School of Science & Mathematics Education

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Browsing by Author "Julie, C"

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    Continuous professional learning community of mathematics teachers in the Western Cape: developing a professional learning community through a school-university partnership
    (University of the Western Cape, 2015-11) Smith, Charles Raymond; Julie, C; Holtman, L; Smith, J
    Ways of enacting effective professional development (PD) and professional learning (PL) of teachers are diverse and often contested and therefore needs sustained inquiry (Schuck, Aubussona, Kearney, & Burden, 2013). The “quick fix” mentality that is endemic to most including those aimed at educational systems leads to very superficial implementation of improvement strategies, including teacher development. These strategies are usually bureaucratically mandated and superficially implemented in a top-down manner. One of the critical drawbacks of such superficial implementation of top-down improvement strategies is that it fails to appeal to teachers because of their historical experiences of such short term and intermittent improvement interventions. This study focussed on the development of a Professional Learning Community (PLC) as a possible continuous professional teacher development (CPTD) model with a promise to deliver effective CPTD. Literature in this regard indicates this model of CPTD as highly effective to support sustained teacher development. The efficacy a PLC is predicated on a collaborative and relational approach to teacher development and professional learning underpinned by a microclimate of commonality. The initiation of PLCs is a complex task. It requires a deep understanding of the processes involved in orientating teachers to processes that involve reflective dialogue and collaborative inquiry. Hence this study sought to investigate experiences of teachers in a PLC established through an alliance involving teachers, didacticians and education officials. This study found that the PLC signifier conveys significant meaning for teachers in terms of their engagement in the PLC. Moreover, teachers’ experiences of the PLC model confirmed the generally accepted features of a PLC. The importance of having a common vision, norms and standards was shown to be an important dimension of the PLC. Besides the fact that the active promotion of this shared vision by the PLC leadership and other education administrators was highlighted, teachers in general accepted the importance of being reflective practitioners. Despite this belief in the value of collaborative reflection, this study found that it does not take place as often as one would expect. This is, to some extent, due to the timetabling arrangements at most schools in the sample. Findings of this investigation provided evidence that it is possible in a PLC to effect a shift from professional development to professional learning. This is consistent with literature in this regard, for example, Benken & Brown (2010) support this argument by indicating that CPTD should be viewed as professional learning that is sustained over time. However, the issue of sustainability is an important challenge. This study revealed that teachers see sustainability as a function of three important variables, namely, recognition by school leadership and administrators, support from the organised teacher movements and subject organisations, and teacher commitment. Important affordances of a PLC identified through this study are relational agency, epistemic agency and a micro-climate of commonality. These affordances are viewed as important enablers of collaborative inquiry and reflective dialogue and underscores the community aspect of a PLC.
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    Investigation of learners’ ways of working with algebraic graphs in high-stakes mathematics examinations
    (University of the Western Cape, 2015-11) Lumbala, Paul Desire Mutombo; Julie, C; Mbekwa, Monde
    Algebraic graphs are a difficult topic for most secondary school mathematics learners. My experience as a Mathematics teacher in the Further Education and Training Phase (FET) is that learners solve problems involving graphs with difficulty. Consequently, the purpose of this research was to investigate learners’ ways of working with algebraic graphs in high-stakes examinations including their errors and misconceptions in this respect. The investigation carried out to identify learners’ errors and misconceptions is based on the analysis of 444 scripts from the 2012 grade 12 final Mathematics examination. More specifically, the study aimed to investigate the ways learners used to solve questions related to graphs in this examination. The focus of the study was the algebraic graphs tested in Paper 1 of the National Senior Certificate (NSC) examination with an emphasis on the identification of errors exhibited in the learners’ scripts. The study adopted a qualitative approach using documentary analysis methodology. As data, the study used the scripts of the final grade 12 Mathematics examinations of schools participating in a project for the improvement of Mathematics based at the University of the Western Cape (UWC). The analysis of learners’ scripts reveals that learners make many errors when they work with algebraic graphs. These errors that have been found in this investigation were coordinate, intercept, domain and range, asymptote, identification, drawing and function errors. Additional errors which were identified are transformation and inverse errors.