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July 2004, Volume 35, Issue 4


Visual Salience of Algebraic Transformations
David Kirshner, Thomas Awtry
Information processing researchers have assumed that algebra symbol skills depend on mastery of the abstract rules presented in the curriculum (Matz, 1980; Sleeman, 1986). Thus, students' ubiquitous algebra errors have been taken as indicating the need  to embed algebra in rich contextual settings (Kaput, 1995; National Council of Teachers of Mathematics [NCTM] Algebra Working Group, 1998). This study  explored a nonrepresentational account of symbolic algebra skills as feature correlation within the visual field. We present evidence that algebra students respond spontaneously to the visual patterns of the notational display apart from engagement with  the declarative content of the rules. Thus, persistent algebra errors may reflect disengagement from declarative content rather than an inability to deal with it. We sketch a Lexical Support System designed to sustain students' engagement with the declarative  content of algebraic rules and processes, thus complementing the exciting curricular possibilities being developed for referentially rich algebra.

Learning Mathematics in a Classroom Community of Inquiry
Merrilyn Goos
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.

A Forum for Researchers: Reviews That Teach
John P. Smith III
Some years ago, Gila Hanna offered the very insightful and useful distinction between mathematical proofs that prove and those that also explain (Hanna, 1989).

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