This paper presents a qualitative study that investigated two third-grade students' understanding of number. The children were videotaped while they worked to record everything they knew about the number, 72. Their artifacts and conversations were then analyzed using the Pirie-Kieren dynamical theory for the growth of mathematical understanding as…

This article describes the experiences of a group of primary-grade students and their teacher as they explore negative numbers over the course of two years. It is just one example of how a problem-solving environment contributes to discussion and understanding in mathematics. (Contains 3 figures.)

This article describes how children learn the basic addition and subtraction facts, why many have difficulty mastering these basic skills, and what teachers can do to prevent or overcome these learning difficulties.

The possible effect of experimenter expectancy in number conservation task experiments was explored. (JMB)

The historical development of the concepts of ratio and proportion is discussed. (SD)

A short story is presented which uses as its characters rational and irrational numbers and numbers involving fractional exponents. (DT)

A developmental mathematics program at Hill Top Preparatory School in Rosemont, Pennsylvania is designed to help learning disabled students prepare for jobs and college work. Intended for non-college bound as well as for the college bound, the program emphasizes aspects of environment (appropriate placement, self pacing, small groups), process…

Euler's famous formula, e to the (i, pi) power equals -1, is developed by a purely algebraic method that avoids the use of both trigonometry and calculus. A heuristic outline is given followed by the rigorous theory. Pedagogical considerations for classroom presentation are suggested. (LS)

Significant questions are addressed in an extensive discussion of the differences between qualitative and quantitative concepts and measurement strategies in the physical sciences. Also included is a discussion of number-generating activities often grouped in the social sciences under the term of measurement. Implications for the redirection of…

This programed mathematics textbook (Volume I) is for student use in vocational education courses. It was developed as part of a programed series covering 21 mathematical competencies which were identified by university researchers through task analysis of several occupational clusters. The development of a sequential content structure was also…