Proposes helping students understand fractions by establishing connections between students' informal knowledge of fractions and the mathematical symbols used to represent fractions. Sample dialogues demonstrate how these connections can be made. (MDH)

Cryptography is the science that renders data unintelligible to prevent its unauthorized disclosure or modification. Presents an application of matrices used in linear transformations to illustrate a cryptographic system. An example is provided. (17 references) (MDH)

Described is a theorem which is generally not present in most high school geometry textbooks. Presented are two proofs and two cases which illustrate the use of the SSA theorem. (CW)

Presents an investigation that focuses on estimation skills as children attempt to solve problems involving concepts of weight, volume, and counting money. (ASK)

Based on research and teacher experience, this resource guide contains teaching methods and activities that teachers can use in teaching mathematics to adult basic education and General Educational Development students. The following eight sections are included: (1) an alternative method for teaching percents; (2) unit conversion or dimensional…

This publication contains revised versions of the major papers presented at a research conference on the learning and teaching of algebra. The papers and discussions focused on four major themes: what is algebra and what should it become, in light of continuing technological advances; what has research told us about the teaching and learning of…

The purpose of this study was to discover what teachers believe about problem solving in mathematics and to what extent their beliefs are reflected in the beliefs of students. Ten 5th-grade teachers in a large rural school district volunteered to participate. Each teacher identified one student perceived as successful and one perceived as…

This project was designed to: (1) assess 7th-graders' metacognitive beliefs and processes and investigate how they affect problem-solving behaviors; and (2) explore the extent to which these students can be taught to be more strategic and aware of their own problem-solving behaviors. The primary assessment was conducted by analyzing video tapes of…

This book, written primarily for college students who feel uncomfortable with mathematics, attempts to provide its readers with new ways of thinking about mathematics, reading mathematics, studying mathematics, talking the language of mathematics and appreciating the power of using mathematics. Chapter 1 deals directly with the problem of math…

The Rice Index is the first measure of voting unity devised. It is noted that this measure was developed on an ad hoc basis for use in rather rough comparisons. This measure is carefully assessed, and is noted to have the virtue of simplicity, useful in certain situations, but associated with certain problems when it is used for a more detailed…

This document consists of three modules. The first looks at applications of analysis to medical radiology. The goals are to provide: 1) acquaintance with a significant applied mathematics problem utilizing Fourier Transforms; 2) generalization of the Fourier Transforms to two dimensions; 3) practice with Fourier Transforms; and 4) introduction to…

This guide provides material for teaching problems with rate and ratio calculations. There has been a traditional and worsening shortfall of student performance on rate and ratio problems which do not apply to other components of the mathematics program. The major problems found with traditional curriculum approaches are: (1) rate and ratio…

This collection of activities shows how teachers can help pupils develop problem-solving techniques or strategies using a basic four-function calculator. The techniques "look for a pattern,""make a chart or organized list," and "guess and check" are used repeatedly in activities that range from discovery to application to strategy games. The…

This student textbook is designed to incorporate programable calculators in grade 11 mathematics. The eight chapters contained in this document are: (1) Using Calculators in Mathematics; (2) Exponents and Logarithms; (3) Trigonometry of the Right Triangle; (4) Trigonometry Beyong the Right Triangle; (5) Graphs of the Trigonometric Functions and…

This supplementary mathematics textbook is designed to teach pupils in the intermediate grades about the vocabulary and use of the metric system of measurement. The book limits exploration to the units of measurement for length, capacity, mass, temperature, area, and volume, with only the following prefixes considered: kilo, hecto, deka, deci,…