Tracing learning of three representations with the differentiation competency framework

Abstract

The support of technology for working with multiple representations of functions has substantial potential for teaching calculus. For teaching differentiation, these representations relate to finding difference quotients, finding gradients of cmwes and tangents, and using symbolic differentiation rules. For students to use them all and link them together requires a wide range of skills, which have been organised into a Differentiation Competency Framework. This paper also describes a balanced Differentiation Competency Test that was created from the Framework and used in two Year 11 classes to monitor students' understanding of introductoi T differentiation. The Framework helps identify both..