In college level chemistry courses, reasoning using molecular and particulate descriptions of matter becomes central to understanding physical and chemical properties. In this study, we used a qualitative approach to analyzing classroom discourse derived from Toulmin's model of argumentation in order to describe the ways in which students develop particulate-level justifications for claims about thermodynamic properties. Our analysis extends the construct of sociomathematical norms to a chemistry context in order to describe disciplinary criteria for reasoning and justification, which we refer to as sociochemical norms. By examining how whole class and small group discussions shape norms related to reasoning, we provide suggestions for teaching practices in inquiry-oriented settings.

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In this report, we adapt and extend a methodology for documenting the collective production of meaning in a classroom community. A cornerstone of the methodological approach that we develop is a close examination of classroom discourse. Our efforts to analyze the collective production of meaning by examining classroom interaction are compatible with the relatively recent emphasis in mathematics and science education research that focuses on how communities of learners establish ideas through discourse and inquiry. The methodological approach we take builds on and extends an approach from mathematics education that uses Toulmin's argumentation model to document and analyze students' conceptual progress. Our modification introduces a new criterion for empirically demonstrating when particular ways of reasoning become part of the normative practices of the community. An example from an undergraduate course in physical chemistry is used to illustrate the methodology.

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This paper reports on a study investigating students' ways of conceptualizing key ideas in linear algebra, with the particular results presented here focusing on student interactions with the notion of subspace. In interviews conducted with eight undergraduates, we found students' initial descriptions of subspace often varied substantially from the language of the concept's formal definition, which is very algebraic in nature. This is consistent with literature in other mathematical content domains that indicates that a learner's primary understanding of a concept is not necessarily informed by that concept's formal definition. We used the analytical tools of concept image and concept definition of Tall and Vinner (Educational Studies in Mathematics, 12(2): [151][152][153][154][155][156][157][158][159][160][161][162][163][164][165][166][167][168][169] 1981) in order to highlight this distinction in student responses. Through grounded analysis, we identified recurring concept imagery that students provided for subspace, namely, geometric object, part of whole, and algebraic object. We also present results regarding the coordination between students' concept image and how they interpret the formal definition, situations in which students recognized a need for the formal definition, and qualities of subspace that students noted were consequences of the formal definition. Furthermore, we found that all students interviewed expressed, to some extent, the technically inaccurate "nested subspace" conception that R k is a subspace of R n for k