Revealing conceptions of rate of change

Rate of change is an important mathematical concept. Research referring to students’ difficulties with this concept spans more than twenty years. Research suggests that problems experienced by some calculus students are likely a result of pre-existing limited or incorrect conceptions of rate of change. This study investigated 23 Victorian Year 10 students’ understanding of rate as revealed by phenomenographic analysis of interviews. Eight conceptions of rate of change emerged. Four important aspects of the concept were identified and gaps in students’ thinking defined. In addition, the employment of phenomenography, to reveal conceptions of rate, is described in detail.