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Abstract Title: Using physics to highlight the underlying structure of Riemann sums in learning definite integrals
Abstract: Several studies have shown that students are most successful solving definite integral application problems when they are able to see the definite integral as the sum of infinitely small products, or in other words when they understand the underlying structure of Riemann sums. This research involves classroom teaching experiments and clinical interviews with first-semester calculus students where initial instruction on definite integrals is centered on physics applications that highlight the underlying structure of Riemann sums. For example, when students approximate the force of water exerted on a dam, they attend to the underlying structure of force as the product of pressure and area. This research aims to identify strengths and weaknesses of the students as they develop an initial understanding of definite integrals, and how they use this understanding to build more formal ideas, such as the Fundamental Theorem of Calculus and the relationship to area under a curve.
Abstract Type: Symposium Talk
Parallel Session: Research on student conceptions of integration in math and physics

Author/Organizer Information

Primary Contact: Vicki L. Sealey
West Virginia University