The derivative of a composite function, taken with the chain rule is one of the important notions in calculus. This paper describes a study conducted in Turkey that shows that the chain rule was given with the formula in function notation and/or the Leibniz notation without relating these formulas to life-related problem situations in the…

Mathematics teachers are seen working in a context affected by three major revolutions. The first, mass secondary education, has been dealt with. The second, technological revolution, is taking place. The third, humanizing mathematics, is viewed as heaving into sight, and seen as possibly a greater upheaval than the others. (Author/MP)

Space and shape, estimating and measuring, and number are viewed as the three strands of mathematics that come together as a child develops mathematically. Five cognitive/mathematical levels of development, labeled discrimination, order, application, operation, and estimation, are identified and discussed. (MP)

Describes study of elementary school children in Australia which was designed to determine their sequential knowledge of measuring length and to apply recent cognitive theories to predict the sequence of development of knowledge. Recent literature is reviewed, information processing skills are discussed, and skills required for measuring length…

The author defines and discusses the cognitive theory of constructivism as it relates to teaching mathematics. It is suggested that the philosophical and theoretical view of knowledge and learning embodied in constructivism offers hope that educational processes will be discovered enabling students to acquire deep understanding rather than…

Children appear to interpret the "equals" sign as an operator ("adds up to") not a relational ("the same as") symbol--e.g., viewing equations like 13 = 7 + 6 or 8 = 8 as senseless. This study, a natural experiment, examined the effects of long-term instruction emphasizing a relational definition of "equals."…

Described is the process approach to mathematics which is gaining momentum in primary schools. Included is a discussion of the origin and features of the movement and possible future directions and consequences of its growth. (PK)

This document primarily consists of papers scheduled for presentation at the third annual meeting of the North American chapter of the International Group for Psychology in Mathematics Education (NA-PME), held in September 1981, at the University of Minnesota. A total of 27 papers are arranged alphabetically by author. An additional three late…

Design and results of an investigation attempting to analyze and improve children's solution processes in elementary addition and subtraction problems are described. As background for the study, a conceptual model was developed based on previous research. One dimension of the model relates to the characteristics of the tasks (numerical versus word…

As part of a larger study regarding an ideal curriculum in five subject matter domains for the elementary school, the views of seven experts in mathematics education were summarized and contrasted. Four experts were nationally and internationally known professors and researchers, and three were elementary school teachers selected by researchers…

The focus of this research was the conduct and analysis of six hours of clinical interviews with sixth and ninth grade students to investigate how they learn geometry in light of the van Hiele model. In chapter 1 an overview of the project and its four major goals is given. The theoretical model is described in chapter 2. In chapter 3 the…

After observing secondary school students having great difficulty learning geometry in their classes, Dutch educators Pierre van Hiele and Dina van Hiele-Geldof developed a theoretical model involving five levels of thought development in geometry. It is the purpose of this monograph to present English translations of some significant works of the…

Presented are transcriptions of a research panel presentation held at the annual meeting of the National Council of Teachers of Mathematics, Boston, Massachusetts, April 1979. The members of the panel are all involved in working directly with children in a clinical setting for pupils with learning disabilities in mathematics and with graduate…

Describes the Agam program, a 36-unit curriculum program to introduce students to basic visual concepts and that applies visual abilities and visual thinking to learning tasks. Describes two units at the third grade level, "Ratio and Proportion" and "Numerical Intuition," and makes observations of the students' learning. (MDH)

Variability stands in the heart of statistics theory and practice. Concepts and judgments involved in comparing groups have been found to be a productive vehicle for motivating learners to reason statistically and are critical for building the intuitive foundation for inferential reasoning. The focus in this paper is on the emergence of beginners'…