Calculational and analytical perspectives in introductory algebra: a theoretical contribution
Résumé
In this theoretical paper we discuss what a calculational perspective on mathematical activity entails and discuss its relevance in terms of related speech genres in the introductory algebra classroom. Learning in the introductory algebra classroom is multifaceted because major shifts in form (the algebraic syntax versus arithmetic syntax) and function (analytic rather than calculational) are expected to take place. This theoretical argument is exemplified through student utterances from a Californian 6th grade classroom discussion, in which students' calculational perspective on mathematical activity is apparent. The data reveal traits and intentions from both traditional and alternative instructional genres. Our main argument is that the students' approaches to generalize provided patterns were limited to their perceptual field and thus fail to include a deductive argument, the key feature of algebraic reasoning.
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