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Abstract Title: Physics and calculus students' understanding of the definite integral using graphical representations
Abstract: Using written surveys and individual interviews administered in introductory calculus-based physics and multivariable calculus classes, we studied the extent to which the conceptual understanding of definite integrals affects the understanding of physics concepts that involve definite integrals. We also elicited specific difficulties that students have with definite integrals, particularly with graphical representations, including applying the Fundamental Theorem of Calculus to find the integral of a graphed function. One strong focus of this work was how students reasoned about integrals that yield a negative result.  We noticed student success invoking physical context to interpret certain aspects of definite integrals. Furthermore, we found that although students dominantly used area-under-the-curve reasoning, including unprompted invocation of the Riemann sum, when contemplating definite integrals, their reasoning was often not sufficiently deep to help think about negative definite integrals.
Abstract Type: Symposium Talk
Parallel Session: Research on student conceptions of integration in math and physics

Author/Organizer Information

Primary Contact: Rabindra R. Bajracharya
Oregon State University
and Co-Presenter(s)
John R. Thompson, University of Maine