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May 2008, Volume 39, Issue 3


ZPC and ZPD: Zones of Teaching and Learning
Anderson Norton Beatriz S. D'Ambrosio
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.

The Impact of Middle-Grades Mathematics Curricula and the Classroom Learning Environment on Student Achievement
James E. Tarr, Robert E. Reys, Barbara J. Reys, Oscar Chavez, Jeffery Shih, and Steven J. Osterlind
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.

Learning to Use Fractions: Examining Middle School Students' Emerging Fraction Literacy
Debra I. Johanning
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 Linear Imperative: An Inventory and Conceptual Analysis of Students' Overuse of Linearity
Wim Van Dooren Dirk De Bock Dirk Janssens Lieven Verschaffel
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.

A View on Reviewing
Steve Williams
Some simple guidelines and characteristics.