A lawn-mowing problem is discussed in terms of clarifying the problem; making initial conjectures; experimenting; developing a solution; and supporting formulas, theorems, and corollaries. (MNS)

Included are brief articles discussing chain letters as an example of exponential growth, a box technique for factoring, and integrating the inverse of a function whose integral is known. (MNS)

Proposed is that the present sequence of algebra followed by geometry leads to frustration. Students should be given the basic skills they need to survive in advanced mathematics and chemistry, with emphasis on percentage and ratio problems. (MNS)

Responses from about 500 average ability students at the end of ninth grade to an algebra assignment are reported and discussed. (MNS)

Algebraic and computer solutions are offered for a problem on time payment scheduling. The problem, falling within the scope of high school algebra, could focus only on the algebraic methods, but including the computer brings out the relationship between the power of algebra and the power of modern technology. (JN)

In this paper we describe a number of types of errors and underlying misconceptions that arise in mathematical reasoning. Other types of mathematical reasoning errors, not associated with specific misconceptions, are also discussed. We hope the characterization and cataloging of common reasoning errors will be useful in studying the teaching of…

Written for all teachers of young children, this book illustrates activities that promote early mathematics development for children ages three to five and "showcases" mathematics for the young child. The thirty-five activities in this book are distributed into five content areas: number and operations, geometry, algebra, measurement, and data…

This document contains the first volume of the proceedings of the 28th Annual Conference of the International Group for the Psychology of Mathematics Education. Conference presentations are centered around the theme "Inclusion and Diversity". In total, 147 presentations centered around the vision of mathematics for all. This volume…

There are two purposes in this study. One is to compare how 7th and 8th graders reason on linear and quadratic geometric number patterns when they have not learned this kind of tasks in school. The other is to explore the hierarchical relations among the four components of reasoning on geometric number patterns: understanding, generalizing,…

Recent curricular reforms are following the lead of the Standards 2000 and, in diverse ways, integrating some algebraic work into primary school mathematics. Our research aims at producing a tool that will allow researchers to track the development of algebraic thinking in children as they progress through various primary programs. In this paper…

The purpose of this series is to provide instructional ideas and materials that support implementation of the Curriculum and Evaluation Standards in local settings. This book addresses in a very practical way the content, pedagogy, and pupil assessment dimensions of reshaping school mathematics. Chapters include discussions and activities that…

A horizontal translation of a function is the focus of this study. We examine the explanations provided by secondary school students and secondary school teachers to a translation of a function, focusing on the example of parabola y = (x - 3)[superscript 2] and its relationship with y = x[superscript 2]. The participants' explanations focused on…

According to the Third International Mathematics and Science Study (TIMSS) which compared student performance in mathematics and science in 41 countries in 1995, fourth grade students in the United States perform only slightly above the international average in mathematics. The study showed that most U.S. students are mastering basic arithmetic;…

This action research project examined the impact of organizational and motivational strategies to increase homework completion among high school students. Participating were high school algebra and biology students in a midwestern, suburban city. The problem of homework completion was evidenced by existing grade and homework reports and teacher…

Alarming questions are being asked of the teaching methods in present use. Are we maximizing the time on task in the classroom? Students (n=98) in a remedial mathematics course were studied for one semester and students (n=56) from a developmental mathematics course were studied in the second semester, at Tennessee Technological University.…