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Editors contains: "Infante, N"

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  1. ; ; ; (, 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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    Accepted Manuscript Full Text Available
  2. ; ; ; ; (, Proceedings of the 26th Annual Conference on Research in Undergraduate Mathematics Education)
    Cook, S; Infante, N (Ed.)
    Even though algebraic conceptual understanding is recognized as a critical skill, existing larger scale validated algebra assessments consist mostly of computational tasks, or only assess a very narrow range of conceptions in a smaller focused domain. Further, few instruments have been validated for use with college students. In this paper, we describe the creation and validation of an algebra concept inventory for college students. We describe how items were administered, revised, and tested for validity and reliability. Results suggest that algebraic conceptual understanding is a measurable construct, and that the instrument has reasonable validity and reliability. Revision and validation is ongoing; however, lessons learned thus far provide information about what conceptual understanding in algebra might look like and how it might be assessed. 
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    Accepted Manuscript Full Text Available
  3. ; ; (, Proceedings for the 25th Annual Conference on Research in Undergraduate Mathematics Education, RUME, http://sigmaa.maa.org/rume/Site/Proceedings.html)
    Cook, S.; Infante, N. (Ed.)
    In the context of proofs, researchers have distinguished between syntactic reasoning and semantic reasoning; however, this distinction has not been well-explored in areas of mathematics education below formal proof, where student reasoning and justification are also important. In this paper we draw on theories of cognitive load and syntactic versus semantic proof-production to explicate a definition for syntactic reasoning outside the context of formal proof, using illustrative examples from algebra. 
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    Accepted Manuscript Full Text Available
  4. ; ; (, Proceedings for the 25th Annual Conference on Research in Undergraduate Mathematics Education)
    Cook, S.; Infante, N. (Ed.)
    In this theoretical paper, we describe how algebraic transformation could be reconceptualized as a process of substitution equivalence, and we discuss how this conceptualization affords mathematical justification of transformation processes. In particular, we describe a model which deconstructs the process of substitution equivalence into core subdomains which could be learned serially and then re-integrated, in order to make them accessible to students with lower prior knowledge in syntactic reasoning. Our aim in presenting this model is to start a conversation about what the core components of knowledge might be in order for students to reason about and justify algebraic transformation using symbolic representations. 
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    Accepted Manuscript Full Text Available
  5. ; ; ; (, Proceedings for the 25th Annual Conference on Research in Undergraduate Mathematics Education)
    Cook, S.; Infante, N. (Ed.)
    Although "developmental math" is widely discussed in higher-education circles, exactly what developmental math encompasses is often underdeveloped. In this theoretical report, we use a sample of highly cited works on developmental math to identify common characterizations of the term "developmental math" in the literature. We then interrogate and problematize each characterization, particularly in terms of whether they serve equity-related goals such as access to college credentials and math learning. We close by proposing an alternative characterization of developmental math and discuss the theoretical implications. We see this as a first step towards conversations about how developmental math could be conceptualized. 
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    Accepted Manuscript Full Text Available
  6. ; ; ; (, Proceedings for the 25th Annual Conference on Research in Undergraduate Mathematics Education)
    Cook, S.; Infante, N. (Ed.)
    In this theoretical paper, our aim is to start a conversation about how "levels" in mathematics are operationalized and defined, with a specific focus on "college level." We approach this from a lens of developmental stages, using this to propose an initial framework for describing how learners might progress along a developmental continuum delineated by the kinds of reasoning/justification, generalization/abstraction, and types of conceptions that they hold, rather than by the particular computations learners are able to do, or the kinds of mathematical objects with which learners are engaging. 
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    Accepted Manuscript Full Text Available