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Representational Competence and Algebraic Modeling

  • Andrew Izsák
Part of the Advances in Mathematics Education book series (AME)

Abstract

This chapter reviews some key empirical results and theoretical perspectives found in the past three decades of research on students’ capacities to reason with algebraic and graphical representations of functions. It then discusses two recent advances in our understanding of students’ developing capacities to use inscriptions for representing situations and solving problems. The first advance is the insight that students have criteria that they use for evaluating external representations commonly found in algebra, such as algebraic and graphical representations. Such criteria are important because they play a central role in learning. The second advance has to do with recognizing the importance of adaptive interpretation, which refers to ways in which students must coordinate shifts in their perspective on external representations with corresponding shifts in their perspective on problem situations. The term adaptive highlights the context sensitive ways in which students must learn to interpret external representations. The chapter concludes with implications of these two advances for future research and algebra instruction.

Keywords

Word Problem Algebraic Representation Algebraic Modeling Equal Sign External Representation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Department of Mathematics and Science EducationUniversity of GeorgiaAthensUSA

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