Most teachers of mathematics would agree that a student's major difficulty when studying mathematics is the mastery of "vocabulary." A taxonomy could provide an outline of the various types of vocabulary and could suggest their relative interrelationships. One proposed taxonomy has five levels that seem to recur. The levels seem to have…

Arguments for and against the use of computers in mathematics classes have centered on whether students benefit from or are merely hindered by practicing computational skills. This paper claims that the true essence of mathematics lies not in computation, basically a mechanical operation, but in problem-solving. Since no amount of computational…

On a triangular grid of equilateral triangles an analytical procedure is presented for solving puzzles that require one to measure out a specified amount of liquid from containers of various volumes. (JP)

The nature of measurement, the standard measurement concepts are discussed in terms of children's preconceptions and activities for building measurement concepts through primary school instruction. A broad range of activities including counting, computation, calibration, and relating measure to size is presented. The metric system is briefly…

This study was designed to compare the relative effectiveness of word problem instruction based on Polya's approach to problem solving with Dahmus' word by word translation approach. When ninth-grade students were randomly assigned to one of these approaches, no differences in mean number of problems solved were observed. (SD)

An activity sequence is described. Several aspects of a population problem are developed using isoperimetric graph paper and symmetry principles to derive general rules. (SD)

The purpose of this study was to ascertain whether children in grade 3 who differ in cognitive processing capacity add and subtract differently. The researchers drew upon information from three sources: individual results from a battery of 14 tests, an objective-referenced achievement test measuring a variety of arithmetic skills related to…

Computers have the power to make drastic changes in modern life and in education particularly. It is uncertain, however, how smoothly computers can be integrated into society and into the schools. The speed of the growth of computer technology is often referred to as a revolution, with a constantly increasing ability to store and recall…

This document consists of three modules concerned with aspects of statistics. The first provides knowledge of the effect of imperfect correlation and random error on differences between means, and the reasons for the necessity of random allocation of objects to experimental and control conditions in scientific experimentation. The second unit…

Recent research on human memory and cognition with particular emphasis on research that might have some promise for mathematics education is reviewed. The focus is on techniques for analyzing the mind in two areas: (1) the architecture of the human memory system, using the information processing model; and (2) the content and structure of…

Although it is commonly assumed that increases in mathematical knowledge and problem-solving skill alter one's understanding of mathematical problems, little research exists to support this assumption. The present study investigated the relationship between mathematical background and problem perception in two experiments. Experiment 1 employed…

The extent to which kindergarten children are able to solve simple quantitative problems merely through the application of counting procedures, before they receive formal instruction in any basic arithmetic operations, is investigated. The study indicates that most kindergarten children can comprehend simple story problems of the type used in…

Presented are twenty essays related to applications in school mathematics and aimed at the classroom teacher. The essays use numerous examples and illustrations that provide the teacher with something tangible for immediate use. Four thematic areas are addressed: (1) What are applications?; (2) Why include applications in school mathematics?; (3)…

An activity for secondary schools is presented and discussed which may be explored with a programmable calculator. The activity is non-standard and could not be easily explored without the use of a programmable calculator. Related activities are also discussed. Flow charts and programs for different programmable calculators are presented. (MP)

This study focuses on the mental processes used during estimation. This research: (1) developed an operational definition of estimation; (2) created an instrument to identify exceptionally good estimators; (3) collected performance level data on 1187 subjects; (4) constructed interview problems and developed protocols to identify the thinking…