Margaret Kendal and Kaye Stacey
ABSTRACT. This study examines how two teachers taught differentiation using a hand held computer algebra system, which made numerical, graphical and symbolic representations of the derivative readily available. The teachers planned the lessons together but taught their Year 11 classes in very different ways. They had fundamentally different conceptions of mathematics with associated teaching practices, innate ²privileging² of representations, and of technology use. This study links these instructional differences to the different differentiation competencies that the classes acquired. Students of the teacher who privileged conceptual understanding and student construction of meaning were more able to interpret derivatives. Students of the teacher who privileged performance of routines made better use of the CAS for solving routine problems. Comparison of the results with an earlier study showed that although each teacher’s teaching approach was stable over two years, each used technology differently with further experience of CAS. The teacher who stressed understanding moved away from using CAS, whilst the teacher who stressed rules, adopted it more. The study highlights that within similar overall attainment on student tests, there can be substantial variations of what students know. New technologies provide more approaches to teaching and so greater variations between teaching and the consequent learning may become evident.