The processes by which conceptual knowledge is constructed during mathematical problem solving were studied, focusing on the cognitive activity of learners (i.e., the ways they elaborate, reorganize, and reconceptualize their solution activity). Underlying this research is the view that learners' mathematical conceptions evolve from their activity…

This publication describes several different teaching strategies employed to enhance students' understanding of mathematics, such as working in cooperative learning groups, giving presentations based on problems that were solved, and writing about solutions that were found. This innovative approach to teaching mathematics resulted in questioning…

The fourth volume of this proceedings contains full research articles. Papers include: (1) "Conceptual and procedural approaches to problem-solving" (Y. Mohammad-Yusof and D. Tall); (2)"Teaching differential equations to chemistry and biology students: An overview on methodology of qualitative research. A case study" (M. Moreno and C. Azcarate);…

These conference proceedings include two invited lectures, four working group reports, five topic group reports, a list of participants, and a list of previous proceedings. The invited lectures were: "Teaching Mathematical Proof: Relevance and Complexity of a Social Approach" (Nicolas Balacheff) and "Geometry Is Alive and…

Students can learn to solve problems of qualitative integration and differentiation independently of their study of formal calculus or algebra. This exploratory study investigated the basic intuitions that elementary school children construct in their daily experience with physical and symbolic change. Elementary school children (n=18) were…

There is a popular view that arithmetic is only a collection of dull algorithms containing no interesting ideas. However, if one goes a little below the surface, it will become apparent that there are many fascinating ideas waiting to be discovered. The paper tries to show that mathematical ideas can be recognized and understood without the use of…

This paper describes a study of the connections between beliefs about mathematics, autonomy, and knowledge structures in mathematics. Assumptions underlying the study were (1) that students' beliefs and knowledge are constructs of the individual and play a dynamic role in the learning and doing of mathematics; and (2) that autonomy theoretically…

A project to develop special training materials to introduce college teachers to the math-language approach is reported. The materials link language learning techniques to mathematics concept formation and are intended for teachers of limited-English-proficient (LEP) students. Specialists in both fields produced a three-part training package…

The goal of this book is to help students make sense of mathematics and become confident in their ability to do so. Section 1: "Foundations of Teaching Mathematics," includes chapters entitled: (1) "Teaching Mathematics: Reflections and Directions"; (2) "Exploring What It Means to Do Mathematics"; (3) "Developing Understanding in Mathematics"; (4)…

Intended for preschool and primary grade teachers, this book draws on guidelines from the National Association for the Education of Young Children (NAEYC) and standards from the National Council of Teachers of Mathematics (NCTM) to offer classroom vignettes and teacher-tested activities and strategies that will inspire early childhood teachers to…

Designed as an avenue of communication for mathematics educators concerned with the views, ideas, and experiences of two-year college students and teachers, this journal contains articles on mathematics exposition and education and regular features presenting book and software reviews, classroom activities, instructor experiences, and math…

The National Assessment of Educational Progress (NAEP) is a congressionally mandated project of the U.S. Department of Education's National Center for Education Statistics. It assesses what students in the United States should know and be able to do in geography, reading, writing, mathematics, science, U.S. history, the arts, civics, and other…

The National Council of Teachers of Mathematics' (NCTM) "Curriculum and Evaluation Standards" recommends that mathematical connections be made between mathematics and other disciplines. This book presents 35 activities for middle school students that integrate the teaching of mathematical concepts with environmental concepts. An…

The 1989 document, "Curriculum and Evaluation Standards for School Mathematics" (the "Standards"), provides a vision and a framework for revising and strengthening the K-12 mathematics curriculum in North American schools and for evaluating both the mathematics curriculum and students' progress. When completed, it is expected…

The National Council of Teachers of Mathematics recently published "Principles and Standards for School Mathematics." For the first time, these new standards include pre-kindergarten standards, while outlining the mathematics that children should learn as they progress through school. The standards present a broad view of what…