Reviews three software packages: (1) "Physics," tutorial, grades 11-12, Macintosh; (2) "Hands On Math: Volume I," interactive math exploration/simulation of manipulatives use, grades K-7, Apple II; and (3) "A.I.: An Experience with Artificial Intelligence," simulation, grades 5-12, Apple II. (MVL)

Proposes guidelines for introducing enrichment materials in the Montessori classroom, focusing on the introduction of numbers to young children and recommendations for specific mathematics activities. Suggests that one reason for adding materials is to revitalize the classroom environment, as children expect novelty and change. The risk is that…

Provides a brief explanation why instruction designed for use with the microcomputer can enhance students' understanding of the concept of function. Presents five lessons designed to help students develop a thorough understanding of functions and their uses, to encourage students to explore and verbalize mathematical ideas, and to assist in the…

Types of questions asked in first-grade mathematics classes in Japan, Taiwan, and the United States were investigated. Observations of 311 lessons by 16 Japanese, 20 Taiwanese, and 33 U.S. teachers suggest that the kinds of questions asked in Taiwan and Japan contribute to more sophisticated mathematical knowledge. (SLD)

This article considers the question of what specific actions a teacher might take to create a culture of inquiry in a secondary school mathematics classroom. Sociocultural theories of learning provide the framework for examining teaching and learning practices in a single classroom over a two-year period. The notion of the zone of proximal…

Debates about the future of school mathematics in the United States often center on whether standards-based instruction is improving or undermining students' achievement. Critical for making progress in these debates is information about the actual nature of classroom practice in U.S. classrooms. This article focuses on one key element of…

This article describes a professional development model in which middle-grades teachers focused on algebraic thinking as part of their participation in a mathematics academy.

The Statistical Reasoning Assessment or SRA is one of the first objective instruments developed to assess students' statistical reasoning. Published in 1998 (Garfield, 1998a), it became widely available after the Garfield (2003) publication. Empirical studies applying the SRA by Garfield and co-authors brought forward two intriguing puzzles: the…

This paper examines ways in which coherent reasoning about key concepts such as variability, sampling, data, and distribution can be developed as part of statistics education. Instructional activities that could support such reasoning were developed through design research conducted with students in grades 7 and 8. Results are reported from a…

This paper outlines the nexus between mathematics content knowledge and pedagogical knowledge in developing pedagogical content knowledge. Increasing expectations about what students should know and be able to do, breakthroughs in research on how children learn, and the increasing diversity of the student population have put significant pressure…

A new method of analyzing mathematics attitudes through symbolic drawings, situated within the field of Jungian-oriented analytical psychology, was applied to 52 preservice elementary teachers before and after a mathematics methods course. In this triangulation mixed methods design study, pretest images related to past mathematics experiences…

The 2007 National Assessment of Educational Progress (NAEP) evaluated students' understanding of mathematics concepts and their ability to apply mathematics to everyday situations. Students demonstrated their knowledge of these critical skills by responding to questions about number properties and operations, measurement, geometry, data analysis…

After 10 years of teaching rule-driven, procedure-based, algorithm-oriented mathematics, an elementary teacher describes how she began to rethink her teaching style after returning to school for a graduate degree. Her rethinking is based on the first of four student teaching events that spanned an entire school year in which she used the…

This book contains a set of authentic performance assessments that offer students the opportunity to demonstrate knowledge and multiple science abilities through communication, problem solving, inventiveness, persistence, and curiosity. The specific knowledge and science abilities are drawn from those identified in Benchmarks for Science Literacy…

The call for educational reform has caused mathematics curriculum, instruction, and assessment to come under both professional and public scrutiny. The three elements contesting for leadership in assessment reform are the conventional testing agencies, reformers led by the National Council of Teachers of Mathematics (NCTM), and political agencies…