Hauger, Garnet S. “Instantaneous rate of change: a numerical approach.” International Journal Of Mathematical Education In Science & Technology 31, no. 6 (November 2000): 891-897.
Abstract: The calculus reform movement has encouraged numerical and graphical approaches to functions in addition to the more traditional analytical approach. While valiant efforts have been made to use these other approaches in newer calculus curricula, more numerical approaches should be introduced. Research on student learning in calculus indicates that particular numerical approaches hold promise for students’ learning of instantaneous rate of change. Numerical approaches involving the average rate of change over successively smaller intervals can be used to obtain the instantaneous rate of change for a given function at a given value of x. These approaches can help students appreciate the fundamental relationship between average and instantaneous rates of change. They can also be used to obtain general expressions for the derivative of most elementary functions. Standard computer spreadsheet programs facilitate this process and make numerical approaches a more viable option for calculus instruction. These are underutilized resources for instruction in calculus, even in reform or other new calculus curricula.
