Abstract / Synopsis
This article describes the way I've been teaching the first day of Calc I, my single-variable Calculus class. By the end of the hour students have (A) dictated difference quotients for me to write on the board, (B) dictated one example of the limit of difference-quotients definition of derivative of a function at a point, and (C) calculated a few derivatives. The more rigorous definitions of function, of operations on functions, and of limits can wait until later. This approach has been very successful, and students have said they "get it this time around."
Cohen, M. D. "The Case of the Missing Speedometer: The First Day of Calculus," Journal of Humanistic Mathematics, Volume 5 Issue 1 (January 2015), pages 180-190. DOI: 10.5642/jhummath.201501.10 . Available at: https://scholarship.claremont.edu/jhm/vol5/iss1/10