Appropriating Mathematical Practices: A Case Study of Learning to Use and Explore Functions Through Interaction with a Tutor

Author: Moschkovich Judit  

Publisher: Springer Publishing Company

ISSN: 0013-1954

Source: Educational Studies in Mathematics, Vol.55, Iss.1-3, 2004-01, pp. : 49-80

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Abstract

This case study uses a socioculturalperspective and the concept ofappropriation (Newman, Griffin and Cole,1989; Rogoff, 1990) to describe how astudent learned to work with linearfunctions. The analysis describes in detailthe impact that interaction with a tutorhad on a learner, how the learnerappropriated goals, actions, perspectives,and meanings that are part of mathematicalpractices, and how the learner was activein transforming several of the goals thatshe appropriated. The paper describes how alearner appropriated two aspects ofmathematical practices that are crucial forworking with functions (Breidenbach,Dubinsky, Nichols and Hawks, 1992; Even,1990; Moschkovich, Schoenfeld and Arcavi,1993; Schwarz and Yerushalmy, 1992; Sfard,1992): a perspective treating lines asobjects and the action of connecting a lineto its corresponding equation in the formy = mx + b. I use examples from theanalysis of two tutoring sessions toillustrate how the tutor introduced threetasks (estimating y-intercepts, evaluatingslopes, and exploring parameters) thatreflect these two aspects of mathematicalpractices in this domain and describe howthe student appropriated goals, actions,meanings, and perspectives for carrying outthese tasks. I describe how appropriationfunctioned in terms of the focus ofattention, the meaning for utterances, andthe goals for these three tasks. I alsoexamine how the learner did not merelyrepeat the goals the tutor introduced butactively transformed some of these goals.