3.5. Teacher knowledge
3.5.3 Pedagogic Content knowledge (PCK)
Shulman (1987) claims that there is a special amalgamation of content knowledge, and pedagogy knowledge that is uniquely the province of teachers and their special forms of professional understanding. He calls this pedagogical content knowledge (PCK). He further states that “pedagogical content knowledge also includes an understanding of what makes the learning of a specific topic easy or difficult; the conceptions and pre-conceptions that students of different ages and backgrounds bring with them to the learning of those tough topics and lessons” (Shulman, 1987, p. 9). Similarly to what Ball et al. (2008) call SCK, Grossman (1991) suggests that “PCK includes knowledge of the most regularly taught topics in one’s subject area, the most useful representations of those ideas, and the most powerful analogies, illustration, examples, explanations, and demonstrations, or ways of representing and formulating the subject that make it comprehensive to others” (Grossman, 1991, p. 7).
She further defines PCK more clearly by unpacking it into four central components:
The first component comprises knowledge and beliefs about the purpose for teaching a subject at different grades. In relation to this study, an example is teachers’
knowledge of the purpose of teaching Business Studies from grades ten to twelve.
The second component of PCK consists of knowledge of students’ understanding, conceptions and misconceptions of particular topics in a subject matter. For example, Economics teachers draw from this knowledge to predict learners’ thinking about the difference between monopoly and monopolistic competition, or the types of market structures in Economics.
The third component of PCK includes knowledge of the curriculum materials available for teaching particular subject matter. In Mathematics, curriculum material includes Sketch pad, a software programme used to teach Mathematics.
The fourth component of PCK includes knowledge of instructional strategies and representations for teaching a particular subject, such as demonstrations, experiments and games.
However, Shulman’s description of PCK has been critiqued by scholars such as Ball, Thames and Phelps (2008). These authors claim that Shulman’s (1987) notion of PCK has lacked definition and empirical foundation, which limits its usefulness (Ball et al. 2008, p. 389).
Thus, they have built on Shulman’s (1987) notion of PCK and suggest three domains for PCK as shown in Figure 9 on the next page:
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Figure 9: Ball, Thames and Phelps (2008) Components of Pedagogical Content Knowledge (PCK)
Knowledge of content and students (KCS). According to Ball et al. (2008), this is the knowledge that combines knowing about learners and knowing about Mathematics content in order for the teachers to predict learners’ thinking. They further explain knowledge of content and students by using an example of exponents. They say that in exponents, a teacher’s knowledge of content and of students enables the teacher to expect students to incorrectly think that = + and to anticipate that misconception about the distributive property and exponents. In other words, knowledge of content and of students allows an interaction between specific Mathematical understanding with students and their Mathematical thinking.
Knowledge of content and teaching (KCT): “is the knowledge that allows an interaction between specific Mathematical understanding and an understanding of pedagogical issues that affects student learning” (Ball, Thames and Phelps, 2008, pp. 389-407). In relation to Mathematics, they suggest that knowledge of content and teaching combines knowing about teaching and knowing about Mathematics. This is in line with Shulman’s (1987) description of PCK when he says that it is the amalgamation of pedagogical and content knowledge.
However, Ball et al. (2008) put it more clearly in a Mathematics context by saying that knowledge of content and teaching is an amalgamation involving a particular Mathematical idea or procedure in addition to familiarity with pedagogical principles for teaching that particular content. On the same point as Grossman’s (1991) third component of PCK, which
Pedagogical Content Knowledge (PCK)
Knowledge of Content and Students (KCS)
Knowledge of
Content and Teaching (KCT)
Knowledge of Content and Curriculum (KCC)
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is instructional strategies and representations, Ball et al. (2008) contend that KCT allows teachers to decide what to do about learners’ misconceptions by choosing which examples to start with and which examples to use to take learners deeper into the content.
Knowledge of content and curriculum (KCS)/ (Horizon). Ball et al. (2008) do not give an explicit description of KCS. Similarly to Grossman (1991), they comment that knowledge about content and curriculum means teachers’ knowledge of the available materials that they can use to support students’ learning. For example, the mathematics teachers drew upon their knowledge of which textbooks are best for teaching geometry and algebra for a certain grade.
Krauss and Blum (2012) argue that curriculum is part of the Mathematics content knowledge and they call it advanced background of the subject matter of the Mathematics curriculum.
A curriculum policy is essentially a course of study or plan of what must be taught and learnt.
In South Africa there have been many changes in the curriculum, due to the number of implementation challenges such as contextual factors. In 1997 Outcomes-based (OBE) was introduced and was reviewed in 2000, which led to the Revised National Curriculum Statement which later developed into the National Curriculum Statement 2002 (Department of Education, 2006). The National Curriculum Statement was amended and the amendments were effected in January 2012 (Department of Basic Education, 2011). So a single comprehensive Curriculum and Assessment Policy Statement (CAPS) for each subject was developed to replace subject statements, learning programme guidelines and subject assessment guidelines. Therefore, CAPS is the curriculum that South African teachers currently need to know. This study was undertaken during the transitional stage of the curriculum at the Further Education and Training level (Grades 10 to 12). CAPS was introduced in 2012 in Grade 10. During my data collection stage in 2013, CAPS was introduced in Grade 11. So the curriculum knowledge in this study is based on CAPS.
Shulman (1987) claims that teachers need to understand the principles underpinning the curriculum. Brown (2005) highlighted that technological advancements have resulted in technological advancement of the curriculum, which implies that technological tools are needed to support students and teachers to be empowered. This would enable them to fit in to the world of technology. The teacher’s knowledge must be shaped to understand the technologically advanced curriculum. This leads us to the importance of Information Communication Technology (ICT). Currently in South Africa, the Department of Basic Education, in partnership with Siyavula-Technology Powered Learning, a technology
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company and Vodacom, is introducing technological teaching and learning of Mathematics in certain schools with a strong focus on schools which are in the rural areas.