Investigating an intervention, informed by variation theory, into the Grade 11 learners' interpretation of algebraic functions

Ramaisa, Mampotse Shirley
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This study investigates to what extent and how teaching informed by variation theory could improve the Grade 11 learners’ interpretation of algebraic functions. The study adopted a learning study approach, where learner difficulties are elicited in a pre-test, and on the basis of the results of the pre-test, a lesson is planned, informed by variation theory, to make it possible for learners to discern what they found difficult. In this study, a pre-test on functions was given to three groups of Grade 11 learners (85 learners in all) in the researcher’s school that enabled the identification of aspects of functions learners found to be most problematic. The lesson was then taught successively to each group. A post-test at the end of each lesson, together with reflection on the lesson led to refinements for the next lesson to the next group. The study describes the changes made to the lessons, and the results of the pre and post tests for each of the three groups. The results showed that while each group improved in the post test, the third group outperformed the others, confirming that an intervention, informed by variation theory, did improved learning. All learners were afforded the opportunity to discern the object of learning and their interpretation of functions improved, with the third group improving the most. Keywords: object of learning, patterns of variation theory, interpretation of functions.
A research report submitted to the Faculty of Science, in partial fulfilment of the requirements for the degree of Master of Science, University of the Witwatersrand, Johannesburg, 2014.