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Journal ArticleDOI

Exploring support strategies for high school mathematics teachers from underachieving schools

08 Jun 2014-International Journal of Embedded Systems (Kaml-Raj)-Vol. 7, Iss: 1, pp 99-107

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.

AbstractAlgebra, 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.

Topics: Curriculum (52%)

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Journal ArticleDOI
Abstract: This paper reports on an exploration into in-service teachers' pedagogical content knowledge required for the delivery of lessons in probability. The section on probability is taught in Mathematical Literacy to the middle school learners in South Africa. As a theoretical framework the work initiated in the nineteen eighties was sought. This paper adopted a refined framework into domains of pedagogical knowledge. The four domains are: Common Content Knowledge; Specialised Content Knowledge; Knowledge of Content and Students as well as Knowledge of Content and Teaching which are defined and applied to show their necessity in a teaching situation. Examples of tasks from an open ended questionnaire were discussed and identification of the pedagogical content knowledge on probability was made. Teachers' written responses were collected and analyzed to verify or refute suggested strands of knowledge provided earlier. The written responses were from in-service teachers (n = 86) who were studying towards an Advanced Certificate in Education (an upgrading qualification) at a South African university.

16 citations


Cites background or result from "Exploring support strategies for hi..."

  • ...This paper reports on this exploration and results from a call made by other research papers (Brijlall and Maharaj 2014; Bansilal et al. 2014)....

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  • ...Brijlall and Maharaj (2014) focussed their work with high school mathematics teachers....

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Journal ArticleDOI
Abstract: KEYWORDS APOS. Functions. Itemized Genetic Decomposition ABSTRACT In this study, the researchers explore the meaning of the, is equal to symbol by exposing pre-service teachers (n = 38) to two tasks. The first task was baseequivalence of two countable infinite sets. The second task focused on the comparison of the two numbers 0,9 and 1.The study was carried out at a South African university, where activity sheets comprising the two tasks were completed by pre-service teachers specializing to become high school mathematics teachers. Their written responses were analyzed against the initial itemized genetic decompositions formulated in accordance with APOS (Action-Process-Object-Schema) Theory. The findings of the exploration led to modified itemized genetic decompositions. These modified genetic decompositions have pedagogical implications. They also contribute to the APOS theory.

6 citations


Cites background from "Exploring support strategies for hi..."

  • ...In South Africa it was found that mathematics teachers lack the appropriate depth in pedagogical content knowledge (Brijlall and Maharaj 2014)....

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Journal ArticleDOI
Abstract: Copyright: 2015. Taylor & Francis Online. Due to copyright restrictions, only the abstract is available. For access to the full text item, please consult the publisher's website. The definitive version of the work is published in Africa Education Review, Vol 12, No 3, pp 361-380.

6 citations


Journal ArticleDOI
Abstract: This paper reports on a small-scale action research, which investigated the processes involved in problem-solving in a mathematics class. Grade ten learners (n = 47) at a South African middle school were involved in the study. The participants from two classes attempted the solution of tasks involving the fraction concept. In one class, the learners worked in groups and in the other class, the learners worked individually. A qualitative method was adopted for data capture and analysis. Social constructivism was adopted as a theoretical framework and the stages advocated by Polya were interrogated when analyzing the learner responses on their problem solutions. The results revealed that those learners working in groups demonstrated most of the stages of the Polya linear problem-solving model. The findings helped identify which stages of the model promote effective problemsolving and some recommendations are made for classroom practitioners engaging their learners in problemsolving.

5 citations


Cites background from "Exploring support strategies for hi..."

  • ...…require not only to have a deep and thorough pedagogical content knowledge (Bansilal et al. 2014; Brijlall 2011, 2014a; Brijlall and Isaac 2011; Brijlall and Maharaj 2014, 2015) but it is also imperative that mathematics teachers adapt learning design to focus on better learner understanding....

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Journal ArticleDOI
Abstract: Addition of fraction is dealt with from grade 6 onwards in South African schools topics as prescribed by the Curriculum and Assessment Policy Statement. This paper reports on a study exploring practical work as a strategy to sustain rural mathematics classrooms. The conceptual perspective for the design and analysis of this study was based on a learning ecology framework consolidated by socio-culturalism and situated learning. This study was a qualitative case study (n = 42). The participants in this study were from a rural school of the Umhlali ward, which is in the Ilembe district in KwaZulu-Natal, South Africa. The learners engaged in four activities in four lessons. They used either diagrams or fraction circles to complete the tasks in the four activities. The researcher analysed the written responses, observed their working in groups and carried out interviews. This case study found that practical work, in a rural setting, was a suitable strategy to sustain an effective mathematics learning ecology.

5 citations


Cites background from "Exploring support strategies for hi..."

  • ...For teachers to design tasks to address a variety of suitable mathematical competence and skills it is expected that these teachers have a firm grounding in their pedagogical content knowledge (Brijlall and Maharaj 2014)....

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  • ...Of course besides creating the appropriate environment for effective learning, it is expected that the mathematics educators have a thorough understanding of the pedagogical content knowledge (Brijlall and Maharaj 2014)....

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References
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Book
01 Jan 1980
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

20,255 citations


Journal ArticleDOI
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.

14,426 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
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,

12,440 citations


Journal ArticleDOI
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, ...

12,151 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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MonographDOI
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

7,572 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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