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Abstract Title: Using the theory of conceptual blending at the mathematics-physics interface
Abstract: Throughout the physics curriculum, students learn and apply mathematics to model and reason about physical systems. Mathematics often serves as the structure for physics ideas. In the past two decades, several physics education researchers have adopted and adapted the conceptual blending framework to productively describe the ways students connect ideas from different conceptual spaces toward deeper content understanding. More recently, this framework has been applied to how students reason with and use mathematics in physics. This session will focus on the details of the theory behind conceptual blending and feature recent research using conceptual blending to describe the process of students combining mathematical and physical ideas while problem solving. Content level ranges from quantitative reasoning in introductory mechanics through vector differentials in intermediate electricity and magnetism to partial differential equations and boundary conditions in the context of heat conduction. This session will conclude with extended time for a deeper discussion of the theory of conceptual blending and questions for all speakers and participants.  If time permits, we will discuss future options for applications of this framework in other research areas.
Abstract Type: Talk Symposium
Session Time: Parallel Sessions Cluster II

Author/Organizer Information

Primary Contact: John Thompson
University of Maine

Symposium Specific Information

Moderator: John Thompson
Presentation 1 Title: Modeling the construction and interpretation of equations: Incorporating symbolic forms into a conceptual blend
Presentation 1 Authors: Benjamin P. Schermerhorn, California State University Fullerton
John R. Thompson, University of Maine
Presentation 1 Abstract: Much of physics involves the construction and interpretation of equations. Sherin designed the symbolic forms analysis to describe students' construction of equations in physics. A symbolic form includes two components: the symbol template to represent the externalized structures of the equation and the conceptual schema to represent the acontextual mathematical justification of the symbol template. We incorporate symbolic forms into a conceptual blending framework to describe the ways in which construct and understand equations. Our model treats the conceptual schema as the underlying generic space of conceptual blending that frames the combination of the contextual information and the symbolic structure. We present this model in the context of student construction of non-Cartesian differential length vectors. We illustrate the affordances of the model by drawing further connections between the frameworks and expanding this approach to other contexts within our research.
Presentation 2 Title: Dynamic conceptual blending analysis to model student reasoning processes while integrating mathematics and physics
Presentation 2 Authors: Sofie van den Eynde, Katholieke Universiteit Leuven
Benjamin P. Schermerhorn, California State University Fullerton
Johan Deprez, KU Leuven
Martin Goedhart, University of Groningen
John R. Thompson, University of Maine
Mieke De Cock, KU Leuven
Presentation 2 Abstract: Conceptual blending has been used to study student reasoning at the math-physics interface, but the current emphasis is mostly on the product of student reasoning, while information about the reasoning process is missing in the analysis. Therefore, we adapted the blending diagrams to also include the dynamics of student reasoning. In this session, we will use data from an interview study that focused on undergraduate students' understanding of boundary conditions for the heat equation. We demonstrate the construction of a dynamic blending diagram (DBD) and its use as an analytical framework. We show that by using a DBD, we can judge the degree to which students integrate their understanding of mathematics and physics. The DBD also enables the reader to follow the line of reasoning of the students. Moreover, a DBD can be used to diagnose difficulties in student reasoning.
Presentation 3 Title: A conceptual blend analysis of student reasoning about Physics Quantitative Literacy Reasoning Inventory (PIQL) items
Presentation 3 Authors: Suzanne White Brahmia, University of Washington
Alexis Olsho, Charlotte Zimmermann, University of Washington
Trevor Smith, Rowan University
Presentation 3 Abstract: Mathematical reasoning flexibility across physics contexts is a desirable learning outcome of introductory physics, where the "math world" and "physical world" intersect. Physics Quantitative Literacy (PQL) is a set of interconnected skills and habits of mind that support quantitative reasoning about the physical world, partially characterized by Sherin's symbolic forms. The Physics Inventory of Quantitative Literacy (PIQL) assesses student facility with the cognitive building blocks for creating symbolic models in physics -- proportional reasoning, co-variational reasoning, and reasoning with signed physics quantities. We apply a conceptual blending theory (CBT) analysis of interviews in which students think-aloud as they answer PIQL items. A CBT analysis helps uncover hierarchical, partially-correct reasoning patterns. CBT holds potential as a framework for mapping the emergence of mathematical reasoning flexibility in the introductory physics sequence that leads to productive reasoning, as characterized by Sherin's symbolic forms.