Developing and connecting calculus students’ notions of rate of change and accumulation: the fundamental theorem of calculus. 866–871), Oklahoma City: SIGMAA-RUME.Ĭarlson, M. Oehrtman (Eds.), Proceedings of the 22nd Annual Conference for Research in Undergraduate Mathematics Education (pp. “Derivative makes more sense with differentials”: how primary historical sources informed a university mathematics instructor’s teaching of derivative. Archive for History of Exact Sciences, 14, 1–90.Ĭan, C., & Aktas, M. Differentials, higher-order differentials and the derivative in the Leibnizian calculus. Differential calculus: from practice to theory. International Journal of Mathematical Education in Science and Technology, 29(3), 389–399.īoman, E., & Rogers, R. First-year university students’ understanding of rate of change. The continuous and the infinitesimal in mathematics and philosophy. Is mathematical history written by the victors? Notices of the AMS, 60(7), 886–904.īell, J. Archive for History of Exact Sciences, 67, 553–593.īair, J., Błaszczyk, P., Ely, R., Henry, V., Kanovei, V., Katz, K., et al. Leibniz’ syncategorematic infinitesimals. In this article I motivate and describe some key elements of differentials-based calculus courses, and I summarize research indicating that students in such courses develop robust quantitative meanings for notations in single- and multi-variable calculus.Īrthur, R. One goal is for students to develop understandings of calculus notation that are imbued with more direct referential meaning, enabling them to better interpret and model situations by means of this notation. dx, not the limit of a sequence of Riemann sums.dx is a relationship between increments of x and y, making dy/ dx an actual quotient rather than code language for \(\underset2x dx\) is a sum of pieces of the form 2 x.In these approaches, a differential equation like dy = 2 x These approaches seek to restore to differential notation the direct referential power it had during the first century after calculus was developed. have been studied recently that are grounded in infinitesimals or differentials rather than limits. Several new approaches to calculus in the U.S.
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