The mathematics curriculum of the 18th and 19th centuries is discussed with particular emphasis on arithmetic and algebra. Comparisons with current practices are made. Sample pages from several early textbooks are reproduced. (SD)

A particular shot on a pool table is analyzed using the concept of similar triangles, to introduce the equivalence of the "incident-reflection" principle and the "minimum-distance" principle. (CR)

A rationale is presented for an honors approach to remedial algebra instruction. Beginning with questions to be considered in the initial placement of students, the paper suggests that remedial students be enrolled at a level low enough to provide them with a reasonable chance to be good, even honors, students. It goes on to identify and contrast…

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 paper outlines the development of an activity that uses the computer's unique capabilities to provide students with a meaningful and highly motivating experience with the graphing of equations. The basic design of the game calls for the computer to display a coordinate grid on which it graphs any equations that are typed in by the student.…

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 is part one of a two-part SMSG text in algebra for students whose mathematical talents are underdeveloped. Additional drill materials are included in this text and terminology is kept to a minimum. Chapter topics include: (1) sets and the number lines; (2) numerals, sentences, and variables; (3) open sentences and truth sets; (4) properties…

This is part two of a two-part SMSG text in algebra for students whose mathematical talents are underdeveloped. Additional drill materials are included in this text and terminology is kept to a minimum. Chapter topics include: (1) factors and exponents; (2) radicals; (3) polynomials; (4) rational expressions; (5) truth sets of open sentences; (6)…

This is part one of a two-part manual for teachers using SMSG text materials for grade 9 students whose mathematical talents are underdeveloped. The overall purpose for each of the chapters is described and the mathematical development detailed. Background information for key concepts, answers for all exercises in each chapter, and suggested test…

This is part two of a two-part manual for teachers using SMSG text materials for grade 9 students whose mathematical talents are underdeveloped. The overall purpose for each of the chapters is described and the mathematical development detailed. Background information for key concepts, answers for all exercises in each chapter, and suggested test…

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…

This volume is an experimental edition for a high school course in the theory of matrices and vectors. One of the basic aims is to demonstrate the structure of mathematics. Another criterion is to provide some tools that will be useful in the student's transition from school to college. A last objective is that the intellectually vigorous students…

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 is the teacher's commentary for part two of a three-part SMSG algebra text for high school students. The principal objective of the text is to help the student develop an understanding and appreciation of some of the algebraic structure as a basis for the techniques of algebra. Chapter topics include addition and multiplication of real…