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

By Judit Moschkovich. 2004

101 citations recorded by the source corpus.

This case study uses a sociocultural perspective and the concept of appropriation (Newman, Griffin and Cole, 1989; Rogoff, 1990) to describe how a student learned to work with linear functions. The analysis describes in detail the impact that interaction with a tutor had on a learner, how the learner appropriated goals, actions, perspectives, and meanings that are part of mathematical practices, and how the learner was active in transforming several of the goals that she appropriated. The paper describes how a learner appropriated two aspects of mathematical practices that are crucial for working 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 as objects and the action of connecting a line to its corresponding equation in the form y = mx + b. I use examples from the analysis of two tutoring sessions to illustrate how the tutor introduced three tasks (estimating y-intercepts, evaluating slopes, and exploring parameters) that reflect these two aspects of mathematical practices in this domain and describe how the student appropriated goals, actions, meanings, and perspectives for carrying out these tasks. I describe how appropriation functioned in terms of the focus of attention, the meaning for utterances, and the goals for these three tasks. I also examine how the learner did not merely repeat the goals the tutor introduced but actively transformed some of these goals.

Subfields: Developmental and Educational Psychology, Education

View Paper: https://www.semanticscholar.org/paper/ad18c3b865b9b652450a65ae9d0d74d374651d15

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In Developmental and Educational Psychology

In Education

Citations in the corpus

Handbook Of Design Research Methods In Education: Innovations In Science, Technology, Engineering, And Mathematics Learning And Teaching (2018, background): “The issue of collective activity is one that resonates with a variety of social theories, among them activity theory (Davydov & Radzikhovskii, 1985; Leont’ev, 1981), sociocultural theory (Lerman, 1996; Moschkovich, 2004; van Oers, 1996), and socioconstructivist theory (Bauersfeld et al.”
A dialectical approach to the formation of mathematical abstractions (2007, background): “With regard to internalisation, Wood and Wood (1996, p. 15) ask, “[Is it speech or] rules of action, in the service of goals, which become activated by symbol systems such as language and diagrams”? With regard to appropriation, a potential alternative to internalisation for those who have a problem”
Framing Interactions to Foster Generative Learning: A Situative Explanation of Transfer in a Community of Learners Classroom (2006, methodology): “…adopted here, I adapt the classic definition to document what a group of students learned during a classroom unit and then show how that group and its individual members appropriated what they learned in some post-unit assessment activities (Moschkovich, 2004; Newman et al., 1989; Rogoff, 1990).”
Growing mathematical objects in the classroom – The case of function (2012, background): “Only a few researchers tried to follow this process as it actually happens in the classroom (Walter & Gerson, 2000; Yerushalmy, 2006), and a small number of others conducted similar investigations in laboratory settings (Chiu et al., 2001; Moschkovich, 2004; Schoenfeld et al., 1993).”
EXAMINING MATHEMATICAL DISCOURSE PRACTICES (2007, background): “This article [1] considers these questions from a socio-cultural and situated perspective of mathematical Discourse practices (Moschkovich, 2002a, 2004) [2].”