In this issue's "Classroom Notes" section, the following papers are discussed: (1) "Constructing a line segment whose length is equal to the measure of a given angle" (W. Jacob and T. J. Osler); (2) "Generating functions for the powers of Fibonacci sequences" (D. Terrana and H. Chen); (3) "Evaluation of mean and variance integrals without…

To date, there has been very little research-based mathematics curriculum for talented elementary students. Yet the gifted education and mathematics literature suggest support for curriculum that is both enriched and accelerated with a focus on developing conceptual understanding and mathematical thinking. Project M[superscript 3]: Mentoring…

Several researchers have noted how children's whole number schemes can interfere with their efforts to learn fractions. An Australian study found that children who were successful with the solution of rational number tasks exhibited greater whole number knowledge and more flexible solution strategies. Behr and Post (1988) indicated that children…

Through her work as a consultant, Burns has found that a handful of students in all classes lack an adequate foundation in basic math concepts and lag far behind their peers in both understanding and skills. Students who lack a foundation on which to build new learning are generally not well served even by well-planned, differentiated instruction;…

The purpose of this article is to describe Discourse Time (D.T.), a teaching practice that aims to integrate argumentative literacy, the third piece of the literacy puzzle, into math learning environments. Snapshots from a tenth grade classroom at Skyview Academy High School in Thornton, Colorado is used to paint a vivid picture of what D.T. looks…

This study explores the ways in which eleven preservice elementary teachers used a web-based teacher resource to apply a mathematical definition, to correct a procedural error in arithmetic, and to make sense of a story requiring the multiplication of fractions. In our analysis we propose a framework to compare the behaviors and values expressed…

EQUALS is a teacher education program that helps elementary and secondary educators acquire methods and materials to attract minority and female students to mathematics. It supports a problem-solving approach to mathematics which has students working in groups, uses active assessment methods, and incorporates a broad mathematics curriculum…

This book is designed to provide teachers with numerous ideas about how to infuse mathematics and writing into their classroom in creative and challenging ways and to encourage students to visualize, speak, and write about math. The activities described here can help students communicate mathematically and realize that there is more to math than…

This document is a compilation of lesson plans designed to teach math/science concepts that have appeared in the journal "School Science and Mathematics". The activities combine important mathematics and science fundamentals in a single lesson and have been tested by classroom teachers. The lesson plans include concepts, objectives, rationale,…

This paper describes the implications of constructivism both for what to teach and for how to teach. The first part discusses three approaches on what to teach: (1) relating mathematical knowledge to other knowledge; (2) checking for self-consistency; and (3) putting thinking before facts. The second part is on how to teach based on…

Drawing from research and observations at Lansing Community College (Michigan) (LCC), this paper argues that typical arithmetic courses do little to prepare students to master algebra, and proposes an alternative set of arithmetic skills as actual prerequisites to algebra. The first section offers a description of the algebra sequence at LCC,…

Precalculus and Discrete Mathematics (PDM) is the sixth and final course in the secondary mathematics curriculum developed by the University of Chicago (Illinois) School Mathematics Project. During the 1989-90 academic year, a formative evaluation of the third field-trial edition of PDM was conducted among a volunteer sample of 9 high schools with…

A study was conducted to test the hypothesis that the ability to comprehend in reading has no effect on mathematical problem solving ability of seventh grade students. Two seventh grade classes were administered a standardized test of reading comprehension and knowledge of mathematical concepts and application at the beginning of a school year.…

Two studies were conducted to compare experimentally the effects of teacher-led instruction and seatwork on acquiring mathematical concepts. In the first study, 255 fourth graders were assigned to groups to be taught a 15-minute teacher-led lesson only, a 15-minute lesson plus 12 minutes of teacher-led follow-up, or a 15-minute lesson plus 12…

An instructional method using flow-chart symbols to make mathematical abstractions more concrete was implemented for a year in a technical mathematics course. Students received instruction in computer applications and programming in the BASIC language in order to increase motivation and firm the mathematical skills and problem-solving approaches…