## Physics Education Research Conference 2017 Invited Talks

## Plenaries

### Quantitative reasoning and mathematical modeling in an introductory calculus sequence

*Keynote speaker: Michael Oehrtman, Oklahoma State University*

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I will report on thematic results drawn from multiple studies of student learning in an introductory calculus sequence pertaining to the nature and roles of quantitative reasoning and mathematical modeling. We investigated calculus students' development of mathematical expressions and equations involving derivatives, definite integrals, and vector-valued functions to represent physical quantities and relationships between those quantities. The presentation will characterize the cognitive challenges that students encountered while constructing these models, how students resolved those challenges, and the resulting conceptual artifacts.

### Student Understanding and Symbolization of Eigentheory

*Keynote speaker: Megan Wawro, Virginia Tech*

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Linear algebra is a key course in students' undergraduate education across multiple STEM-related majors. Eigentheory is a conceptually complex idea that builds from and relies upon multiple key ideas in mathematics, and its application is widespread in mathematics and beyond. In this presentation, I will share research results from individual interviews regarding various ways that students in quantum physics courses reason about and symbolize eigenvectors and eigenvalues for a 2x2 matrix. I will also share an instructional sequence from the Inquiry-Oriented Linear Algebra curriculum created to support students' reinvention of change of basis and eigentheory, as well as how the two are related through diagonalization. Data from introductory linear algebra classes using this sequence will illustrate ways in which students build from their experience with stretch factors and directions to create for themselves ways to determine eigenvalues and eigenvectors for various 2x2 matrices.