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Journal ArticleDOI

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, an exploration into in-service teachers' pedagogical content knowledge required for the delivery of lessons in probability is reported. Butte et al. adopt a refined framework into domains of pedagogy knowledge.
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.

19 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
TL;DR: Taylor et al. as discussed by the authors published an Africa Education Review, Vol 12, No 3, pp 361-380, with an abstract of the full text item, which is available on the publisher's website.
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.

8 citations

Journal ArticleDOI
TL;DR: In this article, the authors investigated the processes involved in problem-solving in a mathematics class and found that learners working in groups demonstrated most of the stages of the Polya linear problem solving model.
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.

7 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
TL;DR: In this article, the authors explore the meaning of the, is equal to symbol by exposing pre-service teachers (n = 38) to two tasks: baseequivalence of two countable infinite sets and comparison of the two numbers 0,9 and 1.
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
TL;DR: In this paper, the authors explored practical work as a strategy to sustain rural mathematics classrooms and found that practical work, in a rural setting, was a suitable strategy for sustaining an effective mathematics learning ecology.
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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Journal ArticleDOI
TL;DR: This article examined how three professional development workshop series grounded in authentic practice impacted 70 elementary, middle, and high school teachers' pedagogical content knowledge (PCK) for scientific argumen- tation.
Abstract: One of the hallmarks of science and science education is the production of new knowledge about the natural world through objective argument and critique. Teach- ers' understanding of scientific argumentation impacts how they incorporate this important scientific practice into science classrooms. This study examined how three professional de- velopment workshop series grounded in authentic practice impacted 70 elementary, middle, and high school teachers' pedagogical content knowledge (PCK) for scientific argumen- tation. Data sources included pre- and postsurveys, videotapes of the workshops, artifacts produced by the teachers, and samples of student writing. Results from the analysis suggest that the workshops were successful in teachers' development of PCK for argumentation in relation to the structural components of students' science writing. However, the teachers also had a number of challenges. Specifically, teachers struggled with analyzing classroom discussions for both structural and dialogic characteristics of argumentation, had difficulty applying the reasoning component of argumentation to classroom practice, and found de- signing argumentation questions to be challenging. Finally, elementary teachers connected argumentation to other disciplines whereas high school teachers focused more on the sci- ence content. These challenges and differences between teachers should be considered in the design of future professional development and preservice teacher education. C � 2013

172 citations


"Exploring support strategies for hi..." refers background in this paper

  • ...McNeill and Knight (2013) examined how three professional development workshop series, in the context of scientific argumentation, impacted on 70 teachers’ PCK....

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Journal ArticleDOI
TL;DR: This article used a teacher profiling instrument with 62 middle school teachers at the start of a 3-year professional learning program to assess the aspects of teachers' knowledge identified by Shulman (1987) refined by Ball et al. (2008) and extended to include teachers' confidence to use and teach various topics in the middle school mathematics curriculum and their beliefs about mathematics teaching and learning.
Abstract: In this article, we report on the use of a teacher profiling instrument with 62 middle school teachers at the start of a 3-year professional learning programme. The instrument was designed to assess the aspects of teachers’ knowledge identified by Shulman (1987) refined by Ball et al. (2008) and extended to include teachers’ confidence to use and teach various topics in the middle school mathematics curriculum and their beliefs about mathematics teaching and learning. Based on a hierarchical coding of items, the application of the partial credit Rasch model revealed that the profile items were measuring a single underlying construct and suggested that the various facets of teacher knowledge develop together. We describe the characteristics of four levels of the hierarchical construct measuring teacher knowledge and understanding for teaching mathematics in the middle years of schooling, and discuss the unique affordances of a holistic view of teacher knowledge in contrast to considerations of multiple knowledge categories.

80 citations


"Exploring support strategies for hi..." refers background in this paper

  • ...Arising from the study by Ball et al. (2008), Beswick et al. (2012) designed research instruments to assess aspects of teachers’ knowledge in an Australian context....

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Book
09 Nov 2004
TL;DR: This book discusses the principles of learning and strategies for Instruction, and the implications of these principles for the integration of technology.
Abstract: Preface Acknowledgements Introduction: Overview: Principles Of Learning And Strategies For Instruction 1: Heuristics And Taxonomy 1. Factors Influencing Acquisition 2. Factors Affecting Transfer Of training 3. Dimensions Affecting Retention 4. Prescriptive Illustration 5. The Interrelatedness Of Domains Of Learning 6. A Potential Taxonomy 7. Schema Construction 2: A Cognitive Domain Example: Reading 1. Introduction 2. Section I: Instructional Guidance 3. Section II: Supporting Research 3: Psychomotor Domain 1. Introduction 2. Section I: Possible Instructional Guidance 3. Section II: Supporting Research 4: Affective Domain 1. Introduction 2. Section I: Instructional Guidance 3. Section II: Supporting Research 5: Interpersonal Domain 1. Introduction 2. Section 1: Possible Instructional Guidance 3. Section II: Supporting Research 6: Suggestions For The Integration Of Technology 1. Technological Accomplishments 2. Section I: Instructional Guidance 3. Section II: Supporting Research 4. Human Concerns: Culture, Organization, And Individual 7: Summary 1. Cognitive Domain 2. Psychomotor Domain 3. Affective Domain 4. Interpersonal Domain 5. Suggestions For The Integration Of Technology 6. Conclusion About The Authors Index

22 citations

Journal Article
TL;DR: In this paper, a qualitative study examined the link between content knowledge and classroom practice from the perceptions of two university lecturers in terms of Vygotsky's educational theory and the process of scaffolding.
Abstract: This qualitative study examined the link between content knowledge and classroom practice from the perceptions of two university lecturers. The study was contextualized at a higher education institution in South Africa where the two university lecturers were lecturing to a second year undergraduate teacher trainee class (n = 78). The research was conceptualised in terms of Vygotsky's educational theory and the process of scaffolding. Questionnaires in which these lecturers expressed their views on content knowledge in general were administered to them. Video recorded lessons on rates of change in Calculus were observed to triangulate actual lesson instruction and their views on content knowledge and classroom practice. Data yielded by these research instruments confirmed certain assumptions and literature claims. The study revealed that the two university lecturers portrayed a strong link between a lecturers' content knowledge and his/her classroom practice.

13 citations


"Exploring support strategies for hi..." refers background in this paper

  • ...For example, one of the authors has explored links between PCK and classroom practice in a calculus class at a South African university (Brijlall and Isaac 2011)....

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