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1. College Students’ Conceptions of Symbolic Properties in Algebra

   Wladis, C.; Sencindiver, B.; Offenholley, K. (October 2023, Proceedings of the 44th Annual Psychology of Mathematics Education-North America (PME-NA) Conference)

   Lamberg, T.; Moss, D. (Ed.)

   Here we investigate how college students may conceptualize symbolic algebraic properties. This work uses the theory of Grundvorstellungen (GVs) to analyze how learners’ conceptions may or may not align with some desired goals of instruction. Through the analysis of interviews with students across a variety of courses, we describe several categories of conceptions, or descriptive GVs, that emerged in the data. We expect these categorizations to be a helpful first step in understanding learners’ thinking and improving instruction on algebraic properties. 

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2. How do college students conceptualize algebraic properties?

   Wladis, C.; Sencindiver, B.; Offenholley, K. (July 2023, Proceedings for the 13th Congress of the European Society for Research in Mathematics Education (CERME13).)

   Here we explore how college students across different courses may conceptualize symbolic algebraic properties. This work draws on the theory of Grundvorstellungen (GVs) as a tool to analyse how learner conceptions do or do not align with some desired goals of instruction. In analysing interviews, several categories of conceptions, or descriptive GVs, emerged, which may be a helpful first step in understanding learners’ thinking and improving instruction on algebraic properties. 

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3. A Model of How Student Definitions of Substitution and Equivalence May Relate to Their Conceptualizations of Algebraic Transformation.

   Wladis, C.; Sencindiver, B.; Offenholley, K.; Jaffe, E.; & Taton, J. (January 2022, Proceedings for the 12th Congress of the European Society for Research in Mathematics Education (CERME12))

   Cho, Sung Je (Ed.)

   This empirical paper explores students’ conceptions of transformation as substitution equivalence by linking it to their definitions of substitution and equivalence. This work draws on Sfard’s (1995) framework to conceptualize conceptions of substitution equivalence and its components, equivalence and substitution, each on a spectrum from computational to structural. We provide examples of student work to illustrate how students’ understandings of substitution, equivalence, and substitution equivalence as an approach to justifying transformation may relate to one another. 

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4. An Exploration of How College Students Think About Parentheses in the Context of Algebraic Syntax.

   Wladis, C.; Sencindiver, B.; Offenholley, K. (November 2022, Proceedings of the 44th Annual Psychology of Mathematics Education-North America (PME-NA) Conference)

   Lischka; A. E., Dyer; Jones, R. S.; Strayer, J.; Drown, S. (Ed.)

   In this paper we explore how college students across different courses appeared to interpret the meaning of parentheses or brackets in the context of algebraic syntax. This work was influenced by theories of computational vs structural thinking, and also considered the extent to which students’ definitions, computational work, and explanations appeared to be consistent with specific normative definitions of parentheses. In analyzing student work, several categories of students’ conceptions emerged, which may be helpful in diagnosing which conceptions may be more productive or problematic as students progress through algebra. For students who appear to conceptualize parentheses as a cue to non-normative procedures, several categories of procedures were found, which could have implications for instruction. 

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5. Conceptualizing Mathematical Transformation as Substitution Equivalence: The Critical Role of Student Definitions.

   Wladis, C.; Sencindiver, B.; Offenholley, K.; Jaffe, E.; Taton, J. (January 2022, Proceedings for the 24th Annual Conference on Research in Undergraduate Mathematics Education)

   Karunakaran, S. S.; Higgins, A. (Ed.)

   This theoretical paper explores student conceptions of transformation as substitution equivalence by linking it to their definitions of substitution and equivalence. This work draws on the work of Sfard (1995) to conceptualize substitution equivalence and its components, equivalence and substitution, as a spectrum from computational to structural. We provide examples of students’ work to illustrate how student notions of substitution, equivalence, and substitution equivalence as an approach to justifying transformation may related to one another. 

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