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July 1999, Volume 30, Issue 4


Fifth Graders' Enumeration of Cubes in 3D Arrays: Conceptual Progress in an Inquiry-Based Classroom
Michael T. Battista
In this study I utilize psychological and sociocultural components of a constructivist paradigm to provide a detailed analysis of how the cognitive constructions students make as they enumerate 3D arrays of cubes develop and change in an inquiry-based problem-centered mathematics classroom. I describe the classroom work of 3 pairs of 5th graders on an instructional activity involving predicting the number of cubes that fit in graphically depicted boxes, and I carefully explicate how the mental processes of abstraction, reflection, perturbation, spatial structuring, and coordination, along with face-to-face social interaction within pairs, brought about meaningful and powerful student learning.

An Exploration of Aspects of Language Proficiency and Algebra Learning
Mollie MacGregor, Elizabeth Price
We have attempted to investigate whether 3 cognitive components of language proficiency--metalinguistic awareness of symbol, syntax, and ambiguity--are associated with students' success in learning the notation of algebra. Pencil-and-paper tests were given to assess students' metalinguistic awareness and their ability to use algebraic notation. In a total sample of more than 1500 students, aged 11 to 15, who were in their 1st to 4th years of algebra learning, we found that very few students with low metalinguistic awareness scores achieved high algebra scores. We discuss implications of this finding for the school algebra curriculum.