Students have difficulty learning fractions, and problems in understanding fractions persist into adulthood, with moderate to severe consequences for everyday and occupational decision-making. Remediation of student misconceptions is hampered by deficiencies in teachers' knowledge of the discipline and pedagogical content knowledge. We theorized…

This paper was prepared in response to the Conference Board of Mathematical Sciences recommendations for the preparation of secondary teachers. It shows how using trigonometry as a conceptual tool in spreadsheet-based applications enables one to develop mathematical understanding in the context of constructing geometric representations of unit…

This book is designed to give mathematics teachers a host of interesting and useful ideas thereby raising their consciousness level and enabling an enrichment of the mathematics instruction program. The chapters in this book capture a broad spectrum of ideas in the area of mathematics problem solving. Chapters are: (1) "Strategies for Problem…

Many students have difficulty finding remainders instead of quotients in the division of two numbers. Students are too quick to use technology and cannot interpret the output correctly. Moreover, many students are not accustomed to doing different yet applicable mathematics. As with all branches of mathematics, modular arithmetic and congruences…

This report evaluates the degree to which the achievement level descriptions adopted by the National Assessment Governing Board (NAGB) for the 1992 National Assessment of Educational Progress (NAEP) assessment in mathematics accurately represent what students at a given achievement level can do. Three different analytical approaches were used in…

The books in this series provide an essential ingredient in the transition from concrete mathematical experience to the symbolic reasoning used in algebra. They aim to guide the student in building and extending manipulative patterns, collecting numerical data, and analyzing the results. The main objective of the activities in this book is for the…

A central component in the young child's construction of a number system is an understanding of correspondence. Although current research demonstrates that preschool children use correspondence in a variety of tasks, the nature of the relationship between the use of correspondence action patterns and the use of correspondence as a quantifier is…

The author's theories concerning the learning of mathematical concepts are outlined. (SD)

Common strategies for teaching proofs are discussed. Prerequisite behaviors, components of a learning hierarchy, are expressed in behavioral terms. The six categories are knowledge about logic, knowledge about the components of a deductive system, knowledge about proof strategies, knowledge of proof formats, proof completion, and generalization.…

Most students leave school with good or acceptable grades in mathematics, despite the fact that very few actually grasp basic mathematical concepts. Schools appear to be providing ways of acquiring the necessary knowledge without promoting true mathematical comprehension. This is made possible by reducing mathematics, cognitively, to a merely…

The purpose of the study was to determine whether students had knowledge of the extension rule (the conjunction of two or more events cannot be greater than the probability of any one of those events) and understanding of conjunction by giving a test of multiplicative probabilities. Involved were 598 students enrolled in introductory psychology…

The bilingual dictionary has been adapted from a dictionary originally developed by Teresa Kow and Euphine Cheung in New York to assist Chinese students in their understanding of mathematics vocabulary and concepts in English. A total of 204 terms and definitions are provided in English with Chinese translations directly below the entries. Each…

Three studies examined the abstractness of children's mental representation of counting, and their understanding of the cardinality principle, namely, that the last number word used in a count tells how many items there are. In the first experiment, 24 toddlers of 2-3 years counted objects, actions, and sounds. Findings revealed that children…

The author shows how a rapid computational "trick" can lead to an investigation of Fibonacci-type sequences. (SD)