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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. College Students’ Conceptualizations of Symbolic Algebraic Properties

   Wladis, C; Sencindiver, B; Offenholley, K; Aly, G (February 2024, Proceedings of the 26th Annual Conference on Research in Undergraduate Mathematics Education)

   Cook, S; Infante, N (Ed.)

   Here we explore how college students across a wide range of courses may conceptualize symbolic algebraic properties. We draw on the theory of Grundvorstellungen (GVs) to analyze how learner conceptions may or may not align with instructional goals. In analyzing interviews, several categories of conceptions (descriptive GVs) emerged that may help us to better understand how students conceptualize symbolic properties during instruction. 

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3. 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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4. How higher education instructors conceptualize diversity: A phenomenographic study

   Suarez, Nicole A.; Wang, Song; Brydges, Stacey; Lo, Stanley M. (January 2022, Proceedings of the 16 th International Conference of the Learning Sciences - ICLS 2022)

   Chinn, C.; Tan, E.; Chan, C.; Kali, Y. (Ed.)

   Higher education institutions around the globe have increasingly made the commitment to diversity. Instructors play an integral role in creating inclusive learning environments. Guided by sociopolitical perspectives on learning, we ask: How do higher education instructors conceptualize diversity? How do these conceptions inform curriculum and instruction? Interview data from 30 instructors teaching at minority-serving institutions in the United States revealed three distinct conceptions of diversity defined by variations in five aspects: student identities, intelligence mindset, pedagogical motivation, learning environment, and legitimized membership. The essentialist conception is based on students having inherently determinate traits described by preexisting universal categories. The functionalist conception differentiates students by academic performance. The existentialist conception acknowledges that students have unique experiences that impact the learning process. Our results indicate that while instructors acknowledge different student features and have varying understanding for why diversity is important, some conceptions of diversity do not necessarily suggest an inclusive culture. 

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5. When Wrong is Right: The Instructional Power of Multiple Conceptions

   https://doi.org/10.1145/3446871.3469750  

   Margulieux, Lauren; Denny, Paul; Cunningham, Kathryn; Deutsch, Michael; Shapiro, Benjamin R. (August 2021, Proceedings of the Sixteenth Annual Conference on International Computing Education Research)

   For many decades, educational communities, including computing education, have debated the value of telling students what they need to know (i.e., direct instruction) compared to guiding them to construct knowledge themselves (i.e., constructivism). Comparisons of these two instructional approaches have inconsistent results. Direct instruction can be more efficient for short-term performance but worse for retention and transfer. Constructivism can produce better retention and transfer, but this outcome is unreliable. To contribute to this debate, we propose a new theory to better explain these research results. Our theory, multiple conceptions theory, states that learners develop better conceptual knowledge when they are guided to compare multiple conceptions of a concept during instruction. To examine the validity of this theory, we used this lens to evaluate the literature for eight instructional techniques that guide learners to compare multiple conceptions, four from direct instruction (i.e., test-enhanced learning, erroneous examples, analogical reasoning, and refutation texts) and four from constructivism (i.e., productive failure, ambitious pedagogy, problem-based learning, and inquiry learning). We specifically searched for variations in the techniques that made them more or less successful, the mechanisms responsible, and how those mechanisms promote conceptual knowledge, which is critical for retention and transfer. To make the paper directly applicable to education, we propose instructional design principles based on the mechanisms that we identified. Moreover, we illustrate the theory by examining instructional techniques commonly used in computing education that compare multiple conceptions. Finally, we propose ways in which this theory can advance our instruction in computing and how computing education researchers can advance this general education theory. 

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