric dot paper). Algebraic concepts are used to relate the triangular unit to the square unit and compare formula's for both units.

Psychology of Learning in the Junior High School
Howard Fehr
Research done on the rate at which students learn at various ages. Research done on motivating students is also included. This article is reprinted from Mathematics Teacher 49 (April 1956).