The purpose of this study was to investigate the areas of agreement or disagreement in teaching secondary school algebra in England and the United States. Textbooks were read and analyzed for the purpose of obtaining data related to the concepts included, and also for noting major developmental steps which occurred in each textbook series. Among…

Presented is an elementary approach to areas, columns and other mathematical concepts usually treated in calculus. The approach is based on the idea of average and this concept is utilized throughout the report. In the beginning the average (arithmetic mean) of a set of numbers is considered and two properties of the average which often simplify…

This is part of a student text which was written with the aim of reflecting the thinking of The Cambridge Conference on School Mathematics (CCSM) regarding the goals and objectives for mathematics. The instructional materials were developed for teaching geometry in the secondary schools. This document is chapter six and titled Motions and…

One major purpose of this investigation was to determine and compare the effects of three different perceptual situations (screening, neutral, and conflict) on kindergarten and first grade children's ability to use the transitive property of the equivalence relation "same length as" and the two order relations "longer than" and…

This is a reprint of the historical capsules dealing with algebra from the 31st Yearbook of NCTM,"Historical Topics for the Mathematics Classroom." Included are such themes as the change from a geometric to an algebraic solution of problems, the development of algebraic symbolism, the algebraic contributions of different countries, the origin and…

Research reported deals with identifying stages in attaining a concept of function by students, eleven through fourteen years of age, of above average ability, taking the experimental mathematics program of the Secondary School Mathematics Curriculum Improvement Study. In order to obtain a hierarchy of the learning stages, both a written test and…

PIAGET'S THEORETICAL FORMULATION OF THE DEVELOPMENT OF CONSERVATION OF CONTINUOUS QUANTITY WAS EXAMINED. CONTROL SUBJECTS IN EACH OF TWO AGE GROUPS (5 AND 6 YEARS) WERE GIVEN A COMPLEX TASK SITUATION THAT IS TYPICAL OF PIAGET'S WORK. THESE SUBJECTS WERE ALSO GIVEN ANOTHER TASK, A MEASURE OF CONSERVATION OF QUANTITY THAT IS INDEPENDENT OF PIAGET'S…

Classroom cooks knead and churn their way to good food, skills and awareness. (Editor)

Investigated distribution of spatial visualization scores (Space Relations test of the Differential Aptitude Test) and mathematical problem-solving scores (Mental Arithmetic Problems) obtained by 161 male and 152 female 9th grade students. No significant sex-related differences were found between mean scores of tests of spatial visualization or…

Children aged 5, 9, and 13 years did work superior to, equal to, or inferior to another child and allocated reward between them. The three age groups showed qualitatively different allocations consistent with hypothesized age-related stages: (1) no relation of allocation to relative work, (2) preservation of rank from work to reward, and (3)…

The author presents a method of teaching the concept of limit. (SD)

The test presents tasks to allow students to demonstrate their ability to carry out practical tasks and communicate mathematical ideas. The two tasks are presented and discussed. (MNS)

Four experiments were conducted to study explanations of why children make relative number judgments inconsistent with their counting. Results are discussed in relation to judgments children make when they use matching, and in light of Klahr and Wallace's (1973) account of number development. (PCB)

Examined whether representational changes in digit memory are functions of children's expertise in mental abacus operation when abacus operators reproduced series of digits forward or backward. Found skilled operators equally facile with forward and backward reproduction, but novices slower going backward. Suggests advanced operators apply their…

How physiological disciplines can contribute to the study of how people learn mathematics is considered. Manipulative and experiential learning, sequential versus hierarchical organization, declarative versus procedural knowledge, and short-term versus long-term memory are among the points discussed. (MNS)