This program is designed to enable students to master the competencies and skills which reflect the learning goals and objectives developed by the Illinois State Board of Education. This document lists the learning objectives by grade level and reporting period for kindergarten through grade three. Topics included are arithmetic, measurement,…

This study sought to determine whether there would be any relationship between age and success for students arbitrarily placed in "college-preparatory" beginning algebra on the basis of the ACT mathematics score. The study was conducted during the first term of 1985-86 at Broward Community College, in Florida. A list of 78 students…

This paper describes a review and synthesis of research on algebra. The purpose was to identify findings that may prove useful to teachers, supervisors, and administrators. Over 300 studies were identified and categorized in terms of classroom instructional practices, cognitive factors, attitudes and affective factors, problem solving, calculators…

This study sought to determine the effectiveness of augmenting instruction of "math-anxious" community college algebra students with a counselor. The control group, with about 25 students, was comprised of students in Term I (August-December 1984) who received algebra instruction in the traditional lecture method. The experimental group,…

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 is the Teacher's Commentary for the Supplementary Units for Junior High School Students. Included in the Commentary are background material for teachers, suggestions for instruction, and answers to student exercises. Also included are comments on how to use the materials with different types of students and time needed for instruction. (RH)

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)…