ETD Collection

Permanent URI for this collectionhttps://wiredspace.wits.ac.za/handle/10539/104


Please note: Digitised content is made available at the best possible quality range, taking into consideration file size and the condition of the original item. These restrictions may sometimes affect the quality of the final published item. For queries regarding content of ETD collection please contact IR specialists by email : IR specialists or Tel : 011 717 4652 / 1954

Follow the link below for important information about Electronic Theses and Dissertations (ETD)

Library Guide about ETD

Browse

Filters

2007 - 200912010 - 20141

Settings

Author: search.filters.author.Pillay, VasenHas files: Yes

Search Results

Now showing 1 - 2 of 2
  • No Thumbnail Available
    Item
    Enhancing mathematics teachers' mediation of a selected object of learning through participation in a learning study : the case of functions in grade 10
    (2014-11-03) Pillay, Vasen
    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.
  • No Thumbnail Available
    Item
    An investigation into mathematics for teaching; The kind of mathematical problem-solving a teacher does as he/she goes about his/her work.
    (2007-03-01T13:17:21Z) Pillay, Vasen
    This study investigates mathematics for teaching, specifically in the case of functions at the grade 10 level. One teacher was studied to gain insights into the mathematical problem-solving a teacher does as he/she goes about his/her work. The analysis of data shows that the mathematical problems that this particular teacher confronts as he goes about his work of teaching can be classified as defining, explaining, representing and questioning. The resources that he draws on to sustain and drive this practice can be described as coming from aspects of mathematics, his own teaching experience and the curriculum with which he works. Of interest in this study are those features of mathematical problemsolving in teaching as intimated by other studies, particularly restructuring tasks and working with learners’ ideas; which are largely absent in this practice. This report argues that these latter aspects of mathematical problem-solving in teaching are aligned to a practice informed by the wider notion of mathematical proficiency. The report concludes with a discussion of why and how external intervention is needed to assist with shifting practices if mathematical proficiency is a desired outcome, as well as with reflections on the study and its methodology.