Examined is the notion of "representation" as it is used in mathematics education. The first section explains what appears to the current "received view" of representation within mathematics education. The second section describes the constructivist view of representation, especially as this view is related to Piaget's theory. The third section…

An understanding of fraction addition can be thought to involve two quantitative ideas: (1) the understanding that adding to an original quantity increases its size, and (2) a sense of how much increase occurs. Both of these ideas should underlie or inform a child's approach to problems involving fraction addition and thereby constrain the class…

Tracing the history of algebra within the U.S. secondary curriculum requires at the same time a review of the various reform movements relevant to secondary education, an acknowledgement of the sociological, political, and psychological perspectives driving these reforms, and most importantly, the perceived role of mathematics in the education of…

The question of the advisability of incorporating discrete mathematics into the mathematics curriculum is addressed by examining the different types of courses typically offered in the first two years of college and the appropriateness of including discrete mathematics topics in these courses. The introductory section explains how the advent of…

This is one of a series of monographs developed by teachers in middle and high schools near Leeds, England. This volume presents a glossary of mathematical terms, in alphabetical order, each with a brief definition. Six appendices contain additional terms (cross-referenced in the main list) grouped by topics. The topics are: numbers,…

This survey provides data on the current status of mathematics programs in Indiana schools. It was intended to stimulate local school systems in the evaluation of their mathematics curricula. Separate sections provide data on elementary schools, junior high and middle schools, and high schools. Included is information on mathematics contests and…

The papers in this document follow the order of the meeting and consist of two guest lecturers and reports from four working groups; two topic group presentations are noted but not included. One lecture, delivered by Peter Hilton, discusses the nature of mathematics today and implications for mathematics teaching, while, in the other paper,…

Reading to learn mathematics forges a new synthesis of the traditional basics of reading and mathematics which aims at fostering critical thinking and may provide an instructional context within which students and teachers can work out meaningful conceptions of mathematics. Benefits of this synthesis of reading and mathematics include: (1)…

This literature review examined the relationship between the type of mathematics courses taken and scholastic mathematics achievement. The paper concludes that there is a high correlation between types of mathematics courses taken and scholastic math achievement. Specifically, higher level mathematics courses enhance and foster analytical thinking…

This monograph aims to provide teachers of grades 7, 8, and 9 with a variety of instructional activities and strategies that identify student difficulties in computing percents and teaching the skills needed for that cluster on the mathematics part of the New Jersey High School Proficiency Test (HSPT). Sections include: (1) "Concepts"…

This book presents activities promoting children's understanding of mathematical ideas while at the same time providing the practice children need to refine their skills in mathematics. Chapter topics include: (1) numbers; (2) number facts and operations; (3) problem solving; (4) calculators; (5) fractions; (6) graphing; (7) geometry; and (8)…

This book was written as a tool to help teachers of prekindergarten to grade 3 make use of recent developments in the cognitive psychology of mathematical learning. Chapters included are: (1) "The Nature of Children's Mathematical Thinking"; (2) "Designing Effective Mathematics Instruction"; (3) "Oral Counting"; (4)…

This paper compares the old and new curricula of elementary mathematics and natural science in the Republic of China. This study, as the second phase of an evaluation period, tested a sample of the students while they were in the ninth grade and compared them to students who received the old curricula during their elementary studies. The data were…

This is the teacher's manual to accompany part 1 of the workbook for grade 3 pupils in the Comprehensive Instructional Management System, a teacher-designed unified mathematics curriculum for kindergarten through grade 7. It is composed of a curriculum, a testing component, and a computer-managed reporting system. The curriculum is organized into…

This is the teacher's manual to accompany part 1 of the workbook for grade 4 pupils in the Comprehensive Instructional Management System, a teacher-designed unified mathematics curriculum for kindergarten through grade 7. It is composed of a curriculum, a testing component, and a computer-managed reporting system. The curriculum is organized into…