Five classroom situations in Japanese elementary schools are described and interpreted from perspective of first four standards in the National Council of Teachers of Mathematics (NCTM) Curriculum and Evaluation Standards. Concludes that Japanese children do so well in mathematics because Japanese teachers embody essence of the standards in…

Presents a series of four worksheets to develop students' perception of spatial relationships. The tasks require students to use cubes to build models and describe the models by representing the front, right, and top views on grid paper. Provides reproducible worksheets. (MDH)

Proposes using student projects to show students how mathematics can be applied to their lives by using statistics. Students identify a topic of interest to them and their community, collect data, discuss the analyzed data in a written report, and present the reports at the local senior-citizen center. (MDH)

Detection of calculation errors, operation errors, and unanswerable problems was studied for 78 third graders and 77 fifth graders. The relationship between mathematics achievement and error detection was also examined. Older children and high achievers detected more errors than did younger students and low achievers. (SLD)

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)

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 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 aims, first, to describe the fundamental characteristics and workings of the AgentGeom artificial tutorial system, which is designed to help students develop knowledge and skills related to problem solving, mathematical proof in geometry, and the use of mathematical language. Following this, we indicate the manner in which a secondary…

Effective teaching should focus on representational change, which is fundamental to learning and education, rather than conceptual change, which involves transformation of theories in science rather than the gradual building of knowledge that occurs in students. This article addresses the question about how to develop more efficient strategies for…

This study examines a series of children's drawings ("Draw for Math" tasks) to determine the relationship of students' spatial understanding and mathematical problem solving. Level of spatial understanding was assessed by applying the framework of central conceptual structures suggested by Case (1996), a cognitive developmental researcher.…

This study examines Indonesian students' understanding of conservation of matter, balancing of equations and stoichiometry. Eight hundred and sixty-seven Grade 12 students from 22 schools across four different cities in two developed provinces in Indonesia participated in the study. Nineteen teachers also participated in order to validate the…

Working memory (WM) has been associated with the acquisition of arithmetic skills, however, the components of WM that underlie this acquisition have not been explored. This study explored the contribution of two WM systems (the phonological loop and the central executive) to mathematical performance in young children. The results showed that a…

A third-grade teacher and a teacher educator argue that, in an elementary mathematics class in which the teacher is encouraging the children to communicate and justify their mathematical ideas, the features of a mathematical task shape the mathematical discourse. They conjecture that divergent tasks, problems with many correct answers, may…

These two booklets (one in English and one in Spanish) are designed to help parents become more involved in their children's mathematics education. The booklets are divided into two sections. The first section explains why mathematics is an important subject for children to learn as they prepare themselves for a place in today's society. The…

Higher order cognitive development and success in the study of high school mathematics and science require an understanding of rational number concepts and facility with proportional reasoning and computation. Proportional reasoning is an essential schema for developing formal operational thought. This study involving 16 ninth-grade students was…