![]() ![]() Student conceptions of definite integration and accumulation functions. Oklahoma City, OK: SIGMAA-RUME.įisher, B., Samuels, J., & Wangberg, A. Oehrtman (Eds.), Proceedings of the 22nd Annual Conference for Research in Undergraduate Mathematics Education (pp. Discovering the linearity in directional derivatives and linear approximation. Dreyfus (Eds.), Calculus in upper secondary and beginning university mathematics – Conference proceedings. Teaching calculus with (informal) infinitesimals. Journal of Mathematical Behavior, 48, 158–167.Įly, R. Reasoning with definite integrals using infinitesimals. Journal for Research in Mathematics Education, 41, 117–146.Įly, R. Nonstandard student conceptions about infinitesimal and infinite numbers. Scaling-continuous variation: supporting students’ algebraic reasoning.Įly, R. College Mathematics Journal, 41, 90–100.Įllis, A. Putting differentials back into calculus. College Mathematics Journal, 34, 283–290.ĭray, T., & Manogue, C. Using differentials to bridge the vector calculus gap. Journal of Mathematical Behavior, 5, 281–303.ĭray, T., & Manogue, C. The notion of limit: some seemingly unavoidable misconception stages. Constructing a schema: the case of the chain rule? Journal of Mathematical Behavior, 16, 345–364.ĭavis, R. M., Cordero, F., Cottrill, J., Czarnocha, B., DeVries, D. Honolulu, HI: CRDG, College of Education, University of Hawai’i.Ĭlark, J. Zilliox (Eds.), Proceedings of the Joint Meeting of PME and PMENA (vol. ![]() 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. ![]() “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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