An understanding of linear measurement depends on principles that include standard unit size, iteration of units, numbering of a unit at its end, and partial units for measuring continuous length. Children may learn these principles at school, for example through experience with informal measurement, or they may learn them through use of…

This article describes the use of the book "Inchworm and a Half" to stimulate children's investigations in measurement and number. During a two-day lesson children used physical models and visual representations to develop measurement skills and explore equivalent relationships.

The description about the changed instruction to encourage student exploration of the graphical and then the algebraic representations of functions is presented, which enables the students to understand how the graph, equation, and table of a function are related. The activity addresses both the Learning Principle and the Connection standard and…

Mathematics and art are often considered opposites in the traditional curriculum. In this project with fourth graders, mathematics and art provided a springboard for using fractions, in particular, the multiplication of fractions, using Chinese kites. The project began with a discussion of, "What does an artist really do in a mathematics…

This study was designed to investigate the impact of using computer-simulated (virtual ) manipulatives and hands-on (concrete) manipulatives on elementary students' learning skills and concepts in equivalent fractions. The researcher's primary interest was whether or not students who used virtual manipulatives would out-perform students who used…

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…