This volume contains abstracts of 33 research papers presented at the 53rd Annual Meeting of the National Council of Teachers of Mathematics. Most papers concerned instructional strategies; fourteen were concerned with sequencing of instruction and/or hierarchical analysis of learning. Four papers dealt with strategies for reviewing and…

Reported are the results of a study to ascertain if verbal, visual-spatial, and numerical abilities were related to the learning of function concepts when taught by instructional approaches thought to be consistent with these abilities. A secondary purpose was to determine the efficacy of these approaches at the eighth grade level. Three subtests…

This teaching guide outlines a college algebra course for use in the secondary school. Units studied are: mathematical induction, functions, groups and fields, linear algebra, and limits. Special emphasis is given to the study of functions and linear algebra. Sequence, textbook references and assignments, and time allotments are suggested. Some…

A pilot study was conducted of the understanding of prospective elementary school teachers of mathematical concepts. Purposes were to test the diagnostic instrument used to measure comprehension of concepts and to determine whether American College Test mathematics scores of student teachers could be used to predict ability to understand concepts…

A series of experiments, all concerned with the topic of mathematical concept learning by the young child, were conducted. The concept mainly focused upon was that of inequalities. Five experiments were run. These are: (1) acquisition of mathematical concepts under experimental situation and in traditional pedagogical situation, (2) cued vs.…

This programmed text of self-instruction is one of a series of manuals on techniques describing procedures for planning and executing specialized work in water-resources investigations. It has been prepared on the assumption that the reader has completed standard courses in calculus and college physics and is presented in eight parts. Part I…

This article states that children in the first grade have usually not developed the thought processes which would enable them to understand the typical first-grade math curriculum. (CD)

The history of mathematics education is examined, especially as it relates to the understanding of mathematical concepts. Earlier segments of this article appear as SE 515 504 and SE 516 064. (SD)

The process of developing a pre-mathematics curriculum for nursery schools and some of the issues involved in creating such a curriculum are discussed. (SD)

Investigates the effectiveness of unit seven of the MINNEMAST program in kindergarten classrooms using a pretest-posttest design. Concludes that this unit, as well as other units of MINNEMAST, would be an applicable science program in kindergarten classrooms. (HM)

It is shown that, by taking as the basis unit vectors along the sides of an equilateral triangle, certain isometric transformations can easily be determined in matrix form. (MN)

Children attempted a division problem in one of four distraction settings: minimal, situational, color-attribute, or spatial-numerical. The effects of both grade level and distraction setting in problem-solving performance were highly significant, with children who used a manipulative approach being more prone to distraction than those using a…

Described are various common misconceptions about the nature of mathematics and suggests that courses or activities based on model building might help change these. Two examples are offered. (SD)

The author develops a four-stage model for concept-internalization. The stages are: (1) concrete structure; (2) linguistic structure; (3) algorithm; and (4) mastery. The model is related to teaching methods and the teaching of long division is examined in detail. (SD)

Describes how a sixth grade teacher and her eleven students (with a typical range of math abilities) explored the mathematical concept of "infinity" through play. Discusses the pedagogy of critical/creative thinking. (SR)