mktafrica.bib

@article{adler2017,
  title = {Mathematics {{Education Research}} in {{South Africa}} 2007\textendash 2015: {{Review}} and {{Reflection}}},
  shorttitle = {Mathematics {{Education Research}} in {{South Africa}} 2007\textendash 2015},
  author = {Adler, Jill and Alshwaikh, Jehad and Essack, Regina and Gcsamba, Lizeka},
  year = {2017},
  month = jan,
  journal = {African Journal of Research in Mathematics, Science and Technology Education},
  volume = {21},
  number = {1},
  pages = {1--14},
  publisher = {{Routledge}},
  issn = {1811-7295},
  doi = {10.1080/18117295.2016.1265858},
  abstract = {This article reports a review of research in mathematics education in South Africa published in local and international journals in the period 2007\textendash 2015. The purpose of the review was to describe the landscape of mathematics education research in the country over the past (almost) decade. Findings indicate that the mathematics education research community has become more established, expanding quantitatively, with the number of articles identified being nearly double, in absolute terms, that in a similar review of research from 2000 to 2006. Trends identified in the earlier review persist, with a dominance of publications in local journals and on small-scale qualitative studies on secondary teaching and learning. There is, importantly, an increase in research on primary mathematics. The review includes critical reflection on these findings, opportunities and threats, new and old, and what these mean for the future of research in this field.},
  keywords = {mathematics education,research review,South Africa},
  annotation = {\_eprint: https://doi.org/10.1080/18117295.2016.1265858},
  file = {/Users/reidarmosvold/Zotero/storage/8SIV3FMS/Adler et al. - 2017 - Mathematics Education Research in South Africa 200.pdf;/Users/reidarmosvold/Zotero/storage/JYLQ389Z/18117295.2016.html}
}


@article{alex2019,
Abstract = {Teachers' content knowledge impacts on what they teach, how they teach and what their students learn. In order to check whether the prospective teachers in a rural South African university know the mathematics content they are expected to teach in the schools, at least at the same depth as their future students expected to attain, the research on the Student-Level Disciplinary Content Knowledge (SLDCK) of a sample of 40 Bachelor of Education (Mathematics) students was conducted. The theoretical framework rests on theories on subject content knowledge of pre-service teachers. The data were generated from the performance of the prospective teachers in two tests on the selected topics in the South African senior secondary school mathematics curriculum and also from document analysis. It was found that the prospective teachers had only limited SLDCK on the topics that they were meant to teach in the schools. An in-depth analysis of the course modules offered at the university also revealed that the prospective teachers' limited SLDCK was due to the curriculum constraints of the university. Effective teaching measures to close the gap in the SLDCK and changes in the teacher training curriculum of the university are recommended to enhance the preparation of prospective teachers of the country.},
Author = {Alex, Jogymol Kalariparampil},
ISSN = {1305-8223},
Journal = {EURASIA Journal of Mathematics, Science and Technology Education},
Keywords = {Preservice Teachers; Secondary School Teachers; Mathematics Teachers; Foreign Countries; Preservice Teacher Education; Knowledge Base for Teaching; Knowledge Level; Pretests Posttests; Money Management; Probability; Geometry; Trigonometry, South Africa},
Number = {12},
Title = {The Preparation of Secondary School Mathematics Teachers in South Africa: Prospective Teachers' Student Level Disciplinary Content Knowledge},
Volume = {15},
Year = {2019/01/01/},
URL = {https://search.ebscohost.com/login.aspx?direct=true&db=eric&AN=EJ1265236&site=ehost-live&scope=site},
}


@article{askew2020,
  title = {Identifying {{Effective Mathematics Teaching}}: {{Some Questions}} for {{Research}}},
  shorttitle = {Identifying {{Effective Mathematics Teaching}}},
  author = {Askew, Mike},
  year = {2020},
  month = jan,
  journal = {African Journal of Research in Mathematics, Science and Technology Education},
  volume = {24},
  number = {1},
  pages = {1--9},
  publisher = {{Routledge}},
  issn = {1811-7295},
  doi = {10.1080/18117295.2019.1710049},
  abstract = {This paper argues that there is a gap in the research on teaching and learning mathematics, and thus a need for research into effective teaching practices. From a selective review of literature, reasons are examined as to why less emphasis appears to have been placed on generating knowledge about teaching and effective mathematical teaching practices than on mathematics teachers and their knowledge. Possible reasons for this lack of attention to teaching include assumptions that, as researchers, we already know what effective teaching is or that if teachers embrace certain principles about teaching or learning, then effective teaching will necessarily ensue. Arguing that both of these positions neglect to address important aspects of developing knowledge about effective teaching, the paper raises a number of questions that research might address in moving the balance more towards examining the actual practices that might characterise effective teaching.},
  keywords = {Effective mathematics teaching,questions for research,teaching practices},
  annotation = {\_eprint: https://doi.org/10.1080/18117295.2019.1710049},
  file = {/Users/reidarmosvold/Zotero/storage/V5UFYTUH/Askew - 2020 - Identifying Effective Mathematics Teaching Some Q.pdf;/Users/reidarmosvold/Zotero/storage/2BLM57I4/18117295.2019.html}
}


@article{asmail2020,
Abstract = {Mathematics is frequently considered as value-free, centering entirely on abstract reasoning. However, more often than not, the teaching of values in mathematics classrooms takes place implicitly through the actions of the teacher. The role values play in mathematics learning is also a growing area of interest and is now viewed by many as a contributing factor in the advancement of the quality of mathematics performance. This paper reports on part of a larger study aiming to establish the components that Grade 8-10 learners from a mathematics-and-science-focus school in Johannesburg value as important in the learning of mathematics. A quantitative survey was used to collect data from 249 participants. Principal component analysis was employed to analyse the data. The main findings revealed seven components that learners appeared to value in the learning of mathematics. Knowledge about what learners value in the learning of mathematics can inform teachers' pedagogical practices and the inculcation of values in mathematics teaching, which may, in turn, improve the quality of learning of mathematics.},
Author = {Asmail, Raeesa and  Spangenberg, Erica Dorethea and  Ramdhany, Viren},
Journal = {African Journal of Research in Mathematics, Science and Technology Education},
Keywords = {Grade 8; Grade 9; Grade 10; Student Attitudes; Value Judgment; Values Education; Mathematics Education; Special Schools; Educational Quality; Problem Solving; Relevance (Education); Foreign Countries, South Africa (Johannesburg)},
Number = {2},
Pages = {241 - 252},
Title = {What Grade 8-10 Learners from a Mathematics-and-Science-Focus School Value as Important in the Learning of Mathematics},
URL = {http://dx.doi.org/10.1080/18117295.2020.1818041},
Volume = {24},
Year = {2020/01/01/},
}


@article{bansilal2014,
Abstract = {Many studies point to the problem of poor mathematics content knowledge of mathematics teachers in South Africa. The purpose of this study was to investigate teachers' knowledge of the mathematics they are themselves teaching. Data was generated from the teachers' (n = 253) written responses to test that was a shortened form of a previous Grade 12 Mathematics Paper One examination. The sample of teachers were studying towards an Advanced Certificate in Education (an upgrading high school mathematics qualification) at the University KwaZulu-Natal in South Africa. The findings revealed that the teachers in this sample obtained an average of 57% in the test. Using an APOS theory analysis it was found that many teachers who were working at an action level of a concept would require help and scaffolding to move to process or object levels of understanding of that concept. Furthermore it was found that on average teachers obtained 29% on questions which were at the problem solving level, raising concerns about how these teachers would mediate tasks that are set at high cognitive levels, with their Grade 12 learners.},
Author = {Bansilal, Sarah and  Brijlall, Deonarain and  Mkhwanazi, Thokozani},
ISSN = {0258-2236},
Journal = {Perspectives in Education},
Keywords = {Foreign Countries; Pedagogical Content Knowledge; Knowledge Base for Teaching; Mathematics Teachers; High Schools; Secondary School Teachers; Teacher Surveys; Teacher Qualifications; Cognitive Ability; Problem Solving; Continuing Education; Concept Formation; Mathematical Concepts; Qualitative Research; Case Studies; Equations (Mathematics); Calculus, South Africa (KwaZulu Natal), South Africa},
Number = {1},
Pages = {30 - 46},
Title = {An Exploration of the Common Content Knowledge of High School Mathematics Teachers},
URL = {http://www.perspectives-in-education.com/ViewPublication.aspx?PublicationID=22},
Volume = {32},
Year = {2014/03/01/},
}


@article{biccard2019,
Abstract = {This article sets out a professional development programme for primary school mathematics teachers. Clark and Hollingsworth's model of teacher change provided the theoretical framework necessary to understand teacher change. A design study allowed for increased programme flexibility and participator involvement. Five volunteer primary school teachers teaching at South African state schools were involved in the programme for a period of one year and their pedagogy, use of mathematical content and context developed during the programme. Twenty lessons were observed over the year-long period. An observation rubric that specifically focused on mathematical pedagogy, use of context and mathematical content scale guided the researcher to gauge global changing teacher practices. Teacher growth was evident through their professional experimentation and changes in their personal domain. The design features emanating from the study are that teachers be given opportunities to experience reform tasks (e.g. model-eliciting tasks) in the role of learners themselves and teachers should be encouraged to use contextual problems to initiate concept development. More mathematical detail in lesson planning is also necessary. Furthermore, teachers need appropriately designed resource materials to teach in new ways. It is recommended that professional development includes teachers engaging collaboratively in solving rich tasks. This study adds to the growing body of knowledge regarding teacher development programmes that focus on how teachers change their own classroom practices.},
Author = {Biccard, Piera},
ISSN = {1012-2346},
Journal = {Pythagoras},
Keywords = {Faculty Development; Mathematics Teachers; Elementary School Teachers; Public Schools; Foreign Countries; Grade 5; Grade 6; Suburban Schools; Classroom Techniques; Modeling (Psychology); Program Effectiveness; Elementary School Mathematics, South Africa},
Number = {1},
Title = {The Professional Development of Primary School Mathematics Teachers through a Design-Based Research Methodology},
Volume = {40},
Year = {2019/01/01/},
URL = {https://search.ebscohost.com/login.aspx?direct=true&db=eric&AN=EJ1241180&site=ehost-live&scope=site},
}


@article{biccard2020,
Abstract = {This study explores student teachers' views regarding problem solving in mathematics classrooms. The participants in the study were Bachelor of Education students registered for their second year of teaching practice (at a distance institution) who were asked about their experiences of teaching a mandatory mathematics problem-solving lesson while on their teaching practice. The responses were mixed, although they conveyed predominantly positive views about the experiences. Students noted positive experiences related to learner and teacher enjoyment of problem-solving lessons, student-teacher development that took place as well as improved learner understanding and autonomy during these lessons. Their negative experiences related to low self-confidence about selecting appropriate tasks, insufficient knowledge of problem solving as a teaching method and classroom norms that do not support problem solving. Both positive and negative experiences were related to student concepts about the nature of learning problem solving (learning for problem solving or learning through problem solving). It is recommended that student teachers (or pre-service teachers) have more exposure to problem-solving pedagogy and that hosting mentor teachers themselves take part in professional development on problem-solving pedagogy while universities include specific problem solving lessons and instruction in their practical modules.},
Author = {Biccard, Piera},
Journal = {African Journal of Research in Mathematics, Science and Technology Education},
Keywords = {Foreign Countries; Student Teacher Attitudes; Undergraduate Students; Mathematics Instruction; Distance Education; Problem Solving; Teaching Methods; Self Esteem; Cooperating Teachers, South Africa},
Number = {2},
Pages = {205 - 215},
Title = {Distance-Education Student Teachers' Views of Teaching Mathematics Problem Solving While on Teaching Practice},
URL = {http://dx.doi.org/10.1080/18117295.2020.1812837},
Volume = {24},
Year = {2020/01/01/},
}


@article{bowie2016,
Abstract = {Regulatory bodies such as the Department of Higher Education and Training (DHET) provide a framework of formal criteria to be addressed by providers of initial teacher education (ITE) but these criteria can be interpreted in many different ways. The Initial Teacher Education Research Project (ITERP) has investigated the preparation of intermediate phase (grades 4 to 6) teachers of mathematics and English at five South African universities, selected as representative of the major "types" of institutions offering ITE. In this article we draw on our analysis of data from this research to describe and discuss the courses in mathematics and English offered by each of the five universities to student teachers specialising in mathematics or English and to "non-specialists". We suggest that while there are examples of excellent curriculum design and implementation, none of the universities in the study is fully addressing the challenges of teaching and learning in diverse intermediate phase classrooms. While acknowledging that answering the question "how much of what?" is particularly complex in teacher education contexts in which some students enter university with an inadequate knowledge base from which to develop content and pedagogic knowledge in a number of disciplines and inter-disciplinary fields, we offer some curriculum suggestions for teacher educators to consider.},
Author = {Bowie, Lynn and  Reed, Yvonne},
ISSN = {0258-2236},
Journal = {Perspectives in Education},
Keywords = {Foreign Countries; Mathematics Curriculum; Teacher Education; Mathematics Instruction; Mathematics Education; English (Second Language); Research Projects; Teacher Education Programs; Universities; Mathematics Teachers; Language Teachers; Second Language Instruction; Second Language Learning; Numeracy; Preservice Teacher Education; Preservice Teachers, South Africa, South Africa},
Number = {1},
Pages = {102 - 119},
Title = {How Much of What? An Analysis of the Espoused and Enacted Mathematics and English Curricula for Intermediate Phase Student Teachers at Five South African Universities},
URL = {http://apps.ufs.ac.za/kovsiejournals/default.aspx?article=2834},
Volume = {34},
Year = {2016/01/01/},
}

@article{bowie2019,
Abstract = {The Primary Teacher Education (PrimTEd) project was established in response to concerns about the pre-service preparation of primary teachers in South Africa. In order to inform the development of appropriate pre-service mathematics courses, an initial need in the PrimTEd project was to establish the nature of the mathematical knowledge of pre-service teachers both near the start and also near the end of their studies, through an online assessment. This paper describes the design of this PrimTEd online mathematics test and reports on the performance on the test of first-year and fourth-year primary mathematics student teachers, at three different universities. The overall performance of students together with the small differences between first and fourth year student performance indicate a need for student teachers to revisit primary school mathematics in a way that provides a deep understanding of key mathematical concepts in order to be better prepared for future teaching careers.},
Author = {Bowie, Lynn and  Venkat, Hamsa and  Askew, Mike},
Journal = {African Journal of Research in Mathematics, Science and Technology Education},
Keywords = {Foreign Countries; Preservice Teachers; Mathematics Teachers; Pedagogical Content Knowledge; Elementary School Mathematics; Preservice Teacher Education; Mathematics Tests; Test Construction; Mathematical Concepts, South Africa},
Number = {3},
Pages = {286 - 297},
Title = {Pre-Service Primary Teachers' Mathematical Content Knowledge: An Exploratory Study},
URL = {http://dx.doi.org/10.1080/18117295.2019.1682777},
Volume = {23},
Year = {2019/01/01/},
}


@article{brijlall2015,
Abstract = {Multiple Intelligence Theory suggests that individuals perceive knowledge in eight different ways. This article reports on a study that explored the role of manipulatives in the teaching and learning of trigonometric ratios in grade 10. The approach attempts in addressing three domains of the Multiple Intelligence Theory (linguistic/verbal intelligence, logical/mathematical intelligence and spatial intelligence). The foundation of this research was a case study contained in the interpretative paradigm involving five grade 10 mathematics pupils at a high school in South Africa. The data was collected from: (1) activity sheet containing written responses of pupils; (2) observations; and (3) semi-structured interviews. The data was analysed and it was found that the use of manipulatives in teaching and learning mathematics played a positive role in learners understanding of trigonometric ratios at grade 10 level. In general the findings of this study supported other research findings that confirm that manipulatives were important mediating tools in the development of conceptual and procedural understanding of mathematical concepts. Besides these pedagogical implications the study proved that the manipulatives effectively consolidated the features of Lesh's model.},
Author = {Brijlall, D. and  Niranjan, C.},
ISSN = {1814-6627},
Journal = {Africa Education Review},
Keywords = {Mathematics Instruction; Teaching Methods; Manipulative Materials; Trigonometry; Foreign Countries; Case Studies; Multiple Intelligences; Grade 10; Secondary School Mathematics; Worksheets; Observation; Semi Structured Interviews; Spatial Ability; Qualitative Research, South Africa, South Africa},
Number = {3},
Pages = {361 - 380},
Title = {Using Manipulatives to Support an Embodied Approach to Learning Trigonometry in a South African School: A Case Study},
URL = {http://dx.doi.org/10.1080/18146627.2015.1110893},
Volume = {12},
Year = {2015/01/01/},
}


@article{brodie2021,
  title={Bridging powerful knowledge and lived experience: Challenges in teaching mathematics through COVID-19},
  author={Brodie, Karin and Gopal, Deepa and Moodliar, Julian and Siala, Takalani},
  journal={Pythagoras},
  volume={42},
  number={1},
  pages={593},
  year={2021},
  publisher={AOSIS}
}


@article{carnow2020,
Abstract = {Background: IsiXhosa students enrolled for the BEd Foundation Phase qualification at a university in South Africa failed their first year in identified at-risk subjects, namely Mathematics in Education, Language in Education and Computer Literacy. The students stated the reasons for failure as not understanding the concepts and terms of the subjects presented to them in English. Objectives: A tutoring programme was initiated in the home language of the students with the aim of improving their understanding and chances at success. Method: Semi-structured interviews and reflective journals within a qualitative case study were used to understand how the tutees and tutors as key role players, the programme coordinator, lecturers in the three subjects and the tutor trainer experienced the tutoring programme. The study was framed within social constructivist theory and an interpretative paradigm employed for analysis of data. Results: The findings suggested that tutoring in their home language grants isiXhosa students an improved understanding of the concepts and terms of the course material, which they had difficulty understanding. Conclusion: Tutoring in the home language should become a mandatory practice for students whose home language is not the language of learning and teaching in the institution. The study contributes to knowledge on how tutoring in the home language provides isiXhosa students access to the curriculum by assisting them in minimising their struggles with English as the language of learning and teaching.},
Author = {Carnow, Anneline J. and  Steenkamp, Andries and  Ekron, Christélle},
ISSN = {2079-8245},
Journal = {Reading & Writing: Journal of the Reading Association of South Africa},
Keywords = {African Languages; Native Language; Undergraduate Students; Academic Failure; Computer Literacy; Mathematics Achievement; Language of Instruction; English (Second Language); Second Language Learning; Student Attitudes; Case Studies; Journal Writing; Tutors; Tutoring; Program Descriptions; Constructivism (Learning); Teaching Methods; Concept Formation; Difficulty Level; Learning Processes; Foreign Countries, South Africa},
Number = {1},
Title = {Experiences in a Tutoring Programme for BEd Foundation Phase isiXhosa First-Language Students},
Volume = {11},
Year = {2020/01/01/},
URL = {https://search.ebscohost.com/login.aspx?direct=true&db=eric&AN=EJ1286703&site=ehost-live&scope=site},
}


@article{chigonga2019,
Abstract = {This paper discusses the extent to which the professional development (cascade model) met its goal of improving mathematics teaching and learning during the implementation of National Curriculum Statement in South Africa. Fifty mathematics teachers from ten public secondary schools in Vhembe District in Limpopo Province of South Africa were chosen purposively. Using a qualitative approach, data were collected through a focus group discussion with five mathematics teachers at each of the ten schools. Teachers disapproved the manner in which the workshops were conducted claiming that they were disconnected from classroom practices. The conclusion was that: (a) the success of in-service programs should be determined by the way that the ideas, knowledge and skills learnt are implemented in a classroom setting; (b) for any in-service program that introduces teachers to a different instructional approach from the traditional one, it has to impact on teachers' concerns (be they self-oriented, task-oriented or impact-oriented).},
Author = {Chigonga, Benard and  Mutodi, Paul},
ISSN = {1305-8223},
Journal = {EURASIA Journal of Mathematics, Science and Technology Education},
Keywords = {Foreign Countries; Faculty Development; Mathematics Teachers; Program Effectiveness; Secondary School Teachers; Mathematics Instruction; Teacher Attitudes; Inservice Teacher Education; Teaching Skills; Teaching Methods; National Curriculum; Communities of Practice; Teacher Competencies; Workshops, South Africa},
Number = {10},
Title = {The Cascade Model of Mathematics Teachers' Professional Development in South Africa: How Well Did It Suit Them?},
Volume = {15},
Year = {2019/01/01/},
URL = {https://search.ebscohost.com/login.aspx?direct=true&db=eric&AN=EJ1302576&site=ehost-live&scope=site},
}


@article{chikiwa2019,
Abstract = {Background: The study on which this article is based investigated the Mathematics Knowledge for Teaching (MKfT) that a well experienced Grade 2 teacher utilized when teaching counting. Aim: In this paper we share excerpts from one of the lessons of this Grade 2 teacher, which we analyzed to illuminate the various domains of MKfT and their interconnectedness in the teaching of counting. Setting: The research was conducted in a former Model C school in the Eastern Cape province of South Africa. Method: Using a case study methodology, 15 Grade 2 mathematics lessons were observed, video recorded and transcribed. Two formal interviews based on two selected video-recorded lessons were conducted to understand this teacher's practice. The data were analysed using Deborah Ball and colleagues' MKfT framework. Results: The study found that Foundation Phase mathematics teaching requires the knowledge and tactful employment of all six knowledge domains as described in the work of Ball and colleagues. The Knowledge of Content and Teaching (KCT) domain, was found to be essential in teaching counting in Grade 2. The other five domains supported and informed the KCT domain. Conclusion: We suggest from the insights gained here that research examining the MKfT that competent teachers draw on in teaching Foundation Phase mathematics could assist in developing curricula for in-service and pre-service teacher education programs.},
Author = {Chikiwa, Samukeliso and  Westaway, Lise and  Graven, Mellony},
ISSN = {2223-7674},
Journal = {South African Journal of Childhood Education},
Keywords = {Foreign Countries; Elementary School Teachers; Mathematics Teachers; Grade 2; Pedagogical Content Knowledge; Mathematics Instruction; Computation; Number Concepts; Teacher Education Programs; Curriculum Development, South Africa},
Number = {1},
Title = {What Mathematics Knowledge for Teaching Is Used by a Grade 2 Teacher When Teaching Counting},
Volume = {9},
Year = {2019/01/01/},
URL = {https://search.ebscohost.com/login.aspx?direct=true&db=eric&AN=EJ1228319&site=ehost-live&scope=site},
}


@article{chikiwa2021,
  title = {How {{Pre-service Teachers Reflect}} on Their Own {{Mathematics Teaching Practice Compared}} with the {{Practice}} of {{Others}}},
  author = {Chikiwa, Samukeliso and Graven, Mellony},
  year = {2021},
  month = may,
  journal = {African Journal of Research in Mathematics, Science and Technology Education},
  volume = {25},
  number = {2},
  pages = {211--224},
  publisher = {{Routledge}},
  issn = {1811-7295},
  doi = {10.1080/18117295.2021.1968164},
  abstract = {Reflective practice is a crucial element of professional growth that is gaining in popularity in teacher education, yet the ability to reflect is a skill that is neither natural nor easy to develop. This paper reports on an investigation that sought to establish if pre-service teachers at a South African university \textendash{} in the process of learning to reflect on practice through analysing video-recorded lessons \textendash{} reflected differently when reflecting on their own practice from the way they reflected on the practice of other teachers. Pre-service teachers were introduced to the Six Lens Framework as a tool to aid reflection on mathematics teaching. The authors compared two sets of reflections written by four pre-service teachers (PSTs) who participated in the study. One set was based on a video-recorded lesson of another teacher's practice while the other was based on a video-recording of their own practice. The study found that the PSTs' reflections in both cases were generally at the lowest level of the reflection spectrum. They mostly described classroom events rather than analysing the lessons to provide explanation suggestions, or reflectivity. We found, however, that all four PSTs reflected at substantially greater length on their own lessons than on those of other teachers. Furthermore, three of the four teachers' reflections on their own practice focused on mathematical rather than general aspects and provided more suggestions for improvement than their reflections on the practice of other teachers.},
  keywords = {mathematics education,pre-service teacher education,Pre-service teachers,Reflective practice},
  annotation = {\_eprint: https://doi.org/10.1080/18117295.2021.1968164},
  file = {/Users/reidarmosvold/Zotero/storage/52VNWQEW/Chikiwa og Graven - 2021 - How Pre-service Teachers Reflect on their own Math.pdf;/Users/reidarmosvold/Zotero/storage/LDPDV9RL/18117295.2021.html}
}


@article{chirinda2021,
  title={Teaching mathematics during the COVID-19 lockdown in a context of historical disadvantage},
  author={Chirinda, Brantina and Ndlovu, Mdutshekelwa and Spangenberg, Erica},
  journal={Education Sciences},
  volume={11},
  number={4},
  pages={177},
  year={2021},
  publisher={Multidisciplinary Digital Publishing Institute}
}


@article{chirinda2021b,
  title={Professional development for teachers’ mathematical problem-solving pedagogy--what counts?},
  author={Chirinda, Brantina},
  journal={Pythagoras},
  volume={42},
  number={1},
  pages={532},
  year={2021},
  publisher={AOSIS}
}


@article{defreitas2019,
Abstract = {Many mathematics teachers struggle to effectively integrate information and communication technology (ICT) in their teaching and need continuous professional development programmes to improve their technological pedagogical content knowledge (TPACK). This article aims to identify mathematics teachers' levels of TPACK and barriers to integrating ICT as a means to inform their continuous professional development needs. The TPACK framework of Mishra and Koehler was used as a lens for this the study. Both quantitative and qualitative research methods were utilised. Ninety-three mathematics teachers, who completed a quantitative questionnaire, reported higher levels of content, pedagogical, and pedagogical content knowledge, with comparatively lower levels of technology, technological pedagogical, and technological content knowledge. Ten of these participants also participated in semi-structured interviews and revealed six primary barriers to integrating ICT in the classroom, namely curriculum-related time constraints, technological infrastructure, impact of ICT use on the learning process, ineffective professional development, teachers' pedagogical beliefs and poor leadership. Continuous professional development programmes addressing specific ICTintegration barriers can effect significant changes in teachers' TPACK, which may promote better teaching and learning of mathematics.},
Author = {De Freitas, Gabrielle and  Spangenberg, Erica D.},
ISSN = {1012-2346},
Journal = {Pythagoras},
Keywords = {Mathematics Teachers; Pedagogical Content Knowledge; Technological Literacy; Educational Technology; Technology Uses in Education; Faculty Development; Barriers; Teacher Attitudes; Foreign Countries; Teacher Competencies; Teaching Methods; Technology Integration; Secondary School Mathematics; Secondary School Teachers, South Africa},
Number = {1},
Title = {Mathematics Teachers' Levels of Technological Pedagogical Content Knowledge and Information and Communication Technology Integration Barriers},
Volume = {40},
Year = {2019/01/01/},
URL = {https://search.ebscohost.com/login.aspx?direct=true&db=eric&AN=EJ1241178&site=ehost-live&scope=site},
}


@article{dhlamini2016,
Abstract = {This paper reports on a pilot study that investigated the effect of implementing a context-based problem solving instruction (CBPSI) to enhance the problem solving performance of high school mathematics learners. Primarily, the pilot study aimed: (1) to evaluate the efficiency of data collection instruments; and, (2) to test the efficacy of CBPSI in relation to learners' problem solving performance. In this paper CBPSI refers to a teaching approach in which everyday problem solving knowledge and practices are uncovered when learners are exposed to tasks that give meaning to their everyday experiences. Given that the design of a pilot study lacked the inclusion of a control group, it is reasonable to conclude that the current design embraced elements of a pre-experimental research approach in which a one-group pre-test post-test design was followed. Participants consisted of a convenient sample of 57 Grade 10 learners who performed poorly in mathematics problem solving. The results of the study informed various conceptual and methodological revisions to strengthen the design of the main study, however, this paper reports only the effect of CBPSI on participants' problem solving performance. The post-intervention achievement test suggested that CBPSI was effective in substantially accelerating learners' problem solving performance (p<0.05). Using a cognitive load theory, it is possible to explain aspects of growth in learners' problem solving performance in relation to the conceptual notion of human cognitive architecture.},
Author = {Dhlamini, Joseph J.},
ISSN = {2468-1954},
Journal = {European Journal of STEM Education},
Keywords = {Problem Solving; Mathematics Instruction; Control Groups; Experimental Groups; Grade 10; High School Students; Comparative Analysis; Pilot Projects; Teaching Methods; Pretests Posttests; Mathematics Tests; Mathematics Achievement; Cognitive Ability; Learning Theories; Scores; Foreign Countries; Semi Structured Interviews; Student Attitudes; Statistical Analysis, South Africa},
Number = {1},
Pages = {27 - 36},
Title = {Enhancing Learners' Problem Solving Performance in Mathematics: A Cognitive Load Perspective},
Volume = {1},
Year = {2016/01/01/},
URL = {https://search.ebscohost.com/login.aspx?direct=true&db=eric&AN=EJ1167384&site=ehost-live&scope=site},
}


@article{dhlamini2019,
Abstract = {The purpose of this study was to explore geometry spatial mathematical reasoning in Grade nine Annual National Assessments, South Africa. Conceptual Blending was the guiding theory. Document analysis within the exploratory case study was used to explore available data, the 2014 Annual National Assessment learners' scripts (n=1250). Results revealed that on average 70.5 percent of the total number of learners remembered and blended irrelevant prior knowledge not reflective to the contexts of the geometry problems. For learners who recalled the correct prior knowledge, its manipulation was either fragmented or irrelevant. The use of recalled information in wrong contexts could be due to the incorrect manipulation of the meaning of the problems. Also, responses reveal challenges on the quality of mathematics education on geometry. Therefore, the teaching and learning of geometry should focus on empowering learners with skills of recalling, blending and on manipulating problems in their contexts.},
Author = {Dhlamini, Zwelithini Bongani and  Chuene, Kabelo and  Masha, Kwena and  Kibirige, Israel},
ISSN = {1305-8223},
Journal = {EURASIA Journal of Mathematics, Science and Technology Education},
Keywords = {Grade 9; Spatial Ability; Geometric Concepts; Mathematical Logic; Problem Solving; Prior Learning; Recall (Psychology); Thinking Skills; National Competency Tests; Mathematics Curriculum; Foreign Countries, South Africa},
Number = {11},
Title = {Exploring Grade Nine Geometry Spatial Mathematical Reasoning in the South African Annual National Assessment},
Volume = {15},
Year = {2019/01/01/},
URL = {https://search.ebscohost.com/login.aspx?direct=true&db=eric&AN=EJ1289260&site=ehost-live&scope=site},
}


@article{dhurumraj2020,
Abstract = {COVID-19 posed formidable challenges to the teaching and learning of subjects with abstract concepts such as Science, Technology, Engineering and Mathematics (STEM). The study explored how STEM teachers transformed their pedagogical practices as an integral part of the transition to online teaching and learning in response to COVID-19 and further examined the effectiveness of online teaching and learning. The study adopted an exploratory descriptive survey design and involved purposively selected STEM teachers from schools operating under the auspices of the Association of Muslim Schools. The Technological Pedagogical Content Knowledge (TPACK) framework underpinned the study. Quantitative data was collected through the administration of a Likert scale instrument. Data was analysed using inferential and descriptive statistics. Findings revealed that COVID-19 essentially compelled teachers to make a transition to online teaching and learning resulting in a concomitant profound impact on their pedagogical practices. Teachers provided various perspectives on the key modalities adopted to navigate online teaching and learning on virtual platforms in an attempt to ensure sustainable, equitable and inclusive teaching and learning. Implications for broadening educational pathways to STEM education through online teaching and learning on virtual platforms and sustainable teacher professional development on technology integration in teaching and learning are discussed.},
Author = {Dhurumraj, Thasmai and  Ramaila, Sam and  Raban, Ferhana and  Ashruf, Ahmed},
ISSN = {1648-3898},
Journal = {Journal of Baltic Science Education},
Keywords = {COVID-19; Pandemics; Foreign Countries; Socioeconomic Influences; STEM Education; Teaching Methods; School Closing; Online Courses; Educational Technology; Technology Uses in Education; Pedagogical Content Knowledge; Technological Literacy; Muslims; Private Schools; Religious Schools; Teacher Attitudes, South Africa},
Pages = {1055 - 1067},
Title = {Broadening Educational Pathways to STEM Education through Online Teaching and Learning during COVID-19: Teachers' Perspectives},
Volume = {19},
Year = {2020/01/01/},
URL = {https://search.ebscohost.com/login.aspx?direct=true&db=eric&AN=EJ1298186&site=ehost-live&scope=site},
}


@article{dossantos2020,
Abstract = {Student-teaching internships in a teacher-preparation programme are a significant way for teachers to gain practical skills and transfer their textbook knowledge into classroom practice. One of the outcomes of student-teaching internships is that pre-service teachers can observe experienced teachers' teaching pedagogy and strategies for implementing their skills. The purpose of the research study reported on here was to explore how pre-service teachers acquire and improve their teaching pedagogy through the peer observation training model at the secondary school at which they intern, with a focus on pre-service teachers with an interest in science, technology, engineering and mathematics (STEM) teaching. The results indicate that most of the participants could learn and improve their teaching pedagogy through the peer observation professional development programme -- particularly young teachers without significant work experience. More importantly, the research proved how a peer observation cycle programme may apply to different educational systems with similar structures internationally, particularly in former European colonised countries with similar backgrounds.},
Author = {Dos Santos, Luis Miguel},
ISSN = {0256-0100},
Journal = {South African Journal of Education},
Keywords = {Preservice Teachers; Professional Development; Observation; Student Teaching; Student Teacher Attitudes; Internship Programs; Secondary School Teachers; Experienced Teachers; Cooperating Teachers; STEM Education; Private Schools; Professional Identity; Self Efficacy; Program Effectiveness; Postcolonialism; Teacher Improvement; Foreign Countries, Macau; South Africa},
Number = {3},
Title = {Pre-Service Teachers' Pedagogical Development through the Peer Observation Professional Development Programme},
Volume = {40},
Year = {2020/08/01/},
URL = {https://search.ebscohost.com/login.aspx?direct=true&db=eric&AN=EJ1268311&site=ehost-live&scope=site},
}


@article{dupreez2018,
Abstract = {Background: South Africa needs citizens who are morally sound, adaptive to change, technologically innovative and literate in socio-scientific issues. The young child is apparently being prepared for active citizenry through basic "Social Science, Natural Sciences and Technology" education as encapsulated in the South African curriculum. Aim: We foreground a theoretical and analytical framework to map the cultural--historical trajectory of South Africa's Beginning Knowledge curriculum. Setting: Cultivating citizenship requires that these "science" subject domains be incorporated in a coherent, well-conceptualised and relevant early childhood curriculum as suggested by international literature. Educators need to be specialists in socio-scientific issues in both the content and pedagogy of these "sciences" in order to expound the curriculum. Methods: Our newly coined hybridised theoretical framework - the 'Hybrid CHAT' - together with an aligned analytical framework enabled us to illuminate the historical subject-didactical genetic development of Beginning Knowledge. An extensive sample of typographical textbooks, artefacts and cultural tools were analysed and interpreted. Results: Beginning Knowledge is afforded limited teaching time. The knowledge, skills and values associated with these "science" subjects serve to support and strengthen the acquisition of language and mathematics competencies. Currently, Beginning Knowledge does not sufficiently prepare child citizens for the global demands of the 21st century. Conclusion: Hybrid CHAT could invite further studies to place Beginning Knowledge on par with international curricula. This would also align the curriculum with the aspirations for an ideal South African citizenry as well as prepare child citizens to pursue Science and Technology for social development.},
Author = {du Preez, Hannelie and  van Niekerk, Retha},
ISSN = {2223-7674},
Journal = {South African Journal of Childhood Education},
Keywords = {Foreign Countries; Social Studies; Natural Sciences; Technology Education; Citizenship; Early Childhood Education; Scientific Principles; Scholarship; Cultural Context; History; Theories, South Africa},
Number = {2},
Title = {Utilising a Cultural-Historical Analysis to Map the Historicity of Social Studies, Natural Science and Technology Education in the Early Years},
Volume = {8},
Year = {2018/01/01/},
URL = {https://search.ebscohost.com/login.aspx?direct=true&db=eric&AN=EJ1198798&site=ehost-live&scope=site},
}


@article{engelbrecht2015,
Abstract = {In keeping with the national mandate of increasing graduates in the sciences in South Africa, a concerted effort in improving the first year experience becomes imperative. First year mathematics courses commonly provide the base knowledge necessary for progression in different degree programmes at university. Success in mathematics courses influences throughputs, retention and graduation rates of various degree programmes. Due to the highly complex and integrated nature of issues pertaining to improving teaching and learning in these courses, a multi-dimensional approach was conceptualized and implemented at the University of Pretoria. This paper reports on the development of a coherent framework, and the process and strategy for improving student success through a number of teaching and learning interventions in the first year mathematics courses, addressing the different dimensions of the framework. The process embarked upon resulted in a coherent, resource-focused approach with a replicable model for similar contexts.},
Author = {Engelbrecht, Johann and  Harding, Ansie},
ISSN = {0020-739X},
Journal = {International Journal of Mathematical Education in Science and Technology},
Keywords = {Foreign Countries; Mathematics Instruction; College Mathematics; College Freshmen; Mathematics Achievement; Teaching Methods; Models; Success; College Readiness; Student Adjustment; Student Behavior; Learner Engagement; Student School Relationship; Academic Support Services; Concept Formation; Intervention; Curriculum Development; At Risk Students; Homework; Educational Technology; Integrated Learning Systems; Student Evaluation; Evaluation Methods; Tutoring, South Africa, South Africa},
Number = {7},
Pages = {1046 - 1060},
Title = {Interventions to Improve Teaching and Learning in First Year Mathematics Courses},
URL = {http://dx.doi.org/10.1080/0020739X.2015.1070441},
Volume = {46},
Year = {2015/01/01/},
}


@article{feza2016,
Abstract = {Mathematics learning and teaching continues to be a challenge in the South African education system. This challenge is observed in the poor performance of students in national and international assessments. Research suggests that teachers' content knowledge and knowledge of teaching mathematics contribute significantly to students' performance. In this paper, I explore educators' understanding of counting concepts and how they go about teaching 5- and 6-year-old children to count. A questionnaire using scenarios was administered to 17 educators in the Eastern Cape to gauge their understanding of these areas. A qualitative analysis was conducted and this was followed by a thematic report. The findings of this study indicate that teacher knowledge for teaching counting is superficial. The building blocks that 5-6 year old students need to develop counting skills are not fully understood by educators. In addition, the educators demonstrated some understanding of the role of assessment in mediating learning but used assessment jargon without necessarily comprehending its meaning.},
Author = {Feza, Nosisi N.},
ISSN = {1082-3301},
Journal = {Early Childhood Education Journal},
Keywords = {Foreign Countries; Mathematics Instruction; Mathematics Achievement; Pedagogical Content Knowledge; Computation; Mathematical Concepts; Young Children; Questionnaires; Vignettes; Qualitative Research; Knowledge Level; Elementary School Teachers, South Africa, South Africa},
Number = {5},
Pages = {483 - 489},
Title = {Teaching 5- and 6-Year-Olds to Count: Knowledge of South African Educators},
URL = {http://dx.doi.org/10.1007/s10643-015-0736-z},
Volume = {44},
Year = {2016/09/01/},
}


@article{feza2016b,
Abstract = {Language in mathematics learning and teaching has a significant role in influencing performance. Literature on language in mathematics learning has evolved from language as a barrier to language as a cultural tool, and recently more research has argued for use of home language as an instructional tool in mathematics classrooms. However, the complexity of language is becoming another emerging challenge from bilingualism to multilingualism in different contexts. The need for access to mathematics knowledge has prompted debate about language policies that are inclusive of previously underrepresented languages, especially in South Africa. This paper therefore extends this debate by exploring Reception class students' basic numeracy abilities and their numeracy levels to see if they speak in accord with the current language policy of South Africa and to assess whether the curriculum connects with the students. A concurrent mixed methods design was employed to investigate context and numeracy knowledge levels for a sample of 26 Reception class students from low socio-economic backgrounds. Both descriptive and thematic analyses were conducted to analyse the biographical, contextual and interview data collected. The findings reveal that the literacies experienced by students in their early ages of life are different from those perceived by policy makers, researchers and curriculum designers. This paper calls for more studies that are interdisciplinary as new identities and literacies are developing.},
Author = {Feza, Nosisi Nellie},
ISSN = {1837-6290},
Journal = {Issues in Educational Research},
Keywords = {Foreign Countries; Numeracy; Academic Ability; Language Proficiency; Educational Policy; Mixed Methods Research; Mathematics Instruction; English (Second Language); Interviews; Language of Instruction; Socioeconomic Background; Mathematical Aptitude; Mathematics Achievement; Minority Group Students; Elementary School Students, South Africa, South Africa},
Number = {4},
Pages = {576 - 591},
Title = {Basic Numeracy Abilities of Xhosa Reception Year Students in South Africa: Language Policy Issues},
URL = {http://www.iier.org.au/iier26/feza.pdf},
Volume = {26},
Year = {2016/01/01/},
}


@article{feza2018,
Abstract = {South Africa's esteem is low with regard to current learner achievement in mathematics. Results from international studies, such as TIMMS and SACMEQ, continuously indicate that South African learners perform below international benchmarks in mathematics. Research and evaluation studies assert that teacher practices and poor early mathematics stimulation influence this state of affairs. Hence, this article reports on a study that explored the developmental progression of Grade R teachers' mathematics knowledge and general knowledge of teaching participating in a professional development intervention. In this article I report on data collected after a two-day workshop conducted with the teachers. The video recordings of 14 teachers' self-selected lessons were collected and transcribed, using a lesson observation tool, and analysed by means of thematic analysis. The findings indicated that teachers' knowledge of number sense forms a strong foundation for improving the quality instruction of number knowledge. The first step seen to be taken by these teachers to engage the learners was the question and answer approach. The lessons of those who tried to let learners engage lacked structure and resulted in chaos. Demonstration and drill were used to develop the learners' content knowledge. The teachers' practices were inadequate as far as developing conceptual understanding is concerned; and their classroom management skills were not sufficiently developed to include all learners in their mediation. In instances where all the learners participated, the teacher directed the participation and did not allow for learner-to-learner engagement. It is crucial to note that they showed potential for growth and willingness to learn despite the limited or minimal the training they received.},
Author = {Feza, Nosisi N.},
ISSN = {1814-6627},
Journal = {Africa Education Review},
Keywords = {Foreign Countries; Knowledge Base for Teaching; Mathematics Instruction; Mathematics Teachers; Mathematical Aptitude; Intervention; Teacher Workshops; Protocol Materials; Protocol Analysis; Lesson Plans; Teacher Competency Testing; Teaching Skills; Qualitative Research; Classroom Observation Techniques; Lesson Observation Criteria; Readiness; Early Childhood Education, South Africa},
Number = {1},
Pages = {72 - 84},
Title = {Teachers' Journeys: A Case of Teachers of Learners Aged Five to Six},
URL = {http://dx.doi.org/10.1080/18146627.2016.1241673},
Volume = {15},
Year = {2018/01/01/},
}


@article{fonseca2015,
Abstract = {This study reports on an intervention that was aimed at improving the content knowledge of first-year intermediate-phase education students at a South African university. The study gives some insight into preservice teachers' perceptions of an online programme for the development of mathematics common content knowledge for teachers of mathematics in the intermediate grades. The effectiveness of the intervention programme was analysed according to Shapiro's evaluation criteria for intervention research. The findings show that there has been a positive shift in preservice teachers' common content knowledge but that there is much room for further development. The student teachers found the programme to be of great benefit with regard to the development of their mathematics knowledge as well as their confidence as future teachers of mathematics. The findings highlighted their disturbingly limited knowledge of mathematics content knowledge and pointed to the responsibility of teacher education departments at universities to implement sufficient maths content courses that will address the status quo of poor mathematics teaching in South African primary schools. The authors conclude that the students need to spend much more time on 'catching up' before they become teachers.},
Author = {Fonseca, Kathleen and  Petersen, Nadine},
ISSN = {2223-7674},
Journal = {South African Journal of Childhood Education},
Keywords = {Mathematics; Mathematics Instruction; Teacher Education Programs; Teacher Educators; Intervention; Mathematical Concepts; Preservice Teachers; Foreign Countries; Pedagogical Content Knowledge; Preservice Teacher Education; Elementary School Teachers, South Africa},
Number = {3},
Title = {Online Supplementary Mathematics Tuition in a First-Year Childhood Teacher Education Programme},
Volume = {5},
Year = {2015/01/01/},
URL = {https://search.ebscohost.com/login.aspx?direct=true&db=eric&AN=EJ1187273&site=ehost-live&scope=site},
}


@article{fonseca2021,
Abstract = {Background: During their university studies, student teachers are equipped for the teaching profession in various domains of knowledge and practice. In addition to learning pedagogic skills for practice purposes, they also expand their knowledge of the subjects that they will teach. In mathematics teacher education, one important principle is that the content of the subject must, somehow, be fused with the pedagogy in what has become known as mathematical knowledge for teaching (MKT). Although several studies have been conducted about students' performance of MKT, there is little research in South Africa about how students routinely experience the coursework itself. In this study, I argue that mathematics knowledge and skills should ideally precede the teaching of pedagogy, for reasons of communicating the concepts clearly and for building a foundation of mathematical thinking prior to practising teaching skills. Aim: To find out what the student teachers' self-reported experience of one component of a mathematics content course are, namely their engagement with problem-solving tasks. Methods: A qualitative case study of student teachers' learning, with the primary source of data, the student teachers' reflective journal entries. Data were analysed through coding, categorising and thematised mindful of the MPSKT framework. Results: The findings indicated that, whilst the students' understanding of the processes of problem-solving was deepened during the course, matters of pedagogy arose spontaneously.},
Author = {Fonseca, Kathleen},
ISSN = {2223-7674},
Journal = {South African Journal of Childhood Education},
Keywords = {Problem Solving; Preservice Teachers; Preservice Teacher Education; Mathematics Education; Mathematics Skills; Mathematical Concepts; Skill Development; Pedagogical Content Knowledge; Prior Learning; Foreign Countries, South Africa},
Number = {1},
Title = {Self-Reported Mathematical Problem-Solving Skills of Future Mathematics Teachers},
Volume = {11},
Year = {2021/01/01/},
URL = {https://search.ebscohost.com/login.aspx?direct=true&db=eric&AN=EJ1317271&site=ehost-live&scope=site},
}


@article{galant2013,
Abstract = {In this article, I present an initial analysis of an empirical study that was undertaken in an attempt to elicit what subject-matter knowledge, pedagogic content knowledge and curriculum knowledge teachers bring to bear on decisions for teaching. The analysis is based on interview data with 46 Grade 3 teachers, who were presented with two mathematical tasks taken from the 2010 NOBE Grade 2 and Grade 3 Numeracy Workbooks. Teachers were required to justify the selection and sequencing of the two mathematical tasks for teaching multiplication. In so doing, they provide some indication of what they know or do not know about the mathematical concepts in the  tasks; about  the connections between mathematical  concepts; about the representations of those concepts, and about how learners learn those concepts. Teachers' responses varied from an articulation of the pedagogic and mathematical intentions of the tasks, to the use and consequences of pictorial representations in the tasks and how learners would respond to the tasks. The variation in responses reflected different criteria that teachers used to justify the selection and sequencing of the tasks. The analysis raises critical questions regarding the interplay between teachers' subject-matter knowledge, their pedagogic content knowledge and curricular knowledge, which they bring to bear on pedagogic decisions. The analysis raises further critical questions concerning the pedagogic and mathematical explicitness of tasks in the NOBE Numeracy Workbooks. The analysis suggests that careful consideration must  be given  to the  construction of mathematical tasks in Grade 3, and probably the Foundation Phase, to ensure that the mathematical purpose of tasks is explicit, and that "contextual noise" is not introduced that distracts from  the pedagogic and mathematical intent of the tasks.},
Author = {Galant, Jaamia},
ISSN = {0258-2236},
Journal = {Perspectives in Education},
Keywords = {Knowledge Base for Teaching; Mathematics Instruction; Pedagogical Content Knowledge; Knowledge Level; Teacher Competencies; Interviews; Elementary School Teachers; Grade 3; Workbooks; Mathematics Skills; Mathematical Concepts; Numeracy; Foreign Countries, South Africa, South Africa},
Number = {3},
Pages = {34 - 48},
Title = {Selecting and Sequencing Mathematics Tasks: Seeking Mathematical Knowledge for Teaching},
URL = {http://www.perspectives-in-education.com/ViewPublication.aspx?PublicationID=20},
Volume = {31},
Year = {2013/09/01/},
}


@article{govender2019,
Abstract = {Background: Formative assessment, as an integral component of teaching, has recently gained prominence in educational environments globally. Poor performances in mathematics by learners in early grades, and its negative effect on later learning, have been an ongoing concern in South African schools. Several former studies tend to generalise the pedagogical reasons for learners' underperformance in Foundation Phase teaching. Aim: This case study of selected Grade 3 teachers examined how the teachers integrated formative assessment into their pedagogy, with the purpose of gaining insight into teachers' understanding of the developmental aspects of learning in mathematics. Setting: This study was conducted at four schools in a selected district in the Gauteng Province. Methods: Data were mainly collected through focus group interviews and observations of at least three classroom sessions for each teacher of mathematics, thereby gaining an overview of their formative assessment practices. Results: This article reports on the two strongest themes to have emerged from the case study, which were teachers' tokenistic use of 'Assessment for Learning' strategies and teachers' awareness of learning processes and curriculum requirements. Conclusion: The study's main conclusion was that teachers are likely to practise formative assessment more intuitively if they had a sound knowledge of children's mathematical cognition and conceptual development. This study pointed out that formative assessment is a co-constructed activity involving the teacher, the learner and peers rather than a teacher-directed activity. The study recommends how continuous professional learning initiatives can design initiatives that integrate research-based knowledge of children's learning of early grades mathematics.},
Author = {Govender, Poomoney},
ISSN = {2223-7674},
Journal = {South African Journal of Childhood Education},
Keywords = {Formative Evaluation; Grade 3; Elementary School Students; Children; Foreign Countries; Mathematics Instruction; Mathematical Concepts; Professional Continuing Education; Mathematics Achievement; Elementary School Teachers; Concept Formation; Time Management, South Africa},
Number = {1},
Title = {Formative Assessment as 'Formative Pedagogy' in Grade 3 Mathematics},
Volume = {9},
Year = {2019/01/01/},
URL = {https://search.ebscohost.com/login.aspx?direct=true&db=eric&AN=EJ1232204&site=ehost-live&scope=site},
}


@article{govender2020,
Abstract = {This article reports on Grade 2 teachers' perceptions of formative assessment in explaining the phenomenon of the underutilisation of formative assessment practices in mathematics teaching. A qualitative and interpretative case study investigated two Grade 2 teachers' enactment of formative assessment in priority schools in Gauteng. Data were collected through semi-structured interviews and observations of lessons. The basic principles of qualitative content analysis were applied during data analysis and guided by the formative assessment theoretical framework proposed by Black and Wiliam (2009). The study revealed that teachers' enactment of formative assessment was limited by their vague understanding of formative assessment and the tensions between formative assessment and curriculum compliance. The study's central claim is that teachers may know about formative assessment, but if they do not understand how children learn and engage in mathematics learning, then they are unlikely to enact it correctly. While teachers who attended the in-service training programme were able to use some of the strategies as singular tools, they were still unable to implement the combined strategies that constitute the formative assessment pedagogy. Hence, the formative assessment practices of teachers bore limited possible returns on investment to improve learning outcomes in mathematics. The unique contribution of this study is its potential to inform teacher development, policy and practice as it yielded important insights while reinforcing and amplifying existing knowledge.},
Author = {Govender, Poomoney},
ISSN = {0256-0100},
Journal = {South African Journal of Education},
Keywords = {Elementary School Teachers; Mathematics Teachers; Mathematics Instruction; Grade 2; Teacher Attitudes; Curriculum Implementation; Formative Evaluation; Classroom Techniques; Feedback (Response); Knowledge Level; Professional Development; Inservice Teacher Education; Urban Schools; Public Schools; Young Children; Foreign Countries, South Africa},
Title = {Insights into Grade 2 Teachers' Enactment of Formative Assessment in Mathematics in Selected Priority Schools in Gauteng},
Volume = {40},
Year = {2020/12/01/},
URL = {https://search.ebscohost.com/login.aspx?direct=true&db=eric&AN=EJ1286191&site=ehost-live&scope=site},
}


@article{helmbold2021,
Abstract = {Lesson Study is an internationally recognised professional development approach for teachers. This case study explores the impact of implementing Lesson Study in the early grades of a South African primary school, pertinently targeting early childhood mathematics teachers. The evidence suggests that Lesson Study has the potential to positively influence content knowledge, pedagogical content knowledge, general professional development and creative teaching of early grade teachers. The study established that Lesson Study enhanced intergrade cooperation and curriculum development and flow. Participants regarded the collaborative experience as deeply enriching and fulfilling. Although some implementation challenges were encountered, these were not insurmountable and the overall benefits of Lesson Study outweighed the potential obstacles.},
Author = {Helmbold, Erika and  Venketsamy, Roy and  van Heerden, Judy},
ISSN = {0258-2236},
Journal = {Perspectives in Education},
Keywords = {Professional Development; Elementary School Teachers; Primary Education; Mathematics Teachers; Program Effectiveness; Pedagogical Content Knowledge; Communities of Practice; Lesson Plans; Teacher Collaboration; Self Efficacy; Creative Teaching; Curriculum Development; Foreign Countries, South Africa},
Number = {3},
Pages = {183 - 196},
Title = {Implementing Lesson Study as a Professional Development Approach for Early Grade Teachers: A South African Case Study},
URL = {http://dx.doi.org/10.18820/2519593X/pie.v39.i3.14},
Volume = {39},
Year = {2021/01/01/},
}


@article{jacinto2020,
  title = {Mathematical {{Knowledge}} for {{Teaching}}: {{How}} Do {{Primary Pre-service Teachers}} in {{Malawi Understand}} It?},
  shorttitle = {Mathematical {{Knowledge}} for {{Teaching}}},
  author = {Jacinto, Everton Lacerda and Jakobsen, Arne},
  year = {2020},
  month = jan,
  journal = {African Journal of Research in Mathematics, Science and Technology Education},
  volume = {24},
  number = {1},
  pages = {31--40},
  publisher = {{Routledge}},
  issn = {1811-7295},
  doi = {10.1080/18117295.2020.1735673},
  abstract = {While a consensus within the field exists that pre-service teachers need adequate knowledge and skills to become effective teachers in mathematics, less is known about how they understand the mathematical knowledge needed for teaching in elementary education. This paper explores how Malawian pre-service teachers understand the mathematical knowledge needed for teaching in primary schools. Written answers to a questionnaire survey, and data from six individual interviews collected at the beginning of the teacher-training programme will be presented. The analytical framework is based on the practice-based theory of mathematical knowledge for teaching, with a specific focus on the domains of the common, horizon and specialised content knowledge. The data revealed that, while taking theoretical courses, pre-service teaches develop only intuitive but complementary views of what is proposed by the theory, which is even the case with pre-service teachers with some prior teaching experience. Findings provide insights into the development of pre-service teachers' mathematical knowledge for teaching, and suggest that further research is needed on how pre-service teachers articulate their understanding of teaching in practice.},
  keywords = {Malawian teacher training,mathematical knowledge for teaching,primary school education},
  annotation = {\_eprint: https://doi.org/10.1080/18117295.2020.1735673},
  file = {/Users/reidarmosvold/Zotero/storage/HQYKHFWD/Jacinto og Jakobsen - 2020 - Mathematical Knowledge for Teaching How do Primar.pdf;/Users/reidarmosvold/Zotero/storage/IZKZ2VWB/18117295.2020.html}
}


@article{jita2019,
Abstract = {This qualitative research reports the results of a short learning intervention programme conducted by South African National Roads Agency Limited (SANRAL) Chair in Science and Mathematics Education to enhance the mathematical knowledge of teachers in some South African schools. The short learning programme comprised the fostering of teachers' mathematical knowledge and the formation of lesson study groups to apply the knowledge gained from the intervention programme in different schools in the country. The sample comprised 53 male and 72 female Mathematics teachers who were nominated from several school districts in the country. The participants were trained using Mathematical Knowledge for Teaching (MKT) which included the topics of probability/ratio and proportion (grades 1-9). The MKT consisted of these sets of expertise: Common Content Knowledge (CCK), Specialised Content Knowledge (SCK), Knowledge of Contents and Students (KCS), and Knowledge of Content and Teaching (KCT). The lesson study groups applied the knowledge acquired from the short learning intervention programme to engage in group activities, lesson studies, and to report the major challenges in doing the lesson studies. This model research comprised three stages: the first stage involved active participation in the workshops that took place at the University of the Free State; the teachers that attended the training workshops implemented the knowledge gained in the respective schools in their districts in the second stage; and the third stage involved the compilation and submission of a Portfolio of Evidence (PoE) by the teachers that participated in the training workshops.},
Author = {Jita, Loyiso C. and  Ige, Olugbenga Adedayo},
ISSN = {1822-7864},
Journal = {Problems of Education in the 21st Century},
Keywords = {Pedagogical Content Knowledge; Program Length; Mathematics Teachers; Mathematical Concepts; Professional Development; Workshops; Portfolios (Background Materials); Instructional Improvement; Peer Evaluation; Observation; Teacher Collaboration; Lesson Plans; Feedback (Response); Public Schools; Elementary School Teachers; Secondary School Teachers; Foreign Countries, South Africa},
Number = {6},
Pages = {705 - 721},
Title = {South African Teachers' Mathematical Knowledge: Reflections from Short Learning Intervention Programme (SLIP)},
Volume = {77},
Year = {2019/01/01/},
URL = {https://search.ebscohost.com/login.aspx?direct=true&db=eric&AN=EJ1267892&site=ehost-live&scope=site},
}


@article{joubert2020,
Abstract = {Lesson study (LS) is a form of professional development, with a strong foundation in mathematics education, based on teachers collaborating to design lessons. This collaboration, however, can be challenging for isolated teachers. In 2017, a course was presented at the university to train 52 teachers from all over South Africa as well as Botswana in the use of technology in teaching. These teachers represented all subject fields, including mathematics. The purpose of this course was to develop teachers' knowledge and skills in the use and integration of mobile technology in their teaching. The course was presented in a blended mode. Participants attended a 3-day face-to-face session, followed by 2-months online. The blended learning course had teachers working in subject specific groups in a LS format to plan, present and perfect lessons that can be taught using the technology available to them. In this study we investigate how LS can be adapted into a blended format to support isolated teachers who cannot meet face-to-face on a regular basis. We identified eleven aspects playing an important role in this process, namely technology; group; learning management system; online facilitation; technological pedagogical content knowledge (TPACK); (mobile) learning strategies; a lesson planning form; backward design; time; photos, videos and reports; and reflection questions. The eleven aspects that emerged, lead to the development of a framework consisting of three dimensions of LS namely Collaboration, Instructional Development and the Iterative Improvement Process, supported by the identified aspects.},
Author = {Joubert, Jody and  Callaghan, Ronel and  Engelbrecht, Johann},
ISSN = {1863-9690},
Journal = {ZDM: The International Journal on Mathematics Education},
Keywords = {Foreign Countries; Faculty Development; Communities of Practice; Teacher Collaboration; Educational Technology; Technology Uses in Education; Blended Learning; Integrated Learning Systems; Pedagogical Content Knowledge; Technological Literacy; Telecommunications; Planning; Lesson Plans; Design; Time; Photography; Video Technology; Reflection, South Africa; Botswana},
Number = {5},
Pages = {907 - 925},
Title = {Lesson Study in a Blended Approach to Support Isolated Teachers in Teaching with Technology},
URL = {http://dx.doi.org/10.1007/s11858-020-01161-x},
Volume = {52},
Year = {2020/10/01/},
}


@article{juta2020,
  title = {Classroom {{Management}} as a {{Response}} to {{Challenges}} in {{Mathematics Education}}: {{Experiences}} from a {{Province}} in {{South Africa}}},
  shorttitle = {Classroom {{Management}} as a {{Response}} to {{Challenges}} in {{Mathematics Education}}},
  author = {Juta, Abigail and Van Wyk, Chris},
  year = {2020},
  month = jan,
  journal = {African Journal of Research in Mathematics, Science and Technology Education},
  volume = {24},
  number = {1},
  pages = {21--30},
  publisher = {{Routledge}},
  issn = {1811-7295},
  doi = {10.1080/18117295.2020.1731646},
  abstract = {This paper reports on an investigation into management in Mathematics classrooms. Classroom management is contextualised in terms of the managerial actions required to manage classrooms effectively and the extent to which effective classroom management responds to contextual challenges. Relevant literature is reviewed, and theoretical perspectives with investigative value for classroom management are examined. Data was collected using individual semi-structured interviews with four Mathematics department heads and with five teachers per school, for the four focus group interviews. The interviews were audio-taped, transcribed and the data analysed using a process of abductive data analysis as suggested by McMillan and Schumacher (2010; Research in education: Evidence-based inquiry, 4th ed., Pearson Education). The participants in this study supported the use of different overlapping management styles. Teachers apply these styles by introducing useful and suitable management actions in their classroom practice. It was found that organising group work and motivating learners are actions that encompass the majority of functions related to the management of teaching and learning in Mathematics classrooms. Contextual influences like teachers' professional competencies, curriculum implementation, the maintenance of facilities and the availability of resources and learning materials were highlighted as factors that both support and constrain the effectiveness of classroom management.},
  keywords = {Classroom management,contextual challenges,managerial actions,managerial functions,managerial styles,Mathematics education},
  annotation = {\_eprint: https://doi.org/10.1080/18117295.2020.1731646},
  file = {/Users/reidarmosvold/Zotero/storage/WN8PNWQE/Juta og Van Wyk - 2020 - Classroom Management as a Response to Challenges i.pdf;/Users/reidarmosvold/Zotero/storage/JU824JVZ/18117295.2020.html}
}


@article{kalobo2016,
Abstract = {This paper explores teachers' perceptions of their learners' proficiency in statistical literacy, reasoning and thinking. Research in Statistics education has prompted a move away from the teaching of statistical skills, towards focusing on the development of statistical literacy, reasoning and thinking. The recent South African Grade 10-12 Mathematics curriculum change reflects this move. A specific challenge for South Africa is that teachers should understand the new intended outcomes of statistics when assessing learners. The participants (n = 66) included Grade 12 Mathematics teachers (females = 40%) from a district in the Free State, South Africa, selected through convenience sampling. A quantitative research approach was used by administering a 13-item Likert scale questionnaire with the Grade 12 Mathematics teachers. The responses were summarised descriptively as frequencies and percentages. The results indicated that two in three teachers perceived their learners to obtain acceptable proficiency in statistical literacy as defined by the literature. In contrast, only one in three teachers perceived their learners usually or almost always to be proficient in statistical reasoning and statistical thinking as defined by the literature. The findings of this study showed that about half of the Mathematics teachers do not see the connection between the action words in the curriculum, and the aspects of statistical reasoning and statistical thinking to be assessed. The large percentage of teachers uncertain about the proficiency of their learners in statistical reasoning and statistical thinking leads to the conclusion that teachers need to be provided with pre-service or in-service training strengthening their Subject Matter Knowledge and Pedagogical Content Knowledge related to the key intended outcomes of statistics assessment, that is, proficiency in statistical literacy, reasoning and thinking.},
Author = {Kalobo, Lukanda},
Journal = {African Journal of Research in Mathematics, Science and Technology Education},
Keywords = {Foreign Countries; Secondary School Teachers; Mathematics Teachers; Teacher Attitudes; Mathematics Curriculum; Curriculum Development; Educational Change; Mathematics Instruction; Statistics; Literacy; Abstract Reasoning; Thinking Skills; Questionnaires; Likert Scales; Grade 12; Knowledge Level; Incidence; Pedagogical Content Knowledge; Statistical Analysis, South Africa},
Number = {3},
Pages = {225 - 233},
Title = {Teachers' Perceptions of Learners' Proficiency in Statistical Literacy, Reasoning and Thinking},
URL = {http://dx.doi.org/10.1080/18117295.2016.1215965},
Volume = {20},
Year = {2016/01/01/},
}


@article{kizito2016,
Abstract = {In spite of sustained efforts tertiary institutions implement to try and improve student academic performance, the number of students succeeding in first-year mathematics courses remains disturbingly low. For most students, the gap between their mathematical capability and the competencies they are expected and need to develop to function effectively in these courses persists even after course instruction. In this study, an instrument for identifying and examining factors affecting student performance and success in a first-year Mathematics university course was developed and administered to 86 students. The overall Cronbach's Alpha coefficient for the questionnaire was found to be 0.916. Having identified variables from prior research known to affect student performance, factor analysis was used to identify variables exhibiting the greatest impact on student performance. The variables included prior academic knowledge, workload, student approaches to learning, assessment, student support teaching quality, methods and resources. From the analysis, students' perceptions of their workload emerged as the factor having the greatest impact on student's performance, followed by the matriculation examination score. The findings are discussed and strategies that can be used to improve teaching and contribute to student success in a first-year mathematics course in a South African context are presented.},
Author = {Kizito, Rita and  Munyakazi, Justin and  Basuayi, Clement},
ISSN = {0020-739X},
Journal = {International Journal of Mathematical Education in Science and Technology},
Keywords = {Foreign Countries; College Mathematics; Mathematics Instruction; Student Surveys; Prior Learning; Cognitive Style; Student Evaluation; Educational Quality; Teaching Methods; Student Attitudes; Questionnaires; Difficulty Level; College Freshmen; Statistical Analysis; Factor Analysis; Correlation; Regression (Statistics), South Africa; Bartletts Test of Significance in Factor Analysis; Kolmogorov Smirnov Two Sample Test, South Africa},
Number = {1},
Pages = {100 - 119},
Title = {Factors Affecting Student Success in a First-Year Mathematics Course: A South African Experience},
URL = {http://dx.doi.org/10.1080/0020739X.2015.1057247},
Volume = {47},
Year = {2016/01/01/},
}


@article{kortjass2019,
Abstract = {Background: This article gives an account of what I learned through the process of a self-study research project. Self-study teacher research allows teacher educators and teachers to improve their learning, plan new pedagogies and impact students' learning. Aim: The aim of this self-study research was to improve my own practice in early childhood mathematics teacher education through interaction and collaboration with others, such as colleagues and students. Setting: As a South African university-based teacher educator, I piloted an integrated learning approach (ILA) in the teaching and learning of early childhood mathematics in a selected undergraduate programme. Methods: I began by tracking my personal development in mathematics education and in so doing was able to recognise my personal learning of mathematics as a child growing up in an African township context. I then worked with a class of 38 student teachers to create collages and concept maps to explore their understandings and experiences of ILA. Results: Through this project, I discovered that colleagues in the role of critical friends provided essential feedback on my work in progress. I also learned that student teachers need to be equipped with knowledge and hands-on experience of how integration can take place in teaching and learning early childhood mathematics. I realised that it was essential to constantly reflect on my own personal history and my professional practice to explore new ways of teaching mathematics. Conclusion: Teacher educators may consider engaging in self-study research that includes art-based self-study methods to reflect on their practices and see how they change for the benefit of their students and ultimately for the benefit of the learners.},
Author = {Kortjass, Makie},
ISSN = {2223-7674},
Journal = {South African Journal of Childhood Education},
Keywords = {Reflection; Independent Study; Integrated Activities; Learning Activities; Early Childhood Education; Teacher Educators; Teacher Education; Mathematics Education; Foreign Countries; Student Teachers; Teacher Collaboration; Teacher Background, South Africa},
Number = {1},
Title = {Reflective Self-Study for an Integrated Learning Approach to Early Childhood Mathematics Teacher Education},
Volume = {9},
Year = {2019/01/01/},
URL = {https://search.ebscohost.com/login.aspx?direct=true&db=eric&AN=EJ1203647&site=ehost-live&scope=site},
}


@article{long2014,
Abstract = {A challenge encountered when monitoring mathematics teaching and learning at high school is that taxonomies such as Bloom's, and variations of this work, are not entirely adequate for providing meaningful feedback to teachers beyond very general cognitive categories that are difficult to interpret. Challenges of this nature are also encountered in the setting of examinations, where the requirement is to cover a range of skills and cognitive domains. The contestation as to the cognitive level is inevitable as it is necessary to analyse the relationship between the problem and the learners' background experience. The challenge in the project described in this article was to find descriptive terms that would be meaningful to teachers. The first attempt at providing explicit feedback was to apply the assessment frameworks that include a content component and a cognitive component, namely knowledge, routine procedures, complex procedures and problem solving, currently used in the South African curriculum documents. The second attempt investigated various taxonomies, including those used in international assessments and in mathematics education research, for constructs that teachers of mathematics might find meaningful. The final outcome of this investigation was to apply the dimensions required to understand a mathematical concept proposed by Usiskin (2012): the "skills-algorithm," "property-proof," "use-application" and "representation-metaphor" dimension. A feature of these dimensions is that they are not hierarchical; rather, within each of the dimensions, the mathematical task may demand recall but may also demand the highest level of creativity. For our purpose, we developed a two-way matrix using Usiskin's dimensions on one axis and a variation of Bloom's revised taxonomy on the second axis. Our findings are that this two-way matrix provides an alternative to current taxonomies, is more directly applicable to mathematics and provides the necessary coherence required when reporting test results to classroom teachers. In conclusion we discuss the limitations associated with taxonomies for mathematics.},
Author = {Long, Caroline and  Dunne, Tim and  de Kock, Hendrik},
ISSN = {1012-2346},
Journal = {Pythagoras},
Keywords = {Mathematics Instruction; Problem Solving; Foreign Countries; Mathematics Achievement; International Assessment; Mathematics Tests; Achievement Tests; Mathematical Concepts; Mathematics Teachers; Secondary School Mathematics; Curriculum Design; Educational Objectives; Classification; Grade 9, South Africa, Trends in International Mathematics and Science Study},
Number = {2},
Title = {Mathematics, Curriculum and Assessment: The Role of Taxonomies in the Quest for Coherence},
Volume = {35},
Year = {2014/01/01/},
URL = {https://search.ebscohost.com/login.aspx?direct=true&db=eric&AN=EJ1209461&site=ehost-live&scope=site},
}


@article{long2019,
Abstract = {The chain of progression from teacher education to qualification to classroom instruction and student engagement, and then to learning and achievement, is not as straightforward as often presented. Societal, political and economic pressures create either a positive climate or a stressful one for both teachers and students. Nevertheless it is safe to say that in a subject like mathematics, the importance of subject matter knowledge cannot be underestimated. Research in this area supports the presumption that formal qualifications in the subject, in this case mathematics, are necessary, as this focused engagement with mathematics provides the foundation for mathematics teaching and learning. The allocation of fully qualified teachers to schools has in the past been uneven, with the supposition that students at higher socio-economic levels are being taught by better qualified teachers. In South Africa the improvement of teacher qualifications has been identified as a core area of action with the relevant policy on teacher education renewed in 2007 and again in 2014. The focus of this paper is to understand the change in patterns of teacher qualifications, and the interrelationship with school contextual variables. The analysis is based on the Trends in International Mathematics and Science Study (TIMSS) data from 2003, 2011 and 2015, where teachers from the TIMSS sample provided contextual information. Descriptive statistics were calculated using the IEA IDB Analyzer. The results show that South Africa has made substantial progress in uplifting teachers' formal qualification levels and in reducing structural inequality within its education system. Out-of-field teaching of mathematics is still shown to be a common phenomenon and is unevenly distributed.},
Author = {Long, Caroline and  Wendt, Heike},
Journal = {African Journal of Research in Mathematics, Science and Technology Education},
Keywords = {Mathematics Teachers; Foreign Countries; International Assessment; Achievement Tests; Mathematics Tests; Mathematics Achievement; Teacher Qualifications; Grade 8; Grade 9; Teacher Placement; Educational Attainment; School Location; Disadvantaged Youth; High School Students; Institutional Characteristics; Expertise, South Africa, Trends in International Mathematics and Science Study},
Number = {3},
Pages = {344 - 353},
Title = {Trends in Qualification of South African Mathematics Teachers: Findings from TIMSS 2003, 2011, 2015},
URL = {http://dx.doi.org/10.1080/18117295.2019.1692475},
Volume = {23},
Year = {2019/01/01/},
}


@article{machaba2019,
Abstract = {This article presents balanced views of Mathematical Literacy (ML) and Mathematics (M), from both an analytical perspective and the subjective perspectives of teachers and learners. From the analytical perspective, policy documents and the literature spanning the period from the inception of ML to date are reviewed. Glimpses into the subjective views of teacher and learners come from a case study that involved interviewing a teacher and her learners with a view to understanding how Grade 10 learners and their teacher compared not only the nature of the two subjects but also the teaching and learning strategies associated with M and ML. Our case study confirms to a great extent the sentiments of the researchers, this time from the raw and uncensored views of those teaching and learning the subjects. Triangulating our exploration, we integrate policy, research and experience to redefine the nature, interconnectedness and equal standing of ML and M. In the light of the argument presented, the perceived existing boundaries between M and ML are challenged. The purpose is not to pull down the image and value of M, but to raise the popular image and perceived value of ML to the level of a dignified partner in the mathematics education gallery. We want to advocate the opening of higher educational courses and subsequent career pathways exclusively requiring ML as a prerequisite, justified on basis of the superior problem-solving and other valuable capabilities nurtured within our conceptualisation of the funds of knowledge associated with ML.},
Author = {Machaba, France and  Du Plooy, Maryna},
Journal = {African Journal of Research in Mathematics, Science and Technology Education},
Keywords = {Numeracy; Mathematics; Teacher Attitudes; Student Attitudes; Grade 10; Mathematics Instruction; Learning; Educational Policy; Educational Research; Foreign Countries; Secondary School Students; Secondary School Teachers; Secondary School Mathematics; Learner Engagement; Language Role; Language Usage, South Africa},
Number = {3},
Pages = {363 - 375},
Title = {Mathematics and Mathematical Literacy on the Career Podium -- Sharing Gold?},
URL = {http://dx.doi.org/10.1080/18117295.2019.1694782},
Volume = {23},
Year = {2019/01/01/},
}


@article{madusise2020,
Abstract = {Researchers have generally agreed that textbooks as a major conveyor of the curriculum play a dominant role in modern education scenes across different school subjects. The study analyzed a set of four learners' textbooks and their corresponding teachers' guides which are used as set books for teaching mathematics at Grade 9 level in South Africa. These textbooks were produced in response to the demands of the Grade R-9 National Curriculum Statement (NCS) policy document. A qualitative content analysis on how the recommendations in the policy document were further recontenxtualised in the pedagogic recontextualising field (PRF) by textbook authors into curriculum materials is presented. A vertical analysis approach was used, attending to the ways in which textbooks treat the idea of indigenous mathematical knowledge. Thus, it checks on the provided affordances for connecting culture and mathematics. Indications of affordances for connecting culture and mathematics are awash in the analyzed textbooks. However, authors had few examples from the learners' indigenous cultures but rich implementation ideas using foreign cultures. There is need for further research on where and how this indigenous mathematical knowledge can be extracted so as to be part of the textbooks' content.},
Author = {Madusise, Sylvia},
ISSN = {1990-3839},
Journal = {Educational Research and Reviews},
Keywords = {Culturally Relevant Education; Mathematics Instruction; Textbooks; Textbook Evaluation; Instructional Materials; Grade 9; Secondary School Mathematics; Foreign Countries; Indigenous Knowledge; National Curriculum; Curriculum Evaluation; Mathematics Activities, South Africa},
Number = {9},
Pages = {564 - 574},
Title = {Affordances for Connecting Culture and Mathematics: Moving from Curriculum to School Textbooks},
Volume = {15},
Year = {2020/09/01/},
URL = {https://search.ebscohost.com/login.aspx?direct=true&db=eric&AN=EJ1267548&site=ehost-live&scope=site},
}


@article{mafugu2021,
  title={A Comparison of Selected Assessment Results before and during the COVID-19 Pandemic in One University in South Africa.},
  author={Mafugu, Tafirenyika},
  journal={International Journal of Higher Education},
  volume={10},
  number={7},
  pages={74--83},
  year={2021},
  publisher={ERIC}
}


@article{mahlaba2020,
Abstract = {Mathematics in its nature is exploratory, giving learners a chance to view it from different perspectives. However, during most of their schooling, South African learners are rarely exposed to mathematical explorations, either because of the lack of resources or the nature of the curriculum in use. Perhaps, this is due to teachers' inability to design explorative mathematical tasks, or because suitable productive explorations are difficult for high school students and long explorations tend to elicit little interest from learners (Bansilal, Brijlall & Mkhwanazi, 2014; Bizony, 2016). Students are instead taught procedural and factual knowledge where remembering algorithms and facts is deemed significant, and this is evident in their teachers' content knowledge, which is much stronger in knowledge based questions than application questions (Bansilal, Brijlall & Mkhwanazi, 2014). However young educational researchers seek to understand the methodology and theories applied in teaching and learning, but also look to enrich themselves with simpler methods of teaching content that seems difficult for most learners. Given the rapid changes in technology around the globe, new and sophisticated methods of proof are continually being discovered. Hence, old proofs are continually being refined into new yet rigorous proofs. The author describes how he researched the triangle proportionality theorem to teach it to Grade 12 students.},
Author = {Mahlaba, Sfiso Cebolenkosi},
ISSN = {0228-0671},
Journal = {For the Learning of Mathematics},
Keywords = {Geometry; Logical Thinking; Mathematical Logic; Validity; Secondary School Mathematics; Foreign Countries; Grade 12, South Africa},
Number = {1},
Pages = {36 - 38},
Title = {Do Not Fall into the Same Trap I Nearly Did: Experiences of a Mathematics Education PhD Student Researching the Triangle Proportionality Theorem},
URL = {https://flm-journal.org/index.php?do=search&lang=en&search=Sfiso+Cebolenkosi+Mahlaba&operator=and},
Volume = {40},
Year = {2020/01/01/},
}


@article{mahlambi2021,
Abstract = {The article focused on the use of assessment for learning in promoting active learning and learner participation in mathematics. Assessment for learning (AfL) has been found to enhance learning and improve performance. However, teachers' use of AfL to enhance active learning has not been clearly outlined. This study is part of the broader research study that explored mathematics teachers' use of AfL to enhance mathematics teaching and learning in primary schools in Alexandra Township, Johannesburg. A case study research-type and a qualitative approach were used to collect data from mathematics teachers. Nine teachers were purposefully selected from whom data were collected using semi-structured interviews and non-participant observation. The findings revealed that teachers had limited pedagogical knowledge in using AfL to promote active learning in their classrooms. They failed to apply a learner-centred approach that promotes effective learner participation in mathematics classrooms. Therefore, it is recommended that teachers undergo ongoing continuous development on classroom time management and planning for the effective use of AfL.},
Author = {Mahlambi, Sizwe Blessing},
ISSN = {2469-9632},
Journal = {International Journal of Educational Methodology},
Keywords = {Student Evaluation; Active Learning; Student Participation; Elementary School Teachers; Elementary School Mathematics; Foreign Countries; Mathematics Teachers; Evaluation Methods; Teacher Attitudes, South Africa (Johannesburg)},
Number = {3},
Pages = {473 - 485},
Title = {Assessment for Learning as a Driver for Active Learning and Learner Participation in Mathematics},
Volume = {7},
Year = {2021/01/01/},
URL = {https://search.ebscohost.com/login.aspx?direct=true&db=eric&AN=EJ1309569&site=ehost-live&scope=site},
}


@article{mahofa2018,
Abstract = {The aim of this study was to explore the learning of mathematics word problems by African immigrant early learners in the Western Cape Province of South Africa (SA). Phenomenology was used as the philosophical underpinning for this study and also informed the research method. Purposive sampling methods were used to select 10 African immigrant early learners and their 5 South African teachers as participants from a target population of 1453 learners and their 52 teachers in township schools in Cape Town. Participants were interviewed individually and observed during mathematics classes that dealt with the teaching and learning of mathematics word problems. Data were analysed using Colaizzi's phenomenological data analysis method. The findings revealed that African immigrant learners were challenged with teachers' teaching skills; limited relevant prior knowledge of working with word problems; stigmatisation; the nature of learner-learner and teacher-learner interactions; and teachers' use of code switching in the learning and teaching of mathematics word problems. In order to promote learning of mathematics problems by African immigrant learners it is recommended that teachers should use mixed language groupings and explicit definitions of mathematical terminology, use immigrant early learners' learning experiences as a resource and minimise code switching and stigmatisation.},
Author = {Mahofa, Ernest and  Adendorff, Stanley and  Kwenda, Chiwimbiso},
Journal = {African Journal of Research in Mathematics, Science and Technology Education},
Keywords = {Word Problems (Mathematics); Immigrants; Learning; Phenomenology; Foreign Countries; Early Childhood Education; Qualitative Research; Teaching Skills; Prior Learning; Peer Relationship; Teacher Student Relationship; Educational Discrimination; Code Switching (Language); Semi Structured Interviews; Observation, South Africa (Cape Town)},
Number = {1},
Pages = {27 - 36},
Title = {Exploring the Learning of Mathematics Word Problems by African Immigrant Early Learners},
URL = {http://dx.doi.org/10.1080/18117295.2017.1390935},
Volume = {22},
Year = {2018/01/01/},
}


@article{makonye2020,
Abstract = {This study focuses on the teaching and learning of the pre-numeracy concepts through technology at Foundation Phase. It pre-supposes that the use of information and communication technology resources presents an innovative way to improve teaching and learning mathematics. The author argues that young children's relational conceptions of number lie at the core of their mathematics education as any subsequent mathematics learning heavily depends on it. This learning process is by no little means assisted through the mathematical activities teachers engage their learners and the resources they avail them, such as information and communication technologies. Principally important are the discursive interactions that ought to arise around the activities and the resources used. The author presumes that mastery learning is advanced by teaching using the variation theory. Teaching through variation aims to anchor knowledge; to make mathematical knowledge visible to amateurs through distinguishing the essential features of an 'object of learning' from its non-essential features. A treatment group was taught with information and communication technologies against a control group that used traditional teaching methods. Despite other intervening variables, the results of the study suggested better learning outcomes from the experimental group.},
Author = {Makonye, Judah P.},
ISSN = {0034-5237},
Journal = {Research in Education},
Keywords = {Number Concepts; Young Children; Technology Integration; Mathematics Instruction; Mastery Learning; Multimedia Instruction; Grade 1; Foreign Countries; Elementary Education; Game Based Learning; Experiential Learning; Thinking Skills; Instructional Effectiveness, South Africa (Johannesburg)},
Number = {1},
Pages = {3 - 21},
Title = {Teaching Young Learners Pre-Number Concepts through ICT Mediation},
URL = {http://dx.doi.org/10.1177/0034523719840051},
Volume = {108},
Year = {2020/11/01/},
}


@article{makonye2020b,
Abstract = {This research problematises mathematics teacher knowledge for teaching the Financial Mathematics topic to learners who come from communities where the time-value of money and a banking culture is not well established. The COACTIV framework underpins the study to build a pedagogical framework to teach Financial Mathematics to such learners. Data was collected from a sample of 20 South African mathematics teacher educators and business studies lecturers who teach Financial Mathematics at tertiary levels using a questionnaire. Focus were also held with participants to corroborate the results. The results of the study showed that many learners come from cultures that do not hold a time-value-of-money construct and do not readily learn textbook Financial Mathematics because it is not attuned to their home backgrounds. A pedagogical framework that takes into account learners' cultural knowledge systems is suggested to teach the topic, particularly to learners from disadvantaged communities.},
Author = {Makonye, Judah Paul},
ISSN = {1479-4802},
Journal = {Research in Mathematics Education},
Keywords = {Guidelines; Mathematics Instruction; Pedagogical Content Knowledge; Money Management; Teacher Educators; Business Administration Education; Foreign Countries; Banking; College Faculty; Teacher Attitudes; Cultural Background; Cultural Awareness; Disadvantaged; African Culture; College Students; Culture Conflict, South Africa},
Number = {2},
Pages = {98 - 116},
Title = {Towards a Culturally Embedded Financial Mathematics PCK Framework},
URL = {http://dx.doi.org/10.1080/14794802.2020.1752788},
Volume = {22},
Year = {2020/01/01/},
}


@article{mlotshwa2020,
Abstract = {Many South African educational institutions are adopting learning management systems (LMS) into their daily teaching and learning practice. The Western Cape Education Department piloted Modular Object-Oriented Dynamic Learning Environment (Moodle), an LMS for improving teaching and learning. The objective of the research reported on here was to determine whether Moodle improved Grade 10 learners' conceptual understanding of the topic, functions, in mathematics. The research investigated two classes; one dependent upon a traditional chalk-and-talk teaching method (control), and another exposed to Moodle (experimental). It was found that learners constructed their own knowledge by drawing on resources embedded in Moodle and framed within a Social Constructivist theory. A hybrid e-learning framework was deployed; learners acquired knowledge by interacting with computers. Interaction was monitored and results were recorded using online surveys and tests. A quasi-experimental design was employed to compare the groups. The comparisons were statistically analysed. Results showed that the functionalities within the Moodle LMS were instrumental in improving conceptual understanding of mathematical functions.},
Author = {Mlotshwa, Nicholas and  Tunjera, Nyarai and  Chigona, Agnes},
ISSN = {0256-0100},
Journal = {South African Journal of Education},
Keywords = {Online Courses; Mathematical Concepts; Fundamental Concepts; Foreign Countries; Integrated Learning Systems; Electronic Learning; Grade 10; High School Students; Conventional Instruction; Mathematics Instruction; Constructivism (Learning); Computer Mediated Communication, South Africa},
Number = {3},
Title = {Integration of MOODLE into the Classroom for Better Conceptual Understanding of Functions in Mathematics},
Volume = {40},
Year = {2020/08/01/},
URL = {https://search.ebscohost.com/login.aspx?direct=true&db=eric&AN=EJ1268314&site=ehost-live&scope=site},
}


@article{moleko2020,
Abstract = {Understanding the challenges pertaining to the teaching and learning of mathematics word problems is important in order to formulate effective strategies that will address the challenges. The qualitative case study reported in this article describes the teachers' and the learners' experiences regarding mathematics word problems. Data were collected through focus group discussions and reflection sessions, through the use of the free attitude interview technique used to initiate the conversations. Thematic analysis was used to analyse data. Analysis of data revealed challenges related to lack of English proficiency, limited knowledge of mathematical vocabulary, the effects of "out of context" meanings and lack of understanding mathematical language and structure to be the sources of difficulty for teaching and learning mathematics word problems. Findings of the study suggest the need for challenges to be understood in context in order for meaningful possible solutions to be formulated. Thus the learners' experiences should be regarded as important guidelines for informing better teaching of mathematics word problems.},
Author = {Moleko, Mirriam Matshidiso and  Mosimege, Mogege D.},
ISSN = {1837-6290},
Journal = {Issues in Educational Research},
Keywords = {Instructional Effectiveness; Mathematics Instruction; Word Problems (Mathematics); Problem Solving; Barriers; Learning Strategies; Vocabulary Development; Content Area Reading; Language Proficiency; English (Second Language); Native Language; Language of Instruction; African Languages; High School Students; Adolescents; Student Attitudes; Teacher Attitudes; Mathematics Teachers; Foreign Countries, South Africa},
Number = {4},
Pages = {1375 - 1394},
Title = {Teachers' and Learners' Experiences for Guiding Effective Teaching and Learning of Mathematics Word Problems},
URL = {http://www.iier.org.au/iier30/moleko.pdf},
Volume = {30},
Year = {2020/01/01/},
}


@article{moloi2019,
Abstract = {Within initial teacher education there is increasing pressure to enhance the use of assessment data to support students to improve their knowledge and skills, and to determine what standards they meet upon graduation. For such data to be useful, both programme designers and students require meaningful and comprehensive assessment reports on students' performance. However, current reporting formats, based on percentages, are inadequate for providing meaningful qualitative information on students' mathematics proficiency and, therefore, are unlikely to be used for interventions to improve teaching and enhance learning. This article proposes standard setting as an approach to reporting the assessment results in formats that are meaningful for decision-making and efficacious in subsequent interventions. Mathematics tests, developed through the Primary Teacher Education (PrimTEd) project, were administered electronically on a convenient sample of first-year and fourth-year PrimTEd students (N = 1 377). The data were analysed using traditional descriptive statistical analysis and the Objective Standard Setting method. The two reporting formats -- one using a percentage score and the other using standards-based performance levels -- were then compared. The study identified important distinguishing features of students' mathematical proficiency from the two reporting formats, and makes important findings on the specific knowledge and skills that students in South African initial teacher education programmes demonstrate. We conclude that reporting assessment results in standards-based formats facilitates differentiated interventions to meet students' learning needs. Furthermore, this approach holds good prospects for benchmarking performance across universities and for monitoring national standards.},
Author = {Moloi, Qetelo M. and  Kanjee, Anil and  Roberts, Nicky},
ISSN = {1012-2346},
Journal = {Pythagoras},
Keywords = {Preservice Teacher Education; Teacher Education Programs; Standard Setting; Mathematics Tests; Mathematics Skills; Knowledge Base for Teaching; Teacher Competencies; Foreign Countries; Performance Based Assessment; Knowledge Level; Test Items; Difficulty Level; Cognitive Processes; Cutting Scores; Pedagogical Content Knowledge, South Africa},
Number = {1},
Title = {Using Standard Setting to Promote Meaningful Use of Mathematics Assessment Data within Initial Teacher Education Programmes},
Volume = {40},
Year = {2019/01/01/},
URL = {https://search.ebscohost.com/login.aspx?direct=true&db=eric&AN=EJ1241188&site=ehost-live&scope=site},
}


@article{msimango2020,
Abstract = {This article reports on the mentoring of foundation phase teachers and their development of disciplinary-specific knowledge, particularly how the practicum provides a space for mathematics content knowledge (MCK) and mathematics pedagogical content knowledge (MPCK) for student teachers, given the generalist knowledge base of many primary school teacher mentors. Data was collected through semi-structured interviews with two Grade 2 mentors and focus group interviews with third-year student teachers in an urban university setting. A two-step process of analysis comprising open-ended coding, followed by a form of deductive coding, within a framework derived from literature on the development of MCK and MPCK, lead to two main findings. Firstly, mentors might have hindered student teachers' development of MCK and MPCK, thus impacting on the building of comprehensive conceptual models of good mathematics teaching practice. Secondly, the efficacy of the university-led training is questioned. We therefore recommend that greater emphasis be placed on the development of subject-specific mentoring practices, especially in scarce-skills areas such as mathematics, and argue for a set of standards for mathematics-specific mentoring practices in South African primary school teacher education.},
Author = {Msimango, M. N. and  Fonseca, K. and  Petersen, N. F.},
ISSN = {0258-2236},
Journal = {Perspectives in Education},
Keywords = {Mentors; Preservice Teacher Education; Student Teachers; Elementary School Teachers; Mathematics Teachers; Pedagogical Content Knowledge; Professional Training; Foreign Countries; Student Attitudes; Teaching Methods, South Africa},
Number = {2},
Pages = {272 - 284},
Title = {Mentoring and Preparing Primary School Mathematics Teachers},
URL = {https://doi.org/10.18820/2519593X/pie.v38.i2.18},
Volume = {38},
Year = {2020/01/01/},
}


@article{mutodi2016,
Abstract = {This paper reports on teachers' views on concept mapping: its applicability; reliability; advantages and; difficulties. A close-ended questionnaire was administered to 50 purposefully selected secondary school mathematics teachers from Sekhukhune District, Limpopo, South Africa. The findings indicate that mathematics teachers generally perceive that concept map: is useful; effective; is a practical tool for teaching mathematical concepts; represents and organises knowledge; helps retention and recall of concepts learnt and; provides feedback on the understanding of the concepts learnt. An important implication of this study is that there is a need for teachers to incorporate the concept mapping in the formative assessment process.},
Author = {Mutodi, Paul and  Chigonga, Benard},
ISSN = {1305-8223},
Journal = {EURASIA Journal of Mathematics, Science & Technology Education},
Keywords = {Concept Mapping; Secondary School Mathematics; Mathematics Teachers; Teacher Attitudes; Questionnaires; Mathematics Instruction; Mathematics Education; Foreign Countries; Formative Evaluation; Mathematical Concepts; Case Studies; Correlation; Teacher Effectiveness; Trigonometry; Likert Scales; Qualitative Research, South Africa, South Africa},
Number = {10},
Pages = {2685 - 2696},
Title = {Concept Map as an Assessment Tool in Secondary School Mathematics: An Analysis of Teachers' Perspectives},
URL = {http://www.iserjournals.com/journals/eurasia/articles/10.12973/eurasia.2016.2301a},
Volume = {12},
Year = {2016/10/01/},
}


@article{mwadzaangati2019,
  title = {An {{Exploration}} of {{Teaching}} for {{Understanding}} the {{Problem}} for {{Geometric Proof Development}}: {{The Case}} of {{Two Secondary School Mathematics Teachers}}},
  shorttitle = {An {{Exploration}} of {{Teaching}} for {{Understanding}} the {{Problem}} for {{Geometric Proof Development}}},
  author = {Mwadzaangati, Lisnet and Kazima, Mercy},
  year = {2019},
  month = sep,
  journal = {African Journal of Research in Mathematics, Science and Technology Education},
  volume = {23},
  number = {3},
  pages = {298--308},
  publisher = {{Routledge}},
  issn = {1811-7295},
  doi = {10.1080/18117295.2019.1685221},
  abstract = {Understanding the proof problem is necessary in the development of geometric proof in schools. This paper discusses findings from a qualitative case study which explored the mathematical work done by teachers in helping students to understand geometric proof problems. Data were generated from two teachers through video-recorded observations of 30 lessons and tape-recorded post-lesson interviews. Both types of data were analysed using thematic analysis which involved coding of the data relating to the first stage of Polya's problem-solving framework. The findings suggest that supporting students to understand geometric proof problems involves several tasks, including defining key mathematical terms of the theorem, initiating activities for introducing the theorem and representing the theorem as a statement to be proved. Furthermore, conducting these aspects of mathematical work using empirical exploratory approaches offers students better opportunities to understand the proof problem.},
  keywords = {Geometric proof development,geometric proof problem,mathematical tasks,problem-solving},
  annotation = {\_eprint: https://doi.org/10.1080/18117295.2019.1685221},
  file = {/Users/reidarmosvold/Zotero/storage/BNFAKRMB/Mwadzaangati og Kazima - 2019 - An Exploration of Teaching for Understanding the P.pdf;/Users/reidarmosvold/Zotero/storage/78IH46FE/18117295.2019.html}
}


@article{mwadzaangati2022,
  title = {Mathematics {{Mediational Means}} and {{Learner Centredness}}: {{Insights}} from `Traditional' {{Malawian Secondary School Geometry Lessons}}},
  shorttitle = {Mathematics {{Mediational Means}} and {{Learner Centredness}}},
  author = {Mwadzaangati, Lisnet and Adler, Jill and Kazima, Mercy},
  year = {2022},
  month = apr,
  journal = {African Journal of Research in Mathematics, Science and Technology Education},
  volume = {0},
  number = {0},
  pages = {1--12},
  publisher = {{Routledge}},
  issn = {1811-7295},
  doi = {10.1080/18117295.2022.2055910},
  abstract = {We re-examine a Malawian teacher's lessons which, using the framework of mathematic problem-solving developed by Polya, the typology of levels of task demand from Stein and colleagues and Malawi's description of learner-centred education (LCE), were described as teacher-centred and evaluated as `not good'. We studied seven video-recorded circle geometry lessons taught by the teacher and analysed these first using an LCE framework and then the Mathematics Discourse in Instruction (MDI) framework, adapted to suit the analysis of geometry lessons. The LCE analysis revealed that while the lessons were undoubtedly teacher-centred, they were not at the extreme end of an LCE continuum. Analysis using an adapted MDI framework showed that the teacher's use of mediational means opened opportunities to learn mathematics. We argue that LCE frameworks are useful in mathematics education research as they do not dichotomise teaching practices, but they are insufficient. They can obscure opportunities made available to learn mathematics. Frameworks that illuminate such opportunities are needed to fully describe mathematics teaching practices. Furthermore, we identified links between the elements of LCE exhibited and the mathematical mediational means in use. These suggest that supporting teachers to strengthen their mathematical mediational means in use could enable movement towards more learner-centered teaching.},
  keywords = {geometric proof development,LCE framework,Malawi,MDI framework},
  annotation = {\_eprint: https://doi.org/10.1080/18117295.2022.2055910},
  file = {/Users/reidarmosvold/Zotero/storage/2USJSLNX/Mwadzaangati et al. - 2022 - Mathematics Mediational Means and Learner Centredn.pdf;/Users/reidarmosvold/Zotero/storage/FGIUCP7F/18117295.2022.html}
}


@article{naidoo2018,
Abstract = {This paper seeks to explore the nature of dialogue within calculus lecture rooms. This paper reports on part of a larger study, in which the participants were two lecturers lecturing to 198 third year pre-service teachers at a University in South Africa. This qualitative interpretive study was framed within the ambits of social constructivism and aspects of Mortimer and Scott's framework were used to analyse dialogue in the lecture room. Data for this paper were generated through video-recorded lecture observations. Subsequently, a qualitative data analysis of the generated data revealed that dialogue within the calculus lecture rooms under study may be in the form of explanations and questioning. Questioning included questions that assess students' prior knowledge, probing, follow-up and guiding questions. The findings of this study are of value to both lecturers and students within higher education with implications for teaching and learning mathematics within higher education are presented.},
Author = {Naidoo, Jayaluxmi and  Likwambe, Botshiwe},
Journal = {African Journal of Research in Mathematics, Science and Technology Education},
Keywords = {Classroom Communication; Foreign Countries; Preservice Teachers; Calculus; Teacher Educators; Constructivism (Learning); Mathematics Instruction; Questioning Techniques; Lecture Method, South Africa},
Number = {3},
Pages = {374 - 385},
Title = {Exploring the Nature of Dialogue within South African Pre-Service Teachers' Calculus Lecture Rooms},
URL = {http://dx.doi.org/10.1080/18117295.2018.1533612},
Volume = {22},
Year = {2018/01/01/},
}


@article{naidoo2020,
Abstract = {Within the digital era, as global society embraces the fourth industrial revolution, technology is being integrated swiftly within teaching and learning. Within the Coronavirus disease (COVID-19) pandemic era, education institutions are preparing robustly for digital pedagogy. This article reports on a study focusing on 31 postgraduate mathematics education students' experiences of using digital platforms for learning during the COVID-19 pandemic era. The study was located at one teacher education institution in KwaZulu-Natal, South Africa. The research process encompassed three interactive online workshops and two online discussion forums, which were conducted via different digital platforms (Zoom, Moodle and WhatsApp). The study was framed using the theory of Communities of Practice, which denotes a group of people who share an interest which is enhanced as group members support and interact with each other. Qualitative data generated during the interactive online workshops and discussion forums were analysed thematically. The results exhibit challenges and strengths of using digital platforms as experienced by the participants. The results of this study suggest that before using digital platforms for mathematics learning, it is important for students to be encouraged to practise and engage collaboratively within digital platforms. The study adds to the developing knowledge in the field concerning using digital platforms for learning mathematics within the COVID-19 pandemic era.},
Author = {Naidoo, Jayaluxmi},
ISSN = {1012-2346},
Journal = {Pythagoras},
Keywords = {Mathematics Instruction; Graduate Students; Educational Technology; Electronic Learning; COVID-19; Pandemics; Communities of Practice; Foreign Countries; Mathematics Teachers; Computer Mediated Communication; Social Media; Online Courses; School Closing, South Africa},
Number = {1},
Title = {Postgraduate Mathematics Education Students' Experiences of Using Digital Platforms for Learning within the COVID-19 Pandemic Era},
Volume = {41},
Year = {2020/01/01/},
URL = {https://search.ebscohost.com/login.aspx?direct=true&db=eric&AN=EJ1286885&site=ehost-live&scope=site},
}


@article{ndlovu2014,
Abstract = {The purpose of this article is to report on an investigation of the perceptions and performance of mathematics teachers in a teacher professional learning (TPL) programme based on realistic mathematics education (RME) principles, which included a topic on transformations, undertaken by the researcher. Forty-seven Senior Phase (Grade 7--9) teachers took part in the mixed-methods study in which they answered a questionnaire with both closed and openended items. Fifty teachers took an achievement test at the end of the programme. The TPL programme used the RME approach in the design and delivery of mathematical tasks intended to enhance teachers' mathematical knowledge for teaching. The sessions were conducted in a manner that modelled one way in which RME principles can be adopted as a teacher professional development strategy. The significance of the study is that continuing TPL is acknowledged to contribute to improvement in teaching and learning to address the concern about unsatisfactory learner achievement in mathematics. The responses suggested that the majority of teachers experienced the sessions positively in relation to all but one of the six RME principles. The teachers reported that they took an active part both as individuals and in small groups and expressed their willingness to adopt the type of activities and materials for their classrooms, which is an essential first step in Guskey's first level of evaluation of a teacher TPL programme. The teachers' average performance in an achievement test at the end of the topic was 72% which was indicative of modest learning gains at Guskey's second level of TPL effectiveness.},
Author = {Ndlovu, Mdutshekelwa},
ISSN = {1012-2346},
Journal = {Pythagoras},
Keywords = {Teacher Attitudes; Mathematics Teachers; Faculty Development; Mathematics Education; Grade 7; Grade 8; Grade 9; Secondary School Teachers; Program Effectiveness; Knowledge Base for Teaching; Foreign Countries; Teacher Competencies, South Africa},
Number = {2},
Title = {The Effectiveness of a Teacher Professional Learning Programme: The Perceptions and Performance of Mathematics Teachers},
Volume = {35},
Year = {2014/01/01/},
URL = {https://search.ebscohost.com/login.aspx?direct=true&db=eric&AN=EJ1209541&site=ehost-live&scope=site},
}


@article{ngema2019,
Abstract = {Despite South Africa's high spending in education compared to other sub-Saharan countries, its education system is often criticized as ineffective as evidenced by poor student outcomes in both national and international assessments. This educational inefficiency is often linked to poor teacher quality, particularly in mathematics and science where some teachers are considered to have content knowledge below the level at which they are teaching. The researchers interviewed five primary school principals in KwaZulu-Natal on the training needs analysis methods they used to identify the training needs of foundation phase teachers. They all reported that they only used the Integrated Quality Management System template provided by the Department of Basic Education. However, they did not use it optimally due to a lack of comprehensive knowledge of how it should be implemented. In order to address this, it is recommended that principals should receive thorough training on the implementation of the Integrated Quality Management System, and that training needs analysis should be conducted on a quarterly basis rather than once a year.},
Author = {Ngema, Millicent and  Lekhetho, Mapheleba},
ISSN = {1822-7864},
Journal = {Problems of Education in the 21st Century},
Keywords = {Principals; Administrator Role; School Administration; Management Systems; Professional Development; Elementary School Teachers; Educational Needs; Needs Assessment; Teacher Competencies; Teacher Effectiveness; Educational Quality; Leadership Effectiveness; Role Perception; Context Effect; Foreign Countries, South Africa},
Number = {6},
Pages = {758 - 773},
Title = {Principals' Role in Managing Teacher Professional Development through a Training Needs Analysis},
Volume = {77},
Year = {2019/01/01/},
URL = {https://search.ebscohost.com/login.aspx?direct=true&db=eric&AN=EJ1267883&site=ehost-live&scope=site},
}


@article{nieuwoudt2015,
Abstract = {The teaching of problem-solving through the development of a problem-solving model was investigated in a Grade 4 mathematics classroom. Learners completed a questionnaire regarding their knowledge of mathematical problem-solving, their attitudes towards problem-solving, as well as their experiences in solving problems. Learners' responses revealed overall negative beliefs towards problem-solving as well as a lack of knowledge about what problem-solving in mathematics entails. The teacher then involved the learners in a structured learning programme where they worked in cooperative groups of six on different kinds of mathematical problems to solve. The groups regularly engaged in discussions about the different strategies they were using to solve a specific problem and eventually succeeded in formulating a generic problem-solving model they could call their own. The model was effectively used by the learners to solve various mathematical problems, reflecting their levels of cognitive development to a certain extent.},
Author = {Nieuwoudt, Susan},
ISSN = {1012-2346},
Journal = {Pythagoras},
Keywords = {Models; Problem Solving; Mathematics Instruction; Grade 4; Student Attitudes; Foreign Countries; Mathematics Teachers; Elementary School Students; Elementary School Teachers; Elementary School Mathematics; Mathematics Activities, South Africa},
Number = {2},
Title = {Developing a Model for Problem-Solving in a Grade 4 Mathematics Classroom},
Volume = {36},
Year = {2015/01/01/},
URL = {https://search.ebscohost.com/login.aspx?direct=true&db=eric&AN=EJ1209515&site=ehost-live&scope=site},
}


@article{nixon2019,
Abstract = {Despite agreement among teacher educators, scholars, and policymakers on the importance of teachers' subject matter knowledge (SMK), existing models provide limited information about the nature of this foundational component of teacher knowledge. The common assumption is that teachers need to know more about the science subject matter than their students are expected to learn, but what and how much more is underspecified. In order to more characterize science teachers' SMK, we present the science knowledge for teaching (SKT) model, which has been adapted from the mathematics education literature to apply to science education. The SKT model includes three domains: core content knowledge, specialized content knowledge, and linked content knowledge. We used this model to explore the SMK new secondary chemistry teachers in South Africa and the United States drew on when they explained the conservation of mass and analyzed a related teaching scenario, two important tasks of teaching. Findings indicated these new teachers drew on knowledge from all three SKT domains in order to engage in these tasks of teaching. This result suggests the potential of the SKT model to characterize the nature of science teachers' SMK and thereby better inform teacher preparation and professional development programs.},
Author = {Nixon, Ryan S. and  Toerien, Rene and  Luft, Julie A.},
ISSN = {0036-6803},
Journal = {School Science and Mathematics},
Keywords = {Science Instruction; Pedagogical Content Knowledge; Knowledge Base for Teaching; Secondary School Teachers; Science Teachers; Foreign Countries; Models; Chemistry; Cross Cultural Studies; Vignettes; Teaching Methods; Scientific Principles; Teacher Education Programs; Faculty Development, South Africa; United States},
Number = {3},
Pages = {150 - 160},
Title = {Knowing More than Their Students: Characterizing Secondary Science Teachers' Subject Matter Knowledge},
URL = {http://dx.doi.org/10.1111/ssm.12323},
Volume = {119},
Year = {2019/03/01/},
}


@article{olawale2021,
  title={Critical Social Pedagogy in Mathematics Teacher Education},
  author={Olawale, BE and Mncube, VS and Harber, C},
  journal={International Journal of Higher Education},
  volume={10},
  number={6},
  year={2021}
}


@article{potgieter2018,
Abstract = {The Department of Basic Education in South Africa has identified factorisation as a problem area in Mathematics teaching. Learners in earlier grades are exposed to mathematical tasks, involving concepts, such as factors of integers, fractions, equivalent fractions and prime numbers, that are easier to solve when the divisibility rules are applied. An experiment was designed to investigate the effect of learners' knowledge and their application of the divisibility rules on their gaze behaviour. Seventy-eight learners in Grades 4-7 participated in an eye-tracking study where questions on divisibility were presented on a computer screen. Learners were expected to indicate whether a five-digit dividend was divisible by a divisor and provide reasons for their answers. Gaze behaviour (expressed as the percentage of total fixation time that was spent on each digit), along with learners' verbal responses were used to determine whether a given divisibility rule was applied correctly. The findings show that learners apply different strategies to inspect the dividend when they know the divisibility rules and apply them correctly as opposed to when they do not know the rules and/or apply them incorrectly. It is argued that, since knowledge of the divisibility rules is a reliable predictor for gaze behaviour, gaze behaviour can in turn be used to assist teachers to identify a lack of knowledge and/or the incorrect application of the divisibility rules. Teachers can then cautiously intervene with revision to assist learners whose gaze behaviour indicates that they need assistance.},
Author = {Potgieter, Pieter and  Blignaut, Pieter},
Journal = {African Journal of Research in Mathematics, Science and Technology Education},
Keywords = {Foreign Countries; Mathematics Instruction; Grade 4; Grade 5; Grade 6; Grade 7; Eye Movements; Arithmetic; Visual Stimuli; Problem Solving; Mathematical Logic; Knowledge Level; Predictor Variables; Elementary School Students, South Africa},
Number = {3},
Pages = {351 - 362},
Title = {The Effect of Learners' Knowledge of the Divisibility Rules on Their Gaze Behaviour},
URL = {http://dx.doi.org/10.1080/18117295.2018.1533611},
Volume = {22},
Year = {2018/01/01/},
}


@article{potgieter2021,
Abstract = {Research on puppets in Intermediate Phase mathematics is in its infancy. According to Vygotsky, play affords a playful element that can optimise learning opportunities. However, many mathematics teachers are unfamiliar with the integration of pedagogy of play (PoP) (in this case, puppetry). The aim of this paper is to report on one participant's (an Intermediate Phase mathematics teacher [N=1]) lived experiences of teaching with puppets after a two-day intervention. A case study approach was followed and the participant constantly reflected on his experiences. Data were collected through (i) a semi-structured open-ended interview, (ii) reflective prompts and (iii) a reflective journal with prompts. The data revealed the participant's experiences of puppetry, how his metacognitive awareness developed and how he transferred new knowledge to his Intermediate Phase mathematics classroom. The data were analysed using content analysis. The results show that, although learners often deem mathematics "mundane" and "unexciting", puppetry allowed the participant's learners (according to his reflections) to experience this subject as enjoyable and creative, encouraging participation and liveliness, as the puppet was considered a peer in teaching-learning. The Intermediate Phase mathematics classroom became a space where content became meaningful, accessible and understandable to all learners.},
Author = {Potgieter, Erika and  van der Walt, Marthie},
ISSN = {0258-2236},
Journal = {Perspectives in Education},
Keywords = {Play; Puppetry; Teaching Methods; Instructional Effectiveness; Mathematics Instruction; Mathematics Teachers; Metacognition; Reflective Teaching; Self Management; Intermediate Grades; Foreign Countries, South Africa},
Number = {3},
Pages = {121 - 137},
Title = {Puppetry as a Pedagogy of Play in the Intermediate Phase Mathematics Classroom: A Case Study},
URL = {http://dx.doi.org/10.18820/2519593X/pie.v39.i3.10},
Volume = {39},
Year = {2021/01/01/},
}


@article{pournara2015,
Abstract = {It is wellknown that the majority of South African learners achieve extremely poorly in Mathematics. Many claim that one of the causes of this poor attainment is teachers' weak knowledge of mathematics, and propose that improving teachers' mathematical knowledge would improve learner attainment. However, the evidence-base for this proposed solution is currently relatively weak. We report on a quasi-experimental study examining the learning gains of Grade 10 learners from five secondary schools in the Johannesburg area, whose teachers participated in a year-long professional development course aimed at improving the teachers' knowledge of mathematics for teaching. Statistical analyses of pre- and post-test results show that the intervention group of learners (N = 586) taught by teachers who had participated in the professional development (N = 14) outperformed a matched control group of learners (N = 217) taught by teachers in the same schools (N = 7). An effect size of = 0.17 for the intervention group is equivalent to two months' additional progress. While the learning gains are small, they are statistically significant. These findings provide empirical support for claims that attending to teachers' mathematical knowledge can impact learners' attainment. Suggestions are made regarding the form and substance of such professional development.},
Author = {Pournara, Craig and  Hodgen, Jeremy and  Adler, Jill and  Pillay, Vasen},
ISSN = {0256-0100},
Journal = {South African Journal of Education},
Keywords = {Foreign Countries; Knowledge Base for Teaching; Mathematics Instruction; Mathematics Achievement; Teacher Competencies; Quasiexperimental Design; Grade 10; Secondary School Teachers; Pretests Posttests; Statistical Analysis; Mathematics Tests; Control Groups; Experimental Groups; Comparative Analysis; Effect Size, South Africa},
Number = {3},
Title = {Can Improving Teachers' Knowledge of Mathematics Lead to Gains in Learners' Attainment in Mathematics?},
Volume = {35},
Year = {2015/08/01/},
URL = {https://search.ebscohost.com/login.aspx?direct=true&db=eric&AN=EJ1134890&site=ehost-live&scope=site},
}


@article{ramaligela2021,
Abstract = {Instructional practice plays a significant role in revealing how well teachers understand the subjects they teach. Many studies have been conducted in South Africa on the relationship between teachers' knowledge of well-established subjects like Science and Mathematics and how well teachers apply their knowledge in the classroom. However, relatively little research has been done on the subject of Technology, which was only included in the national school curriculum after 1994. The aim of this study was to explore pre-service (i.e. in-training) Technology teachers' content knowledge and instructional knowledge in the context of various theories about teaching. The study followed a case study approach. Five female pre-service Technology teachers, who were in their final year of teacher training at a South African university of technology and were doing their in-school practicum were observed. Video recorder was used to capture the delivering of a lesson to a class of Grade 8 learners. The researcher used the 9E instructional model, which comprises nine phases in the presentation of a lesson, as the basis for her observation work and final analysis. A key finding was that the content and instructional knowledge displayed by most pre-service Technology teachers was inadequate, which weakened their effectiveness in the classroom. As a result, learners were deprived of the opportunity to sharpen their cognitive skills and develop authentic interest in Technology. This study, though limited in scope, has laid an important foundation for more in-depth studies to be conducted on the extent of content and instructional knowledge in the sphere of Technology Education, which should be of value to other universities offering teacher-training programmes.},
Author = {Ramaligela, S. M.},
Journal = {International Journal of Technology and Design Education},
Keywords = {Preservice Teachers; Pedagogical Content Knowledge; Readiness; Teaching Methods; Foreign Countries; Teaching Skills; Educational Technology, South Africa},
Number = {3},
Pages = {531 - 544},
Title = {Exploring Pre-Service Technology Teachers' Content and Instructional Knowledge to Determine Teaching Readiness},
URL = {http://dx.doi.org/10.1007/s10798-020-09570-5},
Volume = {31},
Year = {2021/07/01/},
}


@article{roux2015,
Abstract = {It is a known fact that South African learners underachieve in mathematics. One possible factor that might have an influence on their mathematics achievement is the conceptual knowledge of mathematics teachers. In order to facilitate conceptual understanding, mathematics teachers themselves must possess profound mathematical knowledge. One key aspect of the complex landscape of pre-service mathematics teacher education is the development of pre-service teachers' mathematical knowledge. Various studies have suggested that pre-service teachers need to be exposed to the meaningful learning of mathematics as a way to develop their mathematical knowledge for teaching. By using a mixed methods approach, this study examined the influence of a technologically enhanced learning environment on the conceptual understanding of mathematical functions of pre-service mathematics teachers. Using a hybrid model of O'Callaghan's framework and Dreyfus's typology, pre-service teachers were tested on the modelling, interpretation, translation and reifying of functions. Data were gathered from a pre-post-test, as well as from task-based interviews. The results revealed that there was no improvement in the first three components, but a significant improvement in the reification component.},
Author = {Roux, Annalie and  Nieuwoudt, Hercules and  Nieuwoudt, Susan},
Journal = {African Journal of Research in Mathematics, Science and Technology Education},
Keywords = {Mathematics Education; Foreign Countries; Mathematics Teachers; Mathematics Achievement; Mixed Methods Research; Preservice Teachers; Preservice Teacher Education; Educational Environment; Pretests Posttests; Teaching Methods; Knowledge Base for Teaching; Mathematics Skills; Achievement Tests; Elementary Secondary Education; International Assessment; Mathematics Tests; Science Achievement; Science Tests, South Africa, Trends in International Mathematics and Science Study},
Number = {3},
Pages = {289 - 305},
Title = {Conceptual Learning of Functions in a Technologically Enhanced Environment},
URL = {http://dx.doi.org/10.1080/10288457.2015.1089674},
Volume = {19},
Year = {2015/01/01/},
}


@article{sari2021,
  title={Validation of a Model of Sustainable Place Value Understanding in Turkey},
  author={Sari, Mehmet Hayri and Herzog, Moritz and Olkun, Sinan and Fritz, Annemarie},
  journal={International Electronic Journal of Mathematics Education},
  volume={16},
  number={3},
  pages={em0659},
  year={2021},
  publisher={Modestum Publishing LTD}
}


@article{sepeng2014,
Abstract = {The study reported in this article sought to explore and observe how grade 9 learners solve real-wor(l)d problems (a) without real context and (b) without real meaning. Learners' abilities to make sense of the decontextualised word problems set in the real world were investigated with regard to learners' use of common sense in relation to problem solving. The results presented in this article are part of a study following a mixed-methods design with the qualitative data informing the quantitative data. The data collection strategies included administering a test to 107 grade 9 learners (in their home language, isiXhosa, and language of learning and teaching, English) and conducting focus group interviews with eight selected learners from a convenience sample. The data demonstrate learners' tendencies to exclude common-sense knowledge, contexts and meaning-making from their solution processes when they engage in word problem-solving in mathematics.},
Author = {Sepeng, Percy},
Journal = {African Journal of Research in Mathematics, Science and Technology Education},
Keywords = {Grade 9; Knowledge Level; Language Usage; Word Problems (Mathematics); Problem Solving; Context Effect; Mixed Methods Research; Focus Groups; Mathematics Instruction; Social Influences; Cultural Influences; English (Second Language); African Languages; Language of Instruction; Foreign Countries; Secondary School Mathematics, South Africa},
Number = {1},
Pages = {14 - 24},
Title = {Use of Common-Sense Knowledge, Language and Reality in Mathematical Word Problem Solving},
URL = {http://dx.doi.org/10.1080/10288457.2014.890808},
Volume = {18},
Year = {2014/01/01/},
}


@article{setoromo2018,
Abstract = {Background: It is important that mathematics teachers have a robust knowledge of the mathematics they teach. They need more than just knowledge of the content because they are expected to facilitate understanding of the content with their learners. This study focused on the knowledge of practising Grade R teachers from Lesotho. Aim: The purpose of this exploratory study was to explore practising Grade R teachers' mathematical knowledge for the teaching of numeracy. Setting: The study was conducted with 48 practising Grade R teachers while they were enrolled in an in-service programme at a College of Education in Lesotho. Methods: Data was generated through the use of questionnaires. The questionnaire included items focusing on the four domains of knowledge, namely common content knowledge, special content knowledge, knowledge of content and students, and knowledge of content and teaching. Results: The findings revealed that some teachers were unable to carry out division problems accurately and many struggled to explain the possible modification of a teaching plan. Only 27% of the group were able to explain that there were levels of understanding numeracy. With respect to ordering a sequence of three topics, only 15% of the teachers produced a reasonable sequence. Conclusion: These teachers' difficulties raise concerns about the effectiveness of their teaching of numeracy. Despite the Lesotho government's commitment to improving the learning of mathematics at the Grade R level, much more work is required to be conducted with teachers so that their mathematical knowledge for teaching (MKT) numeracy can be improved.},
Author = {Setoromo, Mamasiphole and  Bansilal, Sarah and  James, Angela},
ISSN = {2223-7674},
Journal = {South African Journal of Childhood Education},
Keywords = {Foreign Countries; Mathematics Instruction; Mathematics Teachers; Numeracy; Early Childhood Education; Preschool Teachers; Pedagogical Content Knowledge; Teaching Methods; Teacher Effectiveness, Lesotho},
Number = {2},
Title = {Lesotho Grade R Teachers' Mathematical Knowledge for Teaching Numeracy},
Volume = {8},
Year = {2018/01/01/},
URL = {https://search.ebscohost.com/login.aspx?direct=true&db=eric&AN=EJ1198823&site=ehost-live&scope=site},
}


@article{setoromo2020,
Abstract = {Background: Research has indicated that young learners are capable of learning mathematics because they are born with an innate core of mathematics knowledge. Teachers of young learners are, therefore, expected to offer mathematical curriculum that exposes learners to a deep and explicit knowledge of high mathematics. Aim: The study aimed at Grade R in-service teachers' understanding of teaching mathematics in their classrooms. Setting: The study sampled five in-service Grade R teachers from four districts in Lesotho, while they were enrolled in an in-service programme at a college of Education. Methods: This is a qualitative approach, and a case study design was employed. Data sources included teachers' interviews, classroom observations and document analysis for instance, the teachers' files, lesson plans for Grade R curriculum for mathematics and course outline of mathematics offered to in-service teachers during their training in the Lesotho College of Education (LCE). Which focussed on four domains of knowledge, namely, common content knowledge, special content knowledge, knowledge of content and students, and knowledge of content and teaching. Results: The findings revealed that the in-service teachers in the LCE had insufficient understanding of the teaching of mathematics, which in turn had a negative influence on the teaching of mathematics in Grade R classes. Conclusion: Despite the Lesotho government's commitment to improving the learning of mathematics at the Grade R level. Teachers' difficulties raise concerns about the effectiveness of their teaching of mathematics.},
Author = {Setoromo, Mamasiphole and  Hadebe-Ndlovu, Blanche},
ISSN = {2223-7674},
Journal = {South African Journal of Childhood Education},
Keywords = {Foreign Countries; Mathematics Teachers; Elementary School Teachers; Mathematics Instruction; Pedagogical Content Knowledge; Inservice Teacher Education; Instructional Effectiveness, South Africa},
Number = {1},
Title = {An Exploration of In-Service Teachers' Understanding of Teaching Mathematics in Grade R Classrooms: A Case Study of Grade R in Lesotho University of Kwazulu-Natal, South Africa},
Volume = {10},
Year = {2020/01/01/},
URL = {https://search.ebscohost.com/login.aspx?direct=true&db=eric&AN=EJ1268492&site=ehost-live&scope=site},
}

@article{shalem2018,
Abstract = {Standardised curriculum or standardized lesson plans (SLPs) have become an accepted strategy to support and improve instructional practices in schools worldwide. These standardised lesson plans (SLPs) were criticized in the 1970s and 1980s for deskilling the teaching profession and reducing the work of teachers to that of mere technicians. This critique is now returning at a time of growing regulation of teachers' work in many school systems. In this paper, we investigate the potential and limitations of the SLPs which are the main component of the Gauteng Primary Language and Mathematics Strategy (GPLMS), a large-scale multipronged instructional reform established in Gauteng, the most industrialised province of South Africa around Johannesburg and Pretoria. Our interest is to engage with the impact of SLPs on teachers, given the frequent claims that teacher autonomy is seriously eroded and threatened by SLPs. We examine the relationship between autonomy and authority, by drawing on the philosophers Peters and Winch as well as on curriculum theorists Remillard, Morris and Hiebert who have studied standardized curriculum materials and their impact on teachers' work. The paper argues for a deeper analytical understanding of teacher autonomy and offers three conditions that can equip teachers to seize "autonomy opportunities" when working with SLPs: (1) standardised curriculum materials of high quality, sufficiently specified so that correct and incorrect ways of following the content and procedures inscribed in the SLPs and the reasons for them are accessible to all teachers; (2) authority which is considered legitimate, applied in a morally justified manner and managed in an educationally sound way; and (3) appropriate use of professional and personal knowledge, when making decisions and evaluating SLPs' prescriptions in context. In the rest of the paper we evaluate the "autonomy opportunities" provided by the GPLMS standardised lesson plans, by examining whether the three conditions were met.},
Author = {Shalem, Yael and  De Clercq, Francine and  Steinberg, Carola and  Koornhof, Hannchen},
ISSN = {1573-1812},
Journal = {Journal of Educational Change},
Keywords = {Foreign Countries; Professional Autonomy; Lesson Plans; Educational Change; Curriculum Development; Educational Quality; Mathematics Instruction; Reading Instruction; National Curriculum, South Africa},
Number = {2},
Pages = {205 - 222},
Title = {Teacher Autonomy in Times of Standardised Lesson Plans: The Case of a Primary School Language and Mathematics Intervention in South Africa},
URL = {http://dx.doi.org/10.1007/s10833-018-9318-3},
Volume = {19},
Year = {2018/05/01/},
}

@article{sibanda2021,
Abstract = {This study explores the link between a mentorship program for in-service teachers and their professional development. The participants are under-qualified mathematics, science, and technology teachers employed in junior secondary schools. Using a mixed-method approach, data were collected through a questionnaire responded to by 163 mentees, and semi-structured interviews with 4 in-service teachers. Despite tensions between mentors and mentees, the results show a strong link between mentoring and the professional development of in-service teachers. The majority of the sampled teachers learnt new teaching approaches and improved their content knowledge. The findings are emergent, suggesting that experienced in-service teachers require different models of mentoring relationships between mentors and mentees to those suggested in the literature.},
Author = {Sibanda, Doras and  Amin, Nyna},
ISSN = {2158-2440},
Journal = {SAGE Open},
Keywords = {Correlation; Mentors; Intervention; Inservice Teacher Education; Professional Development; Teacher Improvement; Teacher Qualifications; Teacher Attitudes; Program Effectiveness; Junior High School Teachers; Science Education; Technology Education; Mathematics Education; Pedagogical Content Knowledge; Foreign Countries, South Africa},
Number = {1},
Title = {The Link between a Mentorship Programme for Mathematics, Science, and Technology In-Service Teachers and Professional Development},
URL = {http://dx.doi.org/10.1177/2158244020988732},
Volume = {11},
Year = {2021/01/01/},
}

@article{simelane-mnisi2019,
Abstract = {Aim/Purpose: The purpose of the current study was to investigate whether the effectiveness of the Technology-engagement Teaching Strategy using personal response systems with student's approaches to learning will increase the pass rate in the Mathematics course. Background: The challenge in this study was to develop the learning activities that accommodate individual differences and diversity in learning. Furthermore, Studies investigating students' approaches to learning have mostly done this in a face-to-face learning environment as opposed to incorporate exploration thereof when integrating educational technology. Methodology: A mixed method approach was used. The basis of using this method was a combination of quantitative and qualitative approaches which gives a clearer understanding of research problems than either approach alone. Participants were 240 students registered for Mathematics II at a study University of Technology in South Africa. Purposeful, convenience and simple random sampling were used to select the participants. Contribution: No study that has investigated the utility of personal response systems with students' approaches to learning is currently available as observed by the researcher. In this case, the combination of the two variables in this study makes it unique and therefore important in contributing to the body of knowledge focusing on the role of technology in pedagogy. Findings: The results showed that while the majority of students followed the Strategic Approach the same Technology-engagement Teaching Strategy was used for students following Surface Approaches. The Technology-engagement Teaching Strategy was developed in such a manner to accommodate students following different approaches. The personal response system continuous assessments, as well as the semester test, revealed the improvement in academic performance as well as the increase in mathematics pass rates. It was also found that using personal response system enhances students' mathematical communication skills, and helps to develop the skills needed to write and read mathematical proofs. Recommendations for Practitioners: It is recommended that academics take into consideration the students approaches to learning in their teaching practices. It is crucial that lecturers take advantage of technology to enhance their teaching practices and decrease the fear of the unknown and open up to new innovations in teaching. Recommendation for Researchers: It is recommended that the use of personal response systems should be explored in different mathematics settings (different lectures and universities). Such an exploration according to the researcher will be useful in endorsing what has been reported in this paper. Impact on Society: The results revealed that the Strategic Approach was the most dominant among the participants in this study. The results also showed the improvement in students' academic performance as well as the number of students who passed increased. Future Research: A further research study could be conducted with students in a different discipline where poor academic performance is experienced.},
Author = {Simelane-Mnisi, Sibongile and  Mji, Andile},
ISSN = {1547-9714},
Journal = {Journal of Information Technology Education: Research},
Keywords = {Audience Response Systems; Technology Uses in Education; College Mathematics; Mathematics Achievement; College Students; Foreign Countries; Learning Strategies; Communication Skills; Mathematics Instruction; Learning Activities; Student Evaluation; Student Attitudes, South Africa},
Pages = {331 - 353},
Title = {Technology-Engagement Teaching Strategy Using Personal Response Systems on Student's Approaches to Learning to Increase the Mathematics Pass Rate},
URL = {http://www.jite.org/documents/Vol18/JITEv18ResearchP331-353Simelane5551.pdf},
Volume = {18},
Year = {2019/01/01/},
}

@article{siyepui2021,
Abstract = {In this article we report on pre-service teachers' mathematical engagement regarding the total surface areas of geometric solids. Despite several attempts at improvement, the poor performance of South African learners in mathematics persists. This is attributed to instructional approaches. In the study reported on here we explored how pre-service teachers communicate conjectures, justifications, and generalisations to develop formulae for geometric solids. We employed a qualitative descriptive case study within the interpretive paradigm. Data were collected through document analysis and students' written tasks. Four tasks were administered to 30 pre-service teachers to enable the researchers to reflect on their performance. Students' written tasks were analysed with the aid of the model of mathematical knowledge for teaching, which served as the theoretical underpinning of the study. The findings of the study reveal that students can develop mathematical engagement and reasoning when appropriate tasks are designed to facilitate understanding of key concepts that are the cornerstone of learning about geometric solids. Certain concepts, notably, circles, radii, pi, rectangles, cones, Pythagoras' theorem, slanting height, congruence, and prism, were crucial elements that should be explored prior to the introduction of the topic of the total surface areas of geometric solids. The study was an eye-opener to South African policy makers, mathematics teachers and lecturers in terms of identifying students' weaknesses at pre-service level on how to develop logical methods to make sense in the learning of geometrical solids.},
Author = {Siyepui, Sibawu Witness and  Vimbelo, Siphokazi Winniefred},
ISSN = {0256-0100},
Journal = {South African Journal of Education},
Keywords = {Preservice Teachers; Learner Engagement; Mathematics Education; Geometric Concepts; Academic Failure; Foreign Countries, South Africa},
Number = {2},
Title = {Pre-Service Teachers' Mathematical Engagement in Learning about the Total Surface Areas of Geometrical Solids},
Volume = {41},
Year = {2021/05/01/},
URL = {https://search.ebscohost.com/login.aspx?direct=true&db=eric&AN=EJ1304179&site=ehost-live&scope=site},
}

@article{spangenberg2021,
Abstract = {Although trigonometry is an important section in secondary school mathematics curricula, many teachers find it challenging to teach as a result of insufficient pedagogical content knowledge (PCK). Therefore, the aim of this article was to report on how PCK on trigonometry manifests itself in teachers' practice. This exploratory case study was underpinned by the mathematics knowledge for teaching (MKT) model of Hill et al. (2008). Twelve teachers were purposefully selected from six township schools. Qualitative data were collected through semi-structured one-on-one interviews, lesson plans, assessment tasks, and lesson observations; and analyzed using content analysis. The findings show that four elements of PCK on trigonometry manifest themselves in teachers? practice, namely knowledge of subject matter, knowledge of teaching strategies, knowledge of students? conceptions and knowledge of curriculum, but varied in levels of sufficiency. Awareness of these variances forms a useful basis for planning developmental opportunities that could address shortcomings in PCK on trigonometry in teachers? practice. This study adds to few studies in PCK in mathematics by providing empirical evidence on how PCK on trigonometry manifests itself in teachers' practice.},
Author = {Spangenberg, Erica Dorethea},
ISSN = {2602-3717},
Journal = {Journal of Pedagogical Research},
Keywords = {Pedagogical Content Knowledge; Trigonometry; Knowledge Level; Mathematics Teachers; Secondary School Mathematics; Difficulty Level; Mathematical Concepts; Misconceptions; Prior Learning; Teaching Methods; Mathematics Instruction; Instructional Effectiveness; Lesson Plans; Public Schools; Foreign Countries, South Africa},
Number = {3},
Pages = {135 - 163},
Title = {Manifesting of Pedagogical Content Knowledge on Trigonometry in Teachers' Practice},
Volume = {5},
Year = {2021/01/01/},
URL = {https://search.ebscohost.com/login.aspx?direct=true&db=eric&AN=EJ1315132&site=ehost-live&scope=site},
}

@article{stern2020,
Abstract = {The African Data Initiative started as a crowd-sourced campaign to improve the teaching of statistics in African universities. The analysis of climate data provides one suitable context to illustrate ideas that lead to a radical new form of teaching. The problem within the context comes first, the technicalities are largely reduced -- mathematics is supported by meta knowledge and backed up by modelling; calculations are reduced by user-friendly software that is also used by experts. The problems are treated similarly to research questions and the results are often easier to interpret, making sense as potential answers in their context. The criteria of this approach are compared to the framework proposed by W. G. Cobb to reform statistics education in the light of the latest developments in statistics, driven by the huge increase of data. Implementation details are presented around three components: case studies, data, and the required skills. Together, these three components describe an alternative education pathway centred around statistical problem solving. The focus on interpretations of results within a real context enables software, mathematical thinking and modelling to play a supportive role, which flattens the prerequisites of complex methods and encourages their use across all levels of education.},
Author = {Stern, David and  Stern, Roger and  Parsons, Danny and  Musyoka, James and  Torgbor, Francis and  Mbasu, Zach},
ISSN = {1570-1824},
Journal = {Statistics Education Research Journal},
Keywords = {Foreign Countries; Data Collection; Data Analysis; Higher Education; Statistics; Teaching Methods; Mathematics; Computation; Computer Software; Case Studies; Data; Skill Development; Problem Solving; Mathematical Models; Mathematical Logic; Climate; Meteorology; Agricultural Occupations, Africa},
Number = {1},
Pages = {206 - 225},
Title = {Envisioning Change in the Statistics-Education Climate},
URL = {http://iase-web.org/documents/SERJ/SERJ19(1)_Stern.pdf},
Volume = {19},
Year = {2020/02/01/},
}

@article{tachie2019,
Abstract = {Undoubtedly the acquisition of mathematical skills for problem solving is critically important in today's sophisticated technological world. There is growing evidence that meta-cognition application is an important component of academic success in general and impacts on mathematical achievement in particular. Teachers' application of meta-cognition therefore directs and reflects their teaching-practice behaviour which influences their learners' learning with understanding in problem-solving. The purpose of the study reported on in this article was to explore teachers' available meta-cognitive skills in class with the intention of supporting learners' development of mathematics in problem-solving in some selected rural primary schools in the Eastern Cape, South Africa. The participants were three teachers purposefully selected from three primary schools. Interviews were conducted with the three teachers and three lessons were observed. The interviews, as an extension of observation, focused on the teachers' knowledge or understanding of available meta-cognitive skills and how they used these skills in helping their learners' development of mathematics problem-solving. The findings included a detailed exploration of the teachers' acquisition and use of specific metacognitive skills, either consciously or unconsciously, during teaching and learning processes in order to develop their mathematics learners' meta-cognitive skills as well as in solving mathematical problems. The results of the observation showed that there was evidence of teachers applying meta-cognitive skills unconsciously in assisting their learners in problemsolving in class. The interviews confirmed this evidence of available meta-cognitive skills which the teachers usually applied in assisting their learners in problem-solving in class. Recommendations have been made regarding teachers' methods of teaching to improve the development of such skills in the lives of their mathematics learners through problem solving.},
Author = {Tachie, Simon A. and  Molepo, Jacob M.},
ISSN = {1814-6627},
Journal = {Africa Education Review},
Keywords = {Metacognition; Mathematics Skills; Problem Solving; Academic Achievement; Teaching Methods; Rural Schools; Elementary School Students; Foreign Countries; Elementary School Teachers; Teacher Attitudes; Mathematics Instruction; Teaching Skills; Decision Making, South Africa},
Number = {2},
Pages = {143 - 161},
Title = {Exploring Teachers' Meta-Cognitive Skills in Mathematics Classes in Selected Rural Primary Schools in Eastern Cape, South Africa},
URL = {http://dx.doi.org/10.1080/18146627.2017.1384700},
Volume = {16},
Year = {2019/01/01/},
}

@article{taylor2021,
Abstract = {Background: South African schooling is caught in a vicious cycle, characterised by weak initial teacher education (ITE) and weaker-than-average learning outcomes, resulting in low teacher status and attempts to reform schooling by means of continuous professional development (CPD). Aim: The paper attempts to understand the reasons for poor performance in mathematics and to explore avenues for improvement. Setting: Teaching in South African schools. Method: Three mechanisms for improving teaching and learning are identified: ITE, CPD and the management of and support to teachers. Drawing on the research literature, the paper examines the potential of each for reforming the system. Results: Tests based on the school curriculum indicate that final-year BEd students are quite unprepared to teach mathematics in primary schools, revealing very significant shortcomings in ITE curricula. CPD, where it is well designed and rigorously evaluated, has been shown to have small effects on both teacher knowledge and learner performance. However, unless ITE is reformed at the same time, CPD becomes a never ending task of making marginal differences to the shortcomings of each successive cohort of qualified but incompetent teachers emerging from the universities. Conclusion: While the weak state of governance in the civil service remains a major obstacle to improved schooling, and while every effort must be made to raise the capacity of inservice teachers, maximal leverage in boosting teacher capacity sits firmly with the universities. While CPD has, at most a few hours a month to bridge huge gaps in teacher knowledge, ITE has at its disposal four years of full-time study with young, plastic minds.},
Author = {Taylor, Nick},
ISSN = {2223-7674},
Journal = {South African Journal of Childhood Education},
Keywords = {Mathematics Instruction; Outcomes of Education; Faculty Development; Educational Change; Low Achievement; Mathematics Achievement; Educational Improvement; Teaching Methods; Learning Processes; Teacher Education Programs; Elementary School Teachers; Pedagogical Content Knowledge; Elementary School Students; Barriers; Foreign Countries; Mathematics Tests; Governance; Capacity Building; Teacher Effectiveness, South Africa},
Number = {1},
Title = {The Dream of Sisyphus: Mathematics Education in South Africa},
Volume = {11},
Year = {2021/01/01/},
URL = {https://search.ebscohost.com/login.aspx?direct=true&db=eric&AN=EJ1288463&site=ehost-live&scope=site},
}

@article{tlou2017,
Abstract = {In South Africa's reception classes (Grade R), the harsh reality is that the sector is beset by serious challenges. As part of a broader professional development study, this article focuses on the actual operations of Grade R educators as they conduct mathematics lessons using video technology to record their teaching. An observation tool adapted from Clements and Sarama is used to determine the quality of mathematics instruction, and to provide recommendations for bridging the gaps observed. Fourteen Grade R classes were video-recorded as part of the bigger project, with the educators themselves selecting three lessons per class to showcase their practices. For this article, the authors employed a qualitative approach guided by Vygotsky's conceptual development of knowledge theory. A thematic analysis was conducted, mediated by the lesson observation instrument. The findings indicate that Grade R educators lack structure and purpose in their instructional activities. Even when sound content knowledge is demonstrated, the instruction tends to be teacher-centred.},
Author = {Tlou, Faith and  Feza, Nosisi},
ISSN = {2223-7674},
Journal = {South African Journal of Childhood Education},
Keywords = {Foreign Countries; Early Childhood Education; Preschool Teachers; Mathematics Instruction; Video Technology; Teaching Methods; Pedagogical Content Knowledge; Class Size; Teaching Conditions; Educational Resources; Classroom Techniques; Teaching Skills, South Africa},
Number = {1},
Title = {Grade R Educators Voluntarily Share Their Mathematics Practices: Authentic Realities in South Africa Showcased},
Volume = {7},
Year = {2017/01/01/},
URL = {https://search.ebscohost.com/login.aspx?direct=true&db=eric&AN=EJ1186944&site=ehost-live&scope=site},
}

@article{ubah2018,
Abstract = {Background: The concept of rational numbers is one of the learner's first experiences with a Mathematics concept beyond the basic skills operations on whole numbers. The personal knowledge of fractions that teachers bring to the teaching context is important because teachers mediate the conceptions that their learners construct. Aim: This study was set up to apply Action-Process-Object-Schema theory to study primary teachers' understanding of addition and subtraction of fractions. Setting: The participants of this study comprised 60 undergraduate full-time students, studying to become teachers. The participants were enrolled in a foundational course in Mathematics because they had not passed Mathematics at Grade 12 level. This course was intended to help deepen their understanding of basic numeracy, allowing them to continue with further courses if they wanted to specialise in teaching primary mathematics Methods: Data were collected using written responses of the pre-service students to two tasks that focused on operations with fractions. Ten students volunteered to be interviewed of which three are drawn upon in this article. Results: Many of the pre-service teachers coped well with addition and subtraction of common fractions with the same denominator. However, more than 52% struggled to carry out these operations on common fractions with different denominators, showing that their conceptions had not developed into object-level structures. Conclusion: It is evident that the incorrect procedures have become embedded in the students mental schema. It is crucial that programmes for upgrading pre-service teachers should include opportunities for teachers to interrogate their personal understandings of the basic mathematics concepts.},
Author = {Ubah, Ifunanya J. A. and  Bansilal, Sarah},
ISSN = {2223-7674},
Journal = {South African Journal of Childhood Education},
Keywords = {Preservice Teachers; Mathematics Instruction; Fractions; Mathematics Teachers; Mathematical Concepts; Numbers; Undergraduate Students; Addition; Subtraction; Foreign Countries; College Mathematics, South Africa},
Number = {2},
Title = {Pre-Service Primary Mathematics Teachers' Understanding of Fractions: An Action-Process-Object-Schema Perspective},
Volume = {8},
Year = {2018/01/01/},
URL = {https://search.ebscohost.com/login.aspx?direct=true&db=eric&AN=EJ1198847&site=ehost-live&scope=site},
}

@article{ubah2021,
Abstract = {Background: Many teachers for different reasons recognise the teaching of fraction as a challenge. This research explored the teaching of fraction in Grade 5 by three experienced teachers (Ben, Greg and Will) in KwaZulu-Natal province, South Africa. Aim: The purpose of this study was to investigate the impact of different approaches to the teaching of Grade 5 fraction by three experienced teachers. Method: Three teachers and 177 learners were purposively sampled for this study. Classroom observations, interview and fraction achievement test (FAT) were instruments used for data collection. Hence, this study employed a mixed method, where both quantitative and qualitative data sets were collected at the same time, and the data were analysed at the same time in order to discuss the findings. Results: The quantitative data were analysed using descriptive statistics and analysis of covariance (ANCOVA), whilst the qualitative data were analysed in themes. The results showed that learners of teacher Ben performed significantly better than those of teachers Will and Greg. The findings revealed that a combination of good practices and appropriate use of multiple representations by teacher Ben improved his learners' achievement in addition of fraction more than other learners taught by the other two teachers. Conclusion: The study recommends that mathematics teachers should endeavour to facilitate learners' conceptual knowledge of fraction by using appropriate teaching approach in their instruction, namely, learner-centred approach, activity-based learning, use of mother tongue for clarity and use of multiple representations. This recommendation will improve learners' knowledge and conceptual understanding of fraction and algebra in its entity.},
Author = {Ubah, Ifunanya J.A.},
ISSN = {2223-7674},
Journal = {South African Journal of Childhood Education},
Keywords = {Teaching Methods; Mathematics Instruction; Grade 5; Elementary School Teachers; Fractions; Foreign Countries; Instructional Effectiveness; Mathematics Achievement; Experienced Teachers, South Africa},
Number = {1},
Title = {The Impact of Different Approaches to the Teaching of Grade 5 Fraction by Three Experienced Teachers},
Volume = {11},
Year = {2021/01/01/},
URL = {https://search.ebscohost.com/login.aspx?direct=true&db=eric&AN=EJ1288464&site=ehost-live&scope=site},
}

@article{umugiraneza2018,
  title = {Exploring {{Teachers}}' {{Descriptions}} of `{{Ways}} of {{Working}} with the {{Curriculum}}' in {{Teaching Mathematics}} and {{Statistics}}},
  author = {Umugiraneza, Odette and Bansilal, Sarah and North, Delia},
  year = {2018},
  month = jan,
  journal = {African Journal of Research in Mathematics, Science and Technology Education},
  volume = {22},
  number = {1},
  pages = {70--80},
  publisher = {{Routledge}},
  issn = {1811-7295},
  doi = {10.1080/18117295.2018.1445496},
  abstract = {What teachers teach, how they teach it and when they teach it should be guided by the curriculum. This paper focuses on teachers' reports about how they integrate the curriculum documentation in teaching mathematics and statistics concepts. Questionnaires containing both Likert scale and closed and open-ended questions were administered to 75 mathematics teachers who were teaching from Grade 4 to Grade 12 in schools in KwaZulu\textendash Natal province in South Africa. Teachers were requested to indicate their level of the use of national curriculum statement. The findings revealed that they had little idea about how they could integrate the curriculum documentation in mathematics teaching and learning. It is encouraging that some teachers perceived links within the vertical as well as across the horizontal curriculum, both important drivers of quality education. However, it is a concern that most teachers were unable to perceive ways of working within and across the curriculum, suggesting that professional development interventions need to consider ways in which this can be addressed. A further concern is that only 60\% of teachers indicated that they used the National Curriculum Statements Grades R\textendash 12. Teachers' propensity to use the curriculum was moderated by the factors of age and participation in professional development activities.},
  keywords = {CAPS,curriculum integration,horizontal curriculum,Mathematics teachers,NCS Grade R–12,vertical curriculum},
  annotation = {\_eprint: https://doi.org/10.1080/18117295.2018.1445496},
  file = {/Users/reidarmosvold/Zotero/storage/IJW4R245/Umugiraneza et al. - 2018 - Exploring Teachers’ Descriptions of ‘Ways of Worki.pdf;/Users/reidarmosvold/Zotero/storage/LZFHTIJ5/18117295.2018.html}
}

@article{vahed2016,
Abstract = {This paper responds to Muller's notions of "knowing-that" and "knowing how". The paper addresses how educational interventions that are designed in line with targeted discipline-specific subjects can enhance the balance between professional practice and disciplinary knowledge in professionally accredited programmes at universities of technology. The context is a Dental Technology programme at a University of Technology in South Africa. Teaching through discipline-specific games, conceptualised from a game literacies perspective, is proposed as an engaging, interactive pedagogy for learning disciplinary knowledge that potentially encourages access to a particular affinity group. The authors use concepts from Bernstein and Maton to investigate whether epistemic relations or social relations are emphasised through board and digital games designed for two Dental Technology subjects. This paper offers valuable insight into alternative pedagogies that can be adopted into science, technology, engineering, and mathematics education with the aim of paving a pathway towards Muller's Scenario 3.},
Author = {Vahed, A. and  McKenna, S. and  Singh, S.},
ISSN = {0018-1560},
Journal = {Higher Education: The International Journal of Higher Education Research},
Keywords = {Foreign Countries; Educational Games; Computer Games; Dentistry; Allied Health Occupations Education; College Instruction; Epistemology; STEM Education; Intervention, South Africa, South Africa},
Number = {6},
Pages = {781 - 790},
Title = {Linking the "Know-That" and "Know-How" Knowledge through Games: A Quest to Evolve the Future for Science and Engineering Education},
URL = {http://dx.doi.org/10.1007/s10734-015-9956-9},
Volume = {71},
Year = {2016/06/01/},
}

@article{venkat2015,
Abstract = {Background: In this paper, I share a case study of a teacher's work on mathematics tasks in the context of a 'mathematics for teaching' course aiming to develop mathematical content understandings and mathematical practices among primary teachers in one South African province. The course was developed in a national context of concerns about the nature and levels of primary teachers' mathematical knowledge. Theories viewing mathematical practices as fundamental, contrasted with those that view mathematical practices and mathematical content in more separate and 'to be integrated' ways, are used to frame the analysis and critically reflect on the findings. Results: Data from this teacher's pre-test and selected course assessments and interactions suggest that while he was able to develop some aspects of the mathematical practices described in the literature, his overall orientation remained attuned to memorization and recall. Findings also pointed to an ongoing reliance on external validation of the 'correctness' of his answers. Conclusions: The data suggest that the presence of elements of mathematical practices cannot be viewed as equivalent to the presence of mathematical modes of enquiry. The analysis presented in this paper suggests that while elements of mathematical practices can be developed, moving towards an encompassing orientation to mathematical modes of enquiry may require more central focus on problem-solving approaches to achieve a change in orientation.},
Author = {Venkat, Hamsa},
ISSN = {2196-7822},
Journal = {International Journal of STEM Education},
Keywords = {Mathematics Instruction; Case Studies; Mathematical Concepts; Elementary School Teachers; Pedagogical Content Knowledge; Foreign Countries; Pretests Posttests; Teaching Methods; Problem Solving; Inquiry; Faculty Development, South Africa},
Title = {Mathematical Practices and Mathematical Modes of Enquiry: Same or Different?},
URL = {http://dx.doi.org/10.1186/s40594-015-0018-8},
Volume = {2},
Year = {2015/01/01/},
}

@article{vermeulen2017,
Abstract = {This article reports on a study that investigated the extent to which 57 Grade 6 students at a particular school have misconceptions regarding equality, with the equal sign as focus. It also investigated this school's three Grade 5 and 6 teachers' mathematical knowledge for teaching regarding equality, again focusing on the equal sign. The research took the form of a case study in which a qualitative approach was used. Data collection methods included teacher questionnaires and a focus group interview with teachers. Students answered a set of questions after which six students were purposefully selected, based on their responses in the questionnaire, and interviewed. To gauge students' level of understanding of the equal sign, the construction map for knowledge of the equal sign developed by Matthews et al. was used, while the Mathematical Knowledge for Teaching model proposed by Ball et al. was employed to interpret teachers' knowledge. Results indicate that few students had a well-developed relational conception of the equal sign. The majority of students could not describe the meaning of the equal sign correctly. The same group of students that applied "closure" was inclined to "use all the numbers in an equation". Grade 5 and 6 teachers' Mathematical Knowledge for Teaching of the equal sign indicated that in general they lacked the knowledge and skills to identify, prevent, reduce or correct students' misconceptions about the equal sign.},
Author = {Vermeulen, Cornelis and  Meyer, Bronwin},
Journal = {African Journal of Research in Mathematics, Science and Technology Education},
Keywords = {Elementary School Students; Middle School Students; Grade 6; Mathematics Education; Mathematical Concepts; Symbols (Mathematics); Misconceptions; Case Studies; Teacher Surveys; Focus Groups; Knowledge Level; Mathematics Teachers; Pedagogical Content Knowledge; Algebra; Foreign Countries; Grade 5; Qualitative Research; Questionnaires; Interviews, South Africa},
Number = {2},
Pages = {136 - 147},
Title = {The Equal Sign: Teachers' Knowledge and Students' Misconceptions},
URL = {http://dx.doi.org/10.1080/18117295.2017.1321343},
Volume = {21},
Year = {2017/01/01/},
}