Jill Vincent

Do mathematics textbooks cultivate shallow teaching? Applying the TIMSS Video Study criteria to Australian eighth-grade mathematics textbooks

Australian eighth-grade mathematics lessons were shown by the 1999 TIMSS Video Study to use a high proportion of problems of low procedural complexity, with considerable repetition, and an absence of deductive reasoning. Using definitions from the Video Study, this study re-investigated this ‘shallow teaching syndrome’ by examining the problems on three topics in nine eighth-grade textbooks from four Australian states for procedural complexity, type of solving processes, degree of repetition, proportion of ‘application’ problems and proportion of problems requiring deductive reasoning. Overall, there was broad similarity between the characteristics of problems in the textbooks and in the Australian Video Study lessons. There were, however, considerable differences between textbooks and between topics within textbooks. In some books, including the best-selling textbooks in several states, the balance is too far towards repetitive problems of low procedural complexity.

Evaluation of an electronic interview with multimedia stimulus materials for gaining in-depth responses from professionals

In a study of quality mathematics teaching, an electronic interview with multimedia stimulus resources was used with relevant professionals to obtain in-depth data relating to their own beliefs, and their reflective observations and evaluations of mathematics teaching practice. The electronic format enabled presentation of the same questions and multimedia stimulus material to every interviewee. Provision of a personal copy of the interview material, including all the stimulus resources, to the interviewees provided for a richer interview than would have been possible with a face-to-face interview in the more limited timeframe that would have been imposed. The opportunity for interviewees to reflect on questions and edit responses resulted in high quality data and interviewees found the electronic interview convenient and satisfying. Further advantages of the electronic format were the savings in organisation, travel and transcription. We believe that electronic interviews offer great potential to other researchers.

Dynamic Geometry Software and Mechanical Linkages

Widespread interest has arisen in the use of dynamic geometry software as a constructivist learning tool. However, the software has been accused of contributing to an empirical, data-collecting approach to geometry, where students have little or no understanding of deductive reasoning. Mechanical linkages which occur in many common household items, as well as in ‘mathematical machines’ from the past, offer a wealth of geometry appropriate for secondary school mathematics. Dynamic geometry models of these linkages form an interface between the concrete and the theoretical, and create a visually rich environment for students to explore, conjecture and construct geometric proofs.