A case study of a pre-service mathematics education course to grow and develop proficient teaching in mathematics in the intermediate phase
- Authors: Lee, Amanda Jane
- Date: 2014
- Subjects: Mathematics -- Study and teaching -- South Africa , Mathematics teachers -- Training of -- South Africa , Mathematics -- Study and teaching (Elementary) -- South Africa
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:2004 , http://hdl.handle.net/10962/d1015664
- Description: This research study investigated the ways in which a mathematics module, informed by an enactivist philosophy, enabled pre-service teachers to unpack the reality of their teaching practice in terms of proficient teaching. Given the generally poor mathematics results in South Africa it is not enough for teachers to be merely proficient in Mathematics. They also need to be in a position to explain important mathematical concepts to children in a manner that will encourage and develop an understanding of the basic mathematical concepts. It was my intention with this study to determine whether a mathematics education module, that embraced the underlying themes of enactivism as part of its teaching pedagogy, could have the potential to develop and increase the skills of pre-service teachers’ teaching for proficiency in Mathematics. The mathematics module was underpinned by five themes of enactivism namely: autonomy, embodiment, emergence, sense-making and experience and was designed to supplement the pre-service teachers’ basic skills in Mathematics in the Intermediate Phase. This mathematics module was offered to fourth year pre-service teachers completing a B.Ed. in the Foundation Phase at a private institute specialising in the training of teachers. The theoretical framework was informed by enactivism and how the themes of enactivism could be used as a vehicle to develop teaching proficiency. The study was qualitative in nature and situated within an interpretivist paradigm. The specific perspectives of interpretivism that were used were hermeneutics, phenomenology and reflexivity. The research design was a case study that contained elements of action research and encompassed three phases of data collection. The first phase focused on the pre-service teachers’ approach to teaching Mathematics and what this brought forth in terms of the reality of their teaching practice and the problems they encountered. The second phase undertook to determine what growth and development of teaching proficiency in Mathematics had emerged over the research period. The final phase was undertaken after the pre-service teachers had graduated and were employed as full time teachers in the Intermediate Phase. The analytical framework and lens through which the data was analysed was that of Kilpatrick, Swafford and Findell’s (2001) strands of mathematical proficiency. The argument that I present is that the themes of enactivism did contribute to the growth of the pre-service teachers’ teaching for mathematical proficiency. The themes of embodiment and experience were major contributions in revealing that this was a reality for the pre-service teachers from a practical perspective and was what they would be able to take away with them. However the theme of emergence stood out as the principle that generated the most awareness and growth and which, in turn, affected the participants’ autonomy.
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- Date Issued: 2014
Learners' numeracy progression and the role of mediation in the context of two after school mathematics clubs
- Authors: Stott, Deborah Ann
- Date: 2015
- Subjects: Mathematics -- Study and teaching (Elementary) -- South Africa , After-school programs -- South Africa , Numeracy -- Study and teaching (Elementary) -- South Africa , Learning, Psychology of , Education -- Research -- South Africa
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:2017 , http://hdl.handle.net/10962/d1017181
- Description: National and international assessment results, research studies and reports point to South Africa as having educational challenges, specifically with mathematics, science and language. Addressing some of these issues is a key aim for the SANC project at Rhodes University, the context in which this study takes place. Working from a broad Vygotskian perspective of learning and development, this study had a dual focus and investigated how Grade 3 learners’ mathematical proficiency progressed (or not) whilst participating in after school maths clubs over the course of a year, and explored how the mediation offered in the clubs enabled or constrained the emergence of zones of proximal development (ZPD) and thus learning for the club learners. Methodologically, this study works within a largely qualitative, interpretive research paradigm and is designed using a longitudinal case study research strategy. Two after school maths clubs formed the empirical field. The study drew on a range of data collection methods to investigate the dual nature of the research questions for Grade 3 learners. Examples include adapted one-to-one mathematical proficiency interviews and paired task based interviews. The study highlighted the relationship between the multiple roles I played both within the research study and within the SANC project context and emphasises the influence and future implications for these various roles within the SANC project and beyond in terms of my own role as club mentor, for the future design of the SANC project maths club programme and for broader teacher and club facilitator development within and beyond the project. This study has offered insight into how mathematical proficiency may develop in Grade 3 South African learners and as such is an important contribution to the newly developing field of both numeracy and primary educational research in Southern Africa. Additionally, the research findings point to the clubs, as an example of an out-of-school time (OST) programme, providing potentially enabling spaces for both recovery and extension of mathematical proficiency in learners as these spaces are free from several contextual constraints that teachers face in their classrooms. Furthermore, it was found that learners showed development of their conceptual understanding, procedural fluency and adaptive reasoning as proposed by Kilpatrick, Swafford and Findell (2001). The use of various elements of the Maths Recovery (MR) programme (Wright, 2003) in the research process has highlighted various important contributions for broader research. For example, the need to investigate less time consuming approaches to both diagnostic assessment and learner mathematical profiling. Findings from this study support Meira and Lerman’s (2001, 2009) recently developed notion that catching attention is key to the creation or emergence of a ZPD. The study found that a combination of ‘attention catching’ and ‘tuning in’ enabled the creation (emergence) and sustainment of ZPDs in club learners. The study proposed the notion of tuning in where participants in a mathematical interaction continually adjust to each other in order to communicate mathematically. Furthermore, the study found that when attention is not caught or the participants are not tuned in, the learning activity may still be useful in assisting learners to consolidate their existing learning and / or build confidence and as such is particularly relevant to the South African context where fluency in calculating is weak (Hoadley, 2012; Schollar, 2008). This emergent notion of ‘flow’ additionally can play a supporting role in the emergence of a ZPD. The study also found that the manner in which the mediation was offered is important. The results show that the mathematical contributions learners make during interactions captured the mentors’ attention and resulted in mediation that was intentional but spontaneous, flexible, responsive and in-the-moment. This study makes theoretical and methodological contributions to various aspects of mathematics education research particularly with regard to how ZPDs emerge and are sustained and how mediation is offered to facilitate the emergence of ZPDs. Additionally, some aspects of the Learning Framework in Number (LFIN) as part of the Maths Recovery programme have been extended to work in a South African after school club context and to provide useful information for both learner progression over time and for planning of club activities. As such this study thus also contributes to the newly developing field of primary mathematics research in South Africa and to the body of research on primary after school learning programmes both locally and internationally.
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- Date Issued: 2015
Primary maths teacher learning and identity within a numeracy in-service community of practice
- Authors: Pausigere, Peter
- Date: 2015
- Subjects: Mathematics -- Study and teaching (Elementary) -- South Africa , Teachers -- In-service training -- South Africa , Student-centered learning -- South Africa , Communities of practice -- South Africa , Educational change -- South Africa
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:2019 , http://hdl.handle.net/10962/d1017183
- Description: This study focuses on the processes of primary maths teacher learning and how their identities and practices evolve in relation to participation in a primary maths focused in-service teacher education programme, called the Numeracy Inquiry Community of Leader Educators (NICLE).Additionally it investigates activities, relations and forms of participation within the Community of Practice (CoP) which enable or constrain evolving primary maths identities and practices and how these relate to the broader context. The study draws from the situative-participationists (Lave, 1996; Wenger, 1998; Sfard & Prusak, 2005; Wenger et al, 2002) theoretical framework supplemented by Bernstein’s (2000) pedagogic identity model. Using a qualitative educational interpretive approach I sampled 8 primary teachers drawn from NICLE and gathered data through participant observations, interactive interviews, document analysis and reflective journals. Analysing the key data themes that emerged from teacher learning stories, which I have called stelos, the study explains the nature of the primary maths teachers’ learning, transformation and participation experiences in NICLE using the synonyms reinvigoration and remediation and activation and relating these semantics to the teachers’ mathematical identities and histories. The study also explains the processes through which primary maths teacher identities evolve in relation to participation in an in-service CoP as ‘insiding’ and ‘outcropping’. Interpreting qualitative data from the empirical field indicates that teachers participating in NICLE mostly took-up into their maths classrooms key numeracy-domain concepts, resources and issues presented by primary maths experts which are informed by research and theory that link to practices. Teachers collaboratively and actively engaged in a range of activities that relate to classroom practices. Teacher learning was also enabled when teachers engaged in maths overlapping communities of practice, shared classroom experiences in friendly ways with fellow NICLE teachers and engaged with NICLE presenters who mutually respected and regarded them as professionals. Such affordances were said to enable teachers to engage learners in maths classes and improve their understanding of specific primary maths concepts. On the other hand teachers felt challenged by the travelling distance, limited time and also raised the tension of how to scale-up maths professional development initiatives to include schools from their community. The study makes a theoretical contribution by illustrating how Bernstein’s pedagogic identity model and its elaboration by Tyler (1999) provides analytical tools to interrogate macro educational changes and connect these to the micro processes and teacher identities.
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- Date Issued: 2015
IsiXhosa as the language of teaching and learning mathematics in Grade Six: investigating the mother tongue based bilingual education mathematics pilot in the Eastern Cape Province, South Africa
- Authors: Mbude, Naledi Ntombizanele
- Date: 2020
- Subjects: Mathematics -- Study and teaching (Elementary) -- South Africa , Education, Bilingual -- South Africa , Native language and education -- South Africa , Language policy -- South Africa
- Language: English
- Type: text , Thesis , Doctoral , PHD
- Identifier: http://hdl.handle.net/10962/143262 , vital:38215
- Description: This study is an investigation on lessons learnt when the language of learners is maintained for teaching and learning mathematics beyond Grade 3 for another 3 years. It is undertaken in Cofimvaba, a rural village of the Eastern Cape in South Africa. We investigate lessons that can be learnt from the Mother Tongue based- Bilingual Education (MTbBE) strategy, that can be replicated. South Africa post-1994 has a Language-in-Education Policy (1997) that provides for the use of all official languages as Languages of Teaching and Learning (LoLT), this has remained on paper as the schooling system focusses on an early –exit model of three years of the Mother Tongue Education (MTE) for the Foundation Phase (FP) then exit to English instruction in Grade 4; this applies to African language learners only. English and Afrikaans speakers have mother tongue education from cradle to university; a benefit they have enjoyed pre- and post-apartheid. Various studies have been conducted to understand the relationship between language and mathematics learning as it is crucial to design mathematics instruction for students who are English Learners (ELs) and/or bilingual. However, in South Africa, there had not been a direct exploration of the achievement of learners in mathematics when their mother tongue is used and sustained throughout the first six years of learning mathematics, while English is a supportive resource. This is the focus of this study. The study lends itself to the adoption of a mixed methods design (QUALT+QUANT), while also employing documents, observation and test scores of learners to obtain data. Content analysis and thematic analysis approaches were used in analyzing the qualitative-type data while a statistical approach was used in the analysis of quantitative data. The main aim of the study was to establish whether in the Cofimvaba pilot, there is any evidence to make a case for extending Mother Tongue Based-bilingual Education (MTBBE) beyond Grade 3 for black African children. Another aim, was to highlight and document the effort that was the first of its kind in South Africa, undertaken in a small rural area to develop isiXhosa as language of Mathematics and Science. The most salient of this effort was the fact that it was underpinned by deliberate theoretical and empirical foundations central to language policy and planning. The finding of this study is that the use of isiXhosa for MTbBE was effective for boosting mathematical and science skills in the mother tongue and English in Grade 6 as demonstrated in Chapter 7 and 8. Lastly, this study demonstrates the power of political will and how a decision backed by financial investment can transform the wider system despite the challenges of transformation. For the first time in the history of education; a poor department has stuck to its guns; unwearied by the negativity surrounding the development of African languages. It committed to the cause of improving the academic achievement of the poorest of the poor. Historically, in implementing a Mathematics Curriculum, the Department of Education (both officials and teachers) has never efficiently implemented the LiEP (1997) in the manner spelt out in its policy documents viz, multilingualism as the norm. The focus has been on a perspective of learners who are learning and must English, then mathematics and ways to get them to know English at all costs. This view creates inequities in the classroom because it places emphasis on what learners don’t know or can’t do. In contrast, this study proposes a sociocultural perspective that shifts away from deficiency models of bilingual learners and instead focuses on describing the resources bilingual students use to communicate mathematically (Moskovich, 1988). Without this shift we will have a limited view of these learners and will design instruction that neglects the competencies they bring to mathematics classrooms. If, instead, we learn to recognize the mathematical ideas these students express in spite of their accents, code-switching, or missing vocabulary, then instruction can build on students’ competencies and resources (Moskovich, 1998). This study recommends a plethora of strategies that must be taken by the Department of Education to widen epistemological access to mathematics for African language learners using MTbBE as a viable strategy.
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- Date Issued: 2020