The goal of this article is to examine students' mathematical development that occurs as a teacher works within each of 2 zones of learning: students' zones of proximal development (ZPD) and students' zones of potential construction (ZPC). ZPD, proposed by Vygotsky, is grounded in a social constructivist perspective on learning, whereas ZPC, proposed by Steffe, is grounded in a radical constructivist perspective on learning.

This article examines student achievement of 2533 students in 10 middle schools in relation to the implementation of textbooks developed with funding from the National Science Foundation (NSF) or publisher-developed textbooks.

This article describes one prevalent practice that a group of 6th- and 7th-grade students engaged in when they used fractions in the context of area and perimeter, decimal operations, similarity, and ratios and proportions. The study's results revealed that students did not simply take the concepts and skills learned in formal fractions units and use them in these other mathematical content areas. Their understanding of how to use fractions was tied to their understanding of situations in which they could be used.

The overreliance on linear methods in students' reasoning and problem solving has been documented and discussed by several scholars in the field. So far, however, there have been no attempts to assemble the evidence and to analyze it in a systematic way. This article provides an overview and a conceptual analysis of students' tendency to use linear methods beyond their applicability range.

Review of The Mathematics of Games and Gambling (Second Edition) Edward Packel. (2006). Mathematical Association of America. 192 pp., ISBN-10 0-88385-646-8. $44 (hb), $27.95 (pb). Reviewed by Laurie Rubel, Brooklyn College of the City University of New York .

Some simple guidelines and characteristics.