Team research is important in studying cognition as enactive. This paper contains four different pieces of research directed toward the evidences and artifacts of two students in Canada engaging in a sustained mathematical activity. These four portraits of mathematical cognition in action consider the conversation in which the activity occurs; the…

This book contains activities designed to help teachers enrich the mathematical experiences of all children and reach toward fulfillment of the National Council of Teachers of Mathematics (NCTM) Standards. Chapters include: (1) "Prenumber, Number, Non-Number"; (2) "Place Value"; (3) "Addition, Subtraction"; (4)…

The primary purpose of this study was to evaluate the application of a process approach for the teaching of algebra with a heterogeneous class of eighth-grade students. The assessment was conducted by identifying the processes used by above-average, average, and below-average algebra students in solving standard and nonstandard problems ranging…

This paper describes three methods that can be utilized in teaching for meaning in mathematics. These three methods are based on learning theories. Although there may not be consensus of what constitutes meaningful learning in the study of mathematics, there are problems with meaningless mathematics that are widely agreed upon by educators.…

The curriculum for eleven-year old students in the United Kingdom, currently adopted by most schools, includes solving linear equations with the unknown on one side only before moving onto those with the unknown on both sides in later years. School textbooks struggle with the balance between developing algebraic understanding and training…

The focus of this document is on students' understanding of symbolization processes in algebra, and specifically their understanding of semantically laden letters. In the first four sections, four inappropriate ways in which many college students use semantically laden letters are described. Evidence from clinical interview protocols demonstrate…

Two methods for solving problems are presented, designed to help people overcome difficulties that often occur in the problem-solving process. One difficulty people have is in using their knowledge to reach the decisive solution idea. The proposed "method of description" for eliminating this difficulty is based on a directed enrichment of the…

This document contains three modules. The first of these examines applications of algebra to geometry. It is designed to teach students how to algebraically characterize points which may be constructed with a compass and straight edge, and how to use this characterization to obtain classical geometric nonconstructibility results. The second unit…

This report investigates recent tenth-grade algebra achievement, after first suggesting there are good reasons for maintaining algebra in the syllabuses for grades nine and ten. Results indicate the students studied have mastered such algebraic skills as "collecting like terms" and "substitution in formulae." It is noted that…

The goal of this study was to develop a framework for classifying algebra story problems and to determine observed frequencies for each problem type. One thousand ninety-seven algebra story problems were selected from nine standard algebra textbooks. These are divided into eight families based on the nature of the source formula involved; for…

This document provides abstracts of 20 research reports. Topics covered include: children's comprehension of simple story problems; field independence and group instruction; problem-solving competence and memory; spatial visualization and the use of manipulative materials; effects of games on mathematical skills; problem-solving ability and right…

Solving equations in elementary algebra requires knowledge of the permitted operations, and knowledge of what operation to use at a given point in the solution process. While just these kinds of knowledge would be adequate for an ideal solver, human solvers appear to need and use other kinds of knowledge. First, many errors seem to indicate that…

This student discussion guide is intended to accompany "Explorations in Mathematics," a text for teachers. The materials in this booklet relate mainly to variables, graphs, signed numbers, logic, identities, functions and matrices. The materials were designed to be used as supplementary materials with students in grades 5 through 9. (RP)

This report presents a more detailed elaboration and discussion of the mathematical content of the central concepts which have been designated as the Mathematical Strands of the Mathematics Curriculum for grades K-8. In Part I of the report there is a discussion of the pedagogical philosophy which the committee felt was to have an importance equal…

This teacher guide is part of the materials prepared for an individualized program for ninth-grade algebra and basic mathematics students. Materials written for the program are to be used with audiovisual lessons recorded on tape cassettes. For an evaluation of the program see ED 086 545. In this guide, the teacher is provided with objectives for…