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July 2011, Volume 42, Issue 4

FEATURES

Generalizing-Promoting Actions: How Classroom Collaborations Can Support Students’ Mathematical Generalizations
Amy B. Ellis
Generalization is a critical component of mathematical activity and has garnered increased attention in school mathematics at all levels. This study documents the multiple interrelated processes that support productive generalizing in classroom settings. By studying the situated actions of 6 middle school students and their teacher–researcher working on a 3-week unit on quadratic growth that can be represented as y = ax2, the study identified 7 major categories of generalization-promoting actions. These actions represent how teachers and students can act in interaction with other agents to foster students’ generalizing activities.

Anchoring Students’ Metaperspective Discussions of History in Mathematics
Uffe Thomas Jankvist
An empirical study on the use of history (as a goal) in mathematics education is discussed in this article. A historical module was designed and implemented in a Danish upper secondary class to study how students’ discussions of metaperspective issues of the historical development of mathematics may be anchored in the taught and learned subject matter of the module. Based on videos of the implementation (in particular of one focus group of students), students’ hand-in essay assignments, mathematical exercises, questionnaires, and follow-up interviews, the question addressed is how such anchoring may be accomplished

The Splitting Loope
Jesse L. M. Wilkins and Anderson Norton
Researchers have hypothesized that children’s construction of splitting operations is crucial to their construction of more advanced fractions concepts (Steffe, 2002). The authors propose that splitting constitutes a psychological structure similar to that of a mathematical group (Piaget, 1970): a structure that introduces mutual reversibility of students’ partitioning and iterating operations that the authors refer to as the splitting loope. Findings from 66 sixth-grade students’ written performance on 20 tasks are consistent with hypotheses from related teaching experiments. They demonstrate that equipartitioning and the partitive unit fraction scheme mediate the construction of splitting from partitioning and iterating operations.

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