PROCEEDINGS OF THE 20TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2017
San Diego, California
Beyond the product structure for definite integrals
Page: 912
Over the past decade research has shown that a Riemann sum based interpretation of the definite integral supports a robust understanding of the underlying structure of the integrand/differential relationship and facilitates students’ ability to make sense of contextual integral models. However, current studies center this understanding on the multiplicative structure݂ f(x) * Delta x which does not account for many practical uses of integration. In many situations, the Delta x is most productively conceived as a component of another quantity which might then be incorporated in any of a variety of quantitative models, such as an inverse square law rather than a simple product. To fill this gap, this study utilized Dewey’s theory of inquiry to identify three interpretations of the definite integral which proved productive for students when modeling definite integrals that extend beyond the traditionally studied product structure.