The ideas of covariation and rate of change in introductory calculus

Thesis (M.Ed.)--University of Melbourne, 1997This thesis is a formative evaluation of a new curriculum which has evolved at a Victorian secondary school, with the aim of better preparing students for introductory calculus than has traditionally been the case. The new curriculum focuses on the ideas of the rate of change of the dependent variable and the covariation of the variables using tables of values to examine and emphasise the way that the function changes, before moving to the graphical and algebraic representations. This approach is in contrast to the more traditional curriculum where families of functions are introduced using the algebraic representation, and where the central ideas of change and covariation may be obscured. Because of inherent limitations of this study, it was not possible to produce conclusive evidence; however, the results gave a strong indication that the new approach shows promise for an improved understanding of students studying introductory calculus