This issue contains abstracts and critical comments for 11 articles. Three articles focus on problem solving; the remainder concern understanding of the equals sign, mathematical structure, mathematical abilities, the role of language in tasks involving sets, sex differences in mathematical errors, subtraction, algorithms as schemes, and…

The concept of multiplication is described and illustrated using several different representational systems. A conceptual approach to teaching mathematics is compared with the procedural approach commonly found in the school curriculum. Four different methods of representing the multiplication process with numbers larger than ten are presented:…

Research supported by a grant from the Carnegie Corporation.

Using data collected in 1977-78, the Evaluation System has computed fall and spring mathematics scores on the Prescriptive Mathematics Test (PMT) for classes of students in grades one through six. In addition, relationships of performance on the PMT to class size, attendance, percent of males in the class, number of different test levels used in a…

The Pennsylvania Preschool Inventory (PPI) was developed as a straight-forward and efficient measure of the relative cognitive development of the young child, offering an alternative to more complicated, elaborate assessment instruments. Results of the inventory are potentially relevant to both current and future school success of children between…

The uses of verbal rules in solving arithmetic problems are presented. Thirty-six problems were used in individual testing of five students who were enrolled in a remedial mathematics course at a community college. Two or three weeks prior to the individual exams, the students had been tested in their class on the material. The study indicated…

The National Assessment of Educational Progress (NAEP) administered the selected supplemental mathematics exercises to 13-year-old students during October and November 1975 and to 17-year-old students during March and April 1976. This assessment represents a specially modified supplement to 1972-73 full-scale mathematics assessment and was…

THIS PROGRAM INCORPORATES THE TRAINING NEEDS OF THE SEVERELY RETARDED CHILD IN A LOGICAL, PSYCHOLOGICAL SEQUENCE TO PROVIDE THE CHILD WITH THE OPPORTUNITY TO GROW PHYSICALLY, EMOTIONALLY, INTELLECTUALLY, AND SPIRITUALLY IN ORDER THAT ADEQUATE SELF-CARE, SOCIAL ADJUSTMENT, GOOD PLANNING OF LEISURE TIME, AND SATISFYING USEFULNESS MAY BE REALIZED FOR…

A study was conducted to examine the learning of mathematical concepts by English dominant and Spanish dominant primary school children. The concepts considered were number, numeration, and computational procedures. Using the case study method, a three step procedure was designed to study individual math objectives: (1) objectives were first…

This book is intended to make common fourth-grade mathematical concepts both interesting and easy to understand. The text is designed to meet the particular needs of those children who have "accumulated discouragements" in learning mathematics. The reading level required of pupils has been reduced. Individual chapter titles are:…

Presented are student performance objectives, a student progress chart, and assignment sheets with objective and diagnostic measures for the stated performance objectives in college arithmetic and pre-algebra. Topics covered include: sets, whole numbers, integers, decimal fractions, fractions, ratio and proportion, percent, powers and roots, the…

The purpose of this paper is to identify how the theory and techniques of research in cognitive development can be applied to the study of learning and instruction in mathematics. Five basic research paradigms are characterized; major directions of research on number, measurement, geometry, and adolescent reasoning are identified. Most of the…

This booklet is one of a set of five booklets which comprise the basic curriculum for "Mathematics Laboratories for Disadvantaged Students," a nationally validated Title III ESEA project. This publication provides evaluation materials and student materials related to number theory. Topics included in this booklet are prime and composite…

Several methods of teaching college-level mathematics sequences are examined for their advantages, disadvantages, and costs. Materials considered include textbooks, film sequences, videotaped lectures, and individualized teaching machines. (SD)

This mathematics curriculum guide for grades K-8 was developed and evaluated by teachers in the Seaford School District, Delaware. It sets out concepts and skills to be mastered at each grade level. Suggested learning activities are described for each curricular objective identified. The curricular topics addressed include number concepts,…