Expression of Conceptions of Rate

Rate is an important, but difficult mathematical concept. More than twenty years of research, especially with calculus students, report difficulties with this concept. This paper reports on an alternative analysis, from the perspective of multiple representations and context, of interviews probing twenty Victorian Year 10 students ’ conceptions of rate. This analysis shows that multiple representations of functions provide different rate-related information for different students. Understandings of rate in one representation or context are not necessarily transferred to another representation or context. Rate is an important mathematical concept needed for everyday numeracy and important for more advanced areas of study, such as calculus. Despite considerable research in the area it remains a troublesome concept to teach and learn. Even many calculus students have found rate particularly troublesome (Ubuz, 2007). Rate is a complex concept comprising many interwoven ideas. It expresses the change in the dependent variable resulting from a unit change in the independent variable and involves the ideas of change in a quantity; co-ordination of two quantities; and the simultaneous covariation of the quantities (Thompson, 1994). Improvement of conceptions of rate held by students wh