Abstract: Research shows a Riemann sum based interpretation of the definite integral allows students to make sense of contextual integral models while still supporting a robust understanding of the underlying integrand/differential relationship. However, while many practical applications of integration involve quantitative structures more complex than the $f(x)\cdot dx$ multiplicative relationship (e.g the Inverse Square Law), current work does not precisely characterize the ways in which students navigate through these difficult tasks.
In this seminar, I will cover the ways our previous study with Calculus II students allowed us to extend the Multiplicative Based Summation conception of the definite integral (Jones, 2015) to a Quantitatively Based Summation conception. In addition, I'll discuss our current study of upper-division physics students, which we hope will allow us to refine our QBS framework.
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