Enhancing mathematics teachers' mediation of a selected object of learning through participation in a learning study : the case of functions in grade 10

Abstract

This thesis explores the potential of learning study as a teacher professional development model. The learning study is underpinned by variation theory and the judicious use of examples, with the goal of enhancing teachers’ mediation of a selected object of learning. The topic of functions at grade 10 provides the context of the content in which the learning study was implemented. More specifically, the object of learning identified by the teachers was to improve the learners’ ability to identify and name the class of function given its algebraic representation. In the teaching of mathematics, examples form a key resource for teachers to introduce concepts. Within the context of this study the judicious use of examples means that examples are selected and sequenced in a particular fashion so as to create an example space which keeps the critical feature of the object of learning in focus and thereby provides learners with opportunities to discern the object of learning. In selecting and sequencing examples, I draw on principles inherent in variation theory, particularly the idea of varying one aspect whilst keeping other aspects invariant. The learning study cycle reported on in this thesis comprised four lessons. The critical feature for the selected object of learning emerged after the second lesson in the cycle and was focused on only in the last lesson of the cycle. Focusing on the highest power of the independent variable emerged as the feature that enabled learners to discern the object of learning. Describing the enacted object of learning forms the substance of the data analysed in the thesis, with analysis following the production of data from the lesson transcripts. Data production was accomplished by drawing on Bernstein’s theory of the pedagogic device, and specifically the evaluative rule since it concerns itself with the transmission of criteria as to what counts as valid knowledge. To construct a more general account of the operation of evaluative judgement I follow the work of Davis who recruits Hegel’s theory of judgement. Hegelian judgement is used to elaborate Bernstein’s evaluative rule and in doing so, a theory of learning is backgrounded. In this study, I bring a theory of learning into focus by drawing on the principles of variation theory as it provides tools that enable a reading of the opportunities the pedagogy creates that enable learners to see ‘something’ in a certain way. This study demonstrates and so confirms that irrespective of the context in which you work: i) when a critical feature is identified, ii) examples are carefully selected with the critical feature in mind, and iii) if the critical feature is in focus for the teacher, increasingly more learners will begin to discern the intended object of learning.