Exploring support strategies for high school mathematics teachers from underachieving schools
TL;DR: A study exploring practicing teachers’ subject matter knowledge of certain topics they were expected to teach found that certain areas of their pedagogical content knowledge required attention.
Abstract: Algebra, trigonometry and calculus concepts are dealt with in grades 10 to 12 of South African high school topics, as prescribed by the Curriculum and Assessment Policy Statement. This paper reports on a study exploring practicing teachers' subject matter knowledge of certain topics they were expected to teach. The theoretical perspectives for the design and analysis of this study were based on Shulman's conceptual framework. This study was a qualitative case study (n = 28). Practising teachers from the Pinetown district in KwaZulu-Natal participated in this mathematics' teacher intervention. Focused tasks on algebra, trigonometry and calculus were designed and administered to those teachers. The researchers analysed the data from those tests and found that certain areas of their pedagogical content knowledge required attention.
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TL;DR: In this paper, the authors compared the mathematics syllabi for high/secondary schools and bachelor of education degrees in South Africa and tried to establish any discrepancies between them and concluded that the teacher training syllabus goes far beyond the high school syllabus.
Abstract: Delivering competent teachers for the teaching of mathematics and science remains an ongoing challenge in South Africa. This study aims at comparing the mathematics syllabi for high/secondary schools and bachelor of education degrees in the country and tries to establish any discrepancies between them. A cluster sample was drawn from two universities in the province of KwaZulu-Natal. The method of content analysis was used to collect and analyze data. The coded data was quantified to determine the frequency of occurrence and the intensity of common and different themes. The principal observation indicated a distinctive overlap between the syllabi, but also showed that the teacher training syllabus goes far beyond the high school syllabus. The study concludes with recommendations for further research to investigate the proportions of pedagogical content and academic mathematics content in teacher training programs
2 citations
Cites background from "Exploring support strategies for hi..."
...Brijlall and Maharaj (2014) also confirm the views expressed by Ball and Bass about teachers’ mathematics knowledge....
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TL;DR: In this paper, the authors explored the use of virtual mathematics laboratory methodology for undergraduate Calculus teaching and learning as a remote instruction and pedagogy gap revealed during the COVID-19 infections prevention and containment period in Zimbabwe.
Abstract: The COVID-19 pandemic globally transformed the face to face teaching and learning into digital online teaching and learning. The uptake and integration of digital technology in mathematics education have been gradual for many decades. However, the COVID-19 pandemic has reshaped the digital teaching and learning and made it an imperative and safe remote instruction and pedagogy of the day in mathematics education and education in general. We explored the uptake and use of virtual mathematics laboratory methodology for undergraduate Calculus teaching and learning as a remote instruction and pedagogy gap revealed during the COVID-19 infections prevention and containment period in Zimbabwe. The main objective of the study was to identify digital instructional and pedagogical gaps that existed in addressing students' mathematical misconceptions in Calculus learning in using the APOS theory and a virtual mathematics laboratory. Data was collected from 160 undergraduate students taking Calculus courses via APOS theory mediated digital mathematics laboratory for a semester. Results revealed that the undergraduate students who took the Calculus courses via the digital mathematics laboratory methodology performed better than those who used to take the same courses using didactical approaches. This COVID-19 crisis ushered in digital teaching and learning experiences that clearly spelt out the existence of digital instructional and pedagogical gaps in mathematics education.
1 citations
Cites background from "Exploring support strategies for hi..."
...[26, 27] and [28] studied mental constructions of pre-service teachers when learning Calculus, fractions and matrix algebra in separate cases respectively....
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TL;DR: An investigation into the preparedness of a group of mathematics teachers in the Pinetown District, in KwaZulu-Natal, South Africa to teach learners grade twelve mathematics found that for this group of teachers there was a strong positive correlation between their errors, misconceptions or difficulties to those on which the tests were designed.
Abstract: This paper reports on an investigation into the preparedness of a group of mathematics teachers in the Pinetown District, in KwaZulu-Natal, South Africa to teach learners grade twelve mathematics. The teachers were given tests in algebra, trigonometry and calculus. Those tests were based on common errors, misconceptions or difficulties relating to school mathematics made by university students and those reported in the examiners’ reports for the national senior certificate examinations in mathematics. The written responses of those teachers were analysed. It was found that for this group of teachers there was a strong positive correlation between their errors, misconceptions or difficulties to those on which the tests were designed. An implication of this study is that one should not expect teachers to effectively communicate to those they teach, if they themselves do not have a good understanding of the content that they are expected to teach.
1 citations
Cites background or result from "Exploring support strategies for hi..."
...The theoretical framework for this paper is APOS (action-process-objectschema) mental constructions and this is how it differs from the paper by Brijlall and Maharaj (2014)....
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...A number of studies (Stacey 1988; Vinner 1991; Kieran 1992; Esty 1992; Sfard and Linchevski 1994; Bell 1995; Linchevski and Herscovics 1996; Souviney 1996; Dreyfus 1999; Lithner 2000; Mason 2000; Pyke 2003; Maharaj 2005, 2008; Brijlall and Maharaj 2014; Shuilleabhain 2015)) have focused on the teaching and learning of school mathematics....
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...…1991; Kieran 1992; Esty 1992; Sfard and Linchevski 1994; Bell 1995; Linchevski and Herscovics 1996; Souviney 1996; Dreyfus 1999; Lithner 2000; Mason 2000; Pyke 2003; Maharaj 2005, 2008; Brijlall and Maharaj 2014; Shuilleabhain 2015)) have focused on the teaching and learning of school mathematics....
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TL;DR: Brijlall et al. as mentioned in this paper explored the challenges experienced by mathematics teachers and learners of seven high schools in South Africa using interviews and questionnaires, and concluded that intervention strategies that could assist in minimizing or eradicating the challenges faced by the teachers of mathematics, thus improving their socio-economic standing.
Abstract: Objective – This paper explores the challenges experienced by mathematics teachers and learners of seven high schools in South Africa. A mixed method approach involving interviews and questionnaires was used.
Methodology – The sample included 7 principals or deputy principals, 7 departmental heads who supervised mathematics, 1 mathematics teacher who taught mathematics in grades 10 to 12, and 1 mathematics teacher who taught Mathematics in grades 8 and 9. In addition, 1 learner from each grade 8 to 12 was included in the sample. Each participant was interviewed using a structured interview schedule, followed by participants completing a questionnaire.
Findings – Vygotsky's socio-cultural and conceptual development theories in mathematics education formed the basis of this study. The 'Inputs, Processes and Output" model of Howie and Kilpatrick's model of the five strands of achieving 'mathematics proficiency was adopted. We identified many systemic, societal, and pedagogical challenges that teachers and learners experienced, which affected their mathematics teaching and learning. Our findings correlated with research in the literature review.
Novelty – The researchers concluded there were always intervention strategies that could assist in minimizing or eradicating the challenges faced by the teachers and learners of mathematics, thus improving their socio-economic standing.
Type of Paper: Review
JEL Classification: A14, 19.
Keywords: Challenges, Strategies, Blended Learning, Scaffolding, Conceptual Development, Collaborative Learning.
Reference to this paper should be made as follows: Brijlall, D; Ivasen, S.J. (2022). The impact of challenges experienced by teachers and learners on Mathematics performance, in relation to their socio-economic standing, J. Bus. Econ. Review, 7(2), 112–126. https://doi.org/10.35609/jber.2022.7.2(1)
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01 Jan 1980TL;DR: In this article, the context of educational research, planning educational research and the styles of education research are discussed, along with strategies and instruments for data collection and research for data analysis.
Abstract: Part One: The Context Of Educational Research Part Two: Planning Educational Research Part Three: Styles Of Educational Research Part Four: Strategies And Instruments For Data Collection And Researching Part Five: Data Analysis
21,163 citations
TL;DR: In this paper, Shulman observa la historia de evaluaciones docentes, noting that the evaluación docente parecia preocuparse tanto por los conocimientos, como el siglo anterior se preoccupaba por la pedagogia.
Abstract: Este articulo fue un discurso presidencial en la reunion de America Educational Research Association de Chicago el ano 1985. -- Curioso sobre el por que el publico a menudo tiene una baja opinion sobre el conocimiento de los profesores, Shulman observa la historia de evaluaciones docentes. En la segunda mitad del 1800, las evaluaciones para quienes deseaban ensenar se basaban casi por completo en contenido. Para el ano en que el autor escribe el articulo, en 1985, la evaluacion era completamente distinta. En lugar de enfocarse en contenido, se enfocaba en topicos como planificacion de clases, sensibilizacion cultural, y otros aspectos de la conducta docente. Mientras los topicos usualmente tenian raices en la investigacion, claramente no representan el amplio espectro de habilidades y conocimientos que un docente necesita para ser efectivo. Mas especificamente, para los anos 80', la evaluacion docente parecia preocuparse tanto por los conocimientos, como el siglo anterior se preocupaba por la pedagogia.
15,740 citations
"Exploring support strategies for hi..." refers background in this paper
...But to blend properly the two aspects of a teacher’s capacities requires that we pay as much attention to the content aspects of teaching as we have recently devoted to the elements of the teaching process” (Shulman 1986: 8)....
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01 Jan 2005
TL;DR: Lee S. Shulman as mentioned in this paper builds his foundation for teachi ng reform on an idea of teaching that emphasizes comprension and reasoning, transformation and reflection, and argues that this emphasis is justified by the resoluteness with which research and policy have so blatantly ignored those aspects of teaching in the past.
Abstract: Lee S. Shulman builds his foundation for teachi ng reform on an idea of teaching that emphasizes comprension and reasoning, transformation and reflection. "This emphasis is justified" he writes, "by the resoluteness with which research and policy have so blatantly ignored those aspects of teaching in the past". To articulate and justify this conception, Shulman responds to four questions: What are the sources of the knowledge base for teaching? In what terms can these sources be conceptualized? What are the processes of pedagogical reasoning and action? And What are the implications for teaching policy and educational reform? The answers -informed by philosophy, psychology, and a growing body of casework based on young and experienced practitioners- go far beyond current reform assumptions and initiatives. The outcome for educational practitioners, scholars,
13,211 citations
TL;DR: Lee S. Shulman as mentioned in this paper builds his foundation for teaching reform on an idea of teaching that emphasizes comprehension and reasoning, transformation and reflection. "This emphasis is justified," he writes,...
Abstract: Lee S. Shulman builds his foundation for teaching reform on an idea of teaching that emphasizes comprehension and reasoning, transformation and reflection. "This emphasis is justified," he writes, ...
12,926 citations
"Exploring support strategies for hi..." refers background in this paper
...He went against the reforms of the time where the focus was on “how to improve teaching as both an activity and a profession” (Shulman 1987: 3)....
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01 Jan 2012
TL;DR: This chapter discusses the process and problems of Educational Research, the role of educational theory, ethics in research, and ethical issues in research.
Abstract: Preface Part I. Foundations of Research 1. Science, Schooling, and Educational Research Learning About the Educational World The Educational Research Approach Educational Research Philosophies Conclusions 2. The Process and Problems of Educational Research Educational Research Questions Educational Research Basics The Role of Educational Theory Educational Research Goals Educational Research Proposals, Part I Conclusions 3. Ethics in Research Historical Background Ethical Principles Conclusions 4. Conceptualization and Measurement Concepts Measurement Operations Levels of Measurement Evaluating Measures Conclusions 5. Sampling Sample Planning Sampling Methods Sampling Distributions Conclusions Part II. Research Design and Data Collection 6. Causation and Research Design Causal Explanation Criteria for Causal Explanations Types of Research Designs True Experimental Designs Quasi-Experimental Designs Threats to Validity in Experimental Designs Nonexperiments Conclusions 7. Evaluation Research What Is Evaluation Research? What Can an Evaluation Study Focus On? How Can the Program Be Described? Creating a Program Logic Model What Are the Alternatives in Evaluation Design? Ethical Issues in Evaluation Research Conclusions 8. Survey Research Why Is Survey Research So Popular? Errors in Survey Research Questionnaire Design Writing Questions Survey Design Alternatives Combining Methods Survey Research Design in a Diverse Society Ethical Issues in Survey Research Conclusions 9. Qualitative Methods: Observing, Participating, Listening Fundamentals of Qualitative Research Participant Observation Intensive Interviewing Focus Groups Combining Qualitative and Quantitative Methods Ethical Issues in Qualitative Research Conclusions 10. Single-Subject Design Foundations of Single-Subject Design Measuring Targets of Intervention Types of Single-Subject Designs Analyzing Single-Subject Designs Ethical Issues in Single-Subject Design Conclusions 11. Mixing and Comparing Methods and Studies Mixed Methods Comparing Reserch Designs Performing Meta-Analyses Conclusions 12. Teacher Research and Action Research Teacher Research: Three Case Studies Teacher Research: A Self-Planning Outline for Creating Your Own Project Action Research and How It Differs From Teacher Research Validity and Ethical Issues in Teacher Research and Action Research Conclusions Part III. Analyzing and Reporting Data 13. Quantitative Data Analysis Why We Need Statistics Preparing Data for Analysis Displaying Univariate Distributions Summarizing Univariate Distributions Relationships (Associations) Among Variables Presenting Data Ethically: How Not to Lie With Statistics Conclusions 14. Qualitative Data Analysis Features of Qualitative Data Analysis Techniques of Qualitative Data Analysis Alternatives in Qualitative Data Analysis Computer-Assisted Qualitative Data Analysis Ethics in Qualitative Data Analysis Conclusions 15. Proposing and Reporting Research Educational Research Proposals, Part II Reporting Research Ethics, Politics, and Research Reports Conclusions Appendix A: Questions to Ask About a Research Article Appendix B: How to Read a Research Article Appendix C: Finding Information, by Elizabeth Schneider and Russell K. Schutt Appendix D: Table of Random Numbers Glossary References Author Index Subject Index About the Authors
8,706 citations
"Exploring support strategies for hi..." refers background in this paper
...Access is a key issue in research and it is a factor that must be considered early in the research procedure (Cohen et al. 2007: 109)....
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...In qualitative research “validity might be addressed through the honesty, depth, richness and scope of the data achieved, the participants, the extent of the triangulation and the disinterestedness or objectivity of the researcher” (Winter as cited in Cohen et al. 2007: 133)....
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...“A case study is a specific instance that is frequently designed to illustrate a more general principle” (Nisbet and Watt as cited in Cohen et al. 2007: 253)....
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...Ethical Issues “A major ethical dilemma is that which requires researchers to strike a balance between the demands placed on them as professional scientists in pursuit of truth, and their subjects’ rights and values potentially threatened by the research” (Cohen et al. 2007: 51)....
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