Describes a study in which average eighth graders in an urban junior high school were placed into prealgebra classes normally reserved for high achievers. The average achievers in the prealgebra classes understood mathematical concepts better and enrolled in more advanced mathematics classes during high school, than did their cohorts. (GLR)

Proposes angle sense as a fundamental connector between mathematical concepts for middle grade students. Introduces the use of pattern blocks and a goniometer, a tool to measure angles, to help students develop angle sense. Discusses connections between angle measurement and the concepts of rational numbers, circles, area, number theory,…

Discusses the use of writing to enhance learning in mathematics from a conceptual development perspective. Shuell's phases of learning are described as a general model for conceptual development and subsequently matched with Britton's categories for transactional-informative writing. Sample mathematics assignments for each writing category are…

Introduces the constructivist theory of mathematical learning, and illustrates its application in a curriculum focusing on fundamental concepts. How knowledge is constructed, how concepts mature, and what it means to learn and to know mathematics are presented. Pedagogical implications of adopting a constructivist perspective on knowledge and…

Educators recognize that group work and physical involvement with learning materials can greatly enhance the understanding and retention of difficult concepts. As a result, math manipulatives--such as pattern blocks and number lines--have increasingly been making their way into classrooms and children's museums. Yet without the constant guidance…

Rather than focusing on teaching teachers, university researchers helped local teachers study what students thought about math and science ideas--with powerful results. As teachers understood what students were thinking, they modified their practices to promote deeper understanding. Their collaboration created bottom-up change.

The paper describes the use of a spreadsheet in a mathematics teacher education course. It shows how the tool can serve as a link between seemingly disconnected mathematical concepts. The didactical triad of using a spreadsheet as an agent, consumer, and amplifier of mathematical activities allows for an extended investigation of simple yet…

"How can this Abstract Algebra course help me to teach Algebra in high school?" To professors of prospective mathematics teachers, this type of question has a resounding familiarity. Because students are unclear as to the relationship between upper division mathematics courses and the high school curriculum, answering the opening question to the…

"Houghton Mifflin Mathematics" is a core curriculum for kindergarten through grade 6 students at all ability levels. According to its developer, "Houghton Mifflin Mathematics" emphasizes the five content strands and processes recommended by the National Council of Teachers of Mathematics Standards. At each grade level the…

This book presents extensive sampling of a "whole math" curriculum for preschool and kindergarten children ages 3 and older. An introductory chapter is followed by seven curriculum chapters that discuss math manipulatives, collections, grid games, path games, graphing, math and gross-motor play, and the "math suitcase." Each chapter is divided…

Students who are anxious about mathematics elect to take fewer mathematics courses in high school and college. This math avoidance is also typical for many first-year elementary school teachers who show high levels of mathematics anxiety. These teachers schedule less time for mathematics instruction than their less anxious colleagues. This paper…

Eleven experts in mathematics education, special education, and assessment completed an open-ended survey on current math instruction in relation to the "Curriculum and Evaluation Standards" of the National Council of Teachers of Mathematics and the perceived appropriateness and feasibility of the standards for students with…

This study is based on data from a state-wide assessment that included both multiple-choice and constructed-response items. The intent of the study was to see whether item types make a difference in gender results. The items on both tests were categorized according to whether they assessed procedural knowledge, concepts, problem solving, or…

Children begin school with the ability to use their informal and implicit conceptual knowledge to guide their problem solving, but shift to the use of superficial strategies in their attempts to solve word problems as they progress through school. This paper describes a study designed to investigate the effects of an instructional sequence that…

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…