Try to See It My Way: The Discursive Function of Idiosyncratic Mathematical Metaphor

Abstract

What are the nature, forms, and roles of metaphors in mathematics instruction ? We present and closely analyze three examples of idiosyncratic metaphors produced during one-to-one tutorial clinical interviews with 11-year-old participants as they attempted to use unfamiliar artifacts and procedures to reason about realistic probability problems. Our interpretations of these episodes suggest that metaphor is both spurred by and transformative of joint engagement in situated activities: metaphor serves individuals as semiotic means of objectifying and communicating their own evolving understanding of disciplinary representations and procedures, and its multimodal instantiation immediately modifies interlocutors' attention to and interaction with the artifacts. Instructors steer this process toward normative mathematical views by initiating, modifying, or elaborating metaphorical constructions. We speculate on situation parameters affecting students' utilization of idiosyncratic resources as well as how socio-mathematical license for metaphor may contribute to effective instructional discourse.

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