Justificación y objetivos específicos

PCK is about effectively communicating a subject to people for whom the content may be new (Loughran et al., 2012, p. 16). While it requires knowledge of what is taught and how it is taught, it also requires knowledge of how learners think and what they understand before they learn the subject matter, as well as how they think while they are learning. There is a foundation of pedagogy within PCK which is general across curriculum areas and should be developed by all educators (Loughran et al., 2012, p. 19; Shulman, 2015, p. 9). These include planning, teaching methods, group work, individual work, questioning, wait time, feedback, modeling, and evaluations. In this model, Ball and her colleagues highlighted particular categories of knowledge within the PCK and subject matter delineations (see Figure 3.1 above). PCK is divided into: Knowledge of Content and students (KCS); Knowledge of Content and teaching (KCT) and Knowledge of the Curriculum (KCC).

3.4.1 Knowledge of content and students (KCS)

Knowledge of content and students (KCS) can be described as the knowledge that integrates knowing about learners and knowing about geometry in a way that enables educators to relate

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to learners in such a manner that enhances their learning (Nolan et al., 2015, p. 36; Ball et al., 2008, p. 389). Wilkie (2015, p. 246) argued that with this knowledge educators can “attend to how learners typically learn a concept, and to common mistakes and misconceptions” (p. 250). Putnam (2015, p. 24) pointed out that a lack of geometrical context knowledge can impede educators’ abilities to notice and analyze learners’ geometrical thinking. He said that improved geometrical knowledge can also help educators connect geometry to classroom practice as educators analyze and use new curriculum materials.

According to Ball et al. (2008), educators must also be able to hear and interpret learners’ emerging and incomplete thinking as expressed in the ways that pupils use learning (p. 401). The educator should be able to interpret what learners are trying to communicate. South African learners do not only struggle with geometry but also have challenges with literacy (Spaull, 2013, p. 12; Reddy et al., 2015, p. 16). These learners may not be able to explicitly express themselves and the educator should be able to understand and interpret the meaning of their poor expressions through KCS. KCS also includes knowing the misconceptions learners have about geometry and other topics one teaches.

3.4.2 Knowledge of content and teaching (KCT)

According to Ball et al. (2008), knowledge of content and teaching (KCT) is the knowledge that combines knowing about teaching and about geometry. Correspondingly, Wilkie (2015, p. 247) stated that KCT includes knowledge about how to choose appropriate representations and examples, how to build on learners’ thinking, and how to address learner errors effectively (p. 249). Schmidt as cited in Glover (2014, p. 18) proposes that geometrical tasks require a piece of sound geometrical knowledge in order to design instruction. For instance, the educator needs to know what teaching strategies to employ where and when, what resources to use and what representations and examples to employ so that learners can learn with understanding (Shulman, 1987, p. 7). Bansilal et al. (2015, p. 34) stated that educators of geometry need to know how to teach geometry that is prescribed in the “basic skills topics” (DBE, 2011, p.13). Learners’ acquisition of geometric thought depends greatly upon the educator’s geometrical content knowledge (Couto & Vale, 2014, p. 67).

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3.4.3 Knowledge of content and curriculum (KCC)

The curriculum can be defined as the full range of programs that are designed for the teaching of a particular subject and its different topics at a given grade (Petrou & Goulding, 2011). The curriculum includes the variety of instructional materials available in relation to these programs (e.g. the national workbooks). An educator needs proper knowledge of the curriculum and a high level of PCK to assure effective teaching (Shulman, 1986, p. 5). KCC is, therefore, the knowledge that pertains to the knowledge, evaluation, adaptation and use of these materials in the teaching and learning of different geometrical concepts (Ball et al., 2008, p. 31).

3.5 Conclusion

The social constructivist theoretical framework underpinning this study was discussed. The researcher believes that interaction between the learners and the educator and amongst learners is important. The researcher is also of the view that learners cannot be left alone to learn and that an expert, or more capable person, must be available to help with misconceptions or stumbling blocks that may surface during learners’ interaction. Learners, after conceptual understanding, can work independently. Group work is seen as a necessary component of modern classroom practice.

Pedagogical issues also include consideration of task choices and teaching approaches that foster a climate of support and challenge. Domains of MKT (Ball et al., 2008) have been shown to be incorporated and developed through educators’ participation in lesson study.

The next chapter explores the methodology associated with this research and includes a section that outlines the learners and educators who participated in the study, along with ethical considerations, including the role of the researcher. Data-gathering methods discussed include questionnaires, individual and focus group interviews. Finally, the methods and theoretical framework for data analysis are outlined.

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CHAPTER 4

RESEARCH METHODOLOGY AND DESIGN

4.1 Introduction

The previous chapter focused on the theoretical framework about the issues related to the factors influencing grade 11 learner performance in geometry. This chapter described, discussed and justified the research design and methodology used in the study, focusing on the description of the research paradigm, the approach, design and data collection techniques used to build an in-depth understanding of the factors that influence learner performance in geometry in the Umlazi District.

The issues of credibility and trustworthiness as well as ethical considerations are also taken into consideration so that the results can be accepted as meaningful contributions for resolving the research issue and for use by other researchers.