The Deliberate Use of Variation to Teach Algebra: A Realistic Variation Study

This thesis investigates the effect(s) that deliberate and systematic use of dimensions of variation (DoV) in the teaching of mathematics can have for the students' learning. Variation theory, together with its practical application as an educational approach, is introduced (Marton and Booth, 1997). A realistic quasi-experimental longitudinal intervention called the Dimensions of Variation Programme, DVP, was designed and implemented to examine how this approach can potentially influence the understanding of students in algebra classrooms. The design was realistic because careful consideration was given to how the realities of the educational environment 'could be appropriately incorporated into the intervention in order to increase pragmatic validity. Convenience sampling was used to obtain a cohort of approximately 300 students. This sample corresponded to ten intact classes drawn from eight Oxfordshire schools. Six of the classes were taught by intervention teachers with the remaining four classes being taught by comparison teachers. The students were followed over a 14 month period between Year 7 and Year 8. The intervention teachers formed a research community which met regularly to discuss and jointly plan how the algebra content could be handled with awareness to dimensions of variation. o Classes were observed for eight lessons in total during the 14 months, four consecutive algebra lessons at the beginning of the intervention and four consecutive lessons toward .the end of the intervention. During these observations the mathematical dimensions of variation, together with some contextual details, were recorded. This formed the predictive data for the study. The students were pre-, post-, and delayed post-tested using national SAT exams. Scores from these were used as the primary outcome measure. These data were subsequently analysed both qualitatively and quantitatively in order to identify any differences that might exist between the intervention and comparison groups. The findings suggest that the intervention teachers handled the content in qualitatively different ways to the comparison teachers. The principle distinguishing characteristic between groups was that the intervention teachers exhibited an awareness for 'systematicity of inference' while the comparison teachers did not. There is some evidence to suggest that the intervention significantly affected students' learning outcomes in algebra between Year 7 and Year 8.EThOS - Electronic Theses Online ServiceGBUnited Kingdo