3.5. Teacher knowledge
3.5.1 Subject matter knowledge
Subject matter knowledge is regarded as an important aspect of any professional development programme. Adler (2002) defined subject knowledge as relatively broad and deep knowledge of the subject that teachers are teaching. Adler’s (2002) views imply that teachers should have broad knowledge of their subjects (such as Mathematics, Economics Business Studies and Accounting) that they teach in order to be able to answer any questions from different areas of the subject. Furthermore, teachers’ knowledge of the subject must be sufficiently
SUBJECT MATTER KNOWLEDGE
Syntactic
Structures Content Substantive
GENERAL PEDAGOGICAL KNOWLEDGE Learners and
Learning Classroom Management
Curriculum and Instruction
Other
PEDAGOGICAL CONTENT KNOWLEDGE Conceptions of Purpose for Teaching Subject Matter Knowledge of Students’
Understanding Curricular Knowledge Knowledge of
Instructional Strategies
KNOWLEDGE OF CONTEXT Students
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deep and the teachers must be able to relate the subject to the learners’ reality as well as to the careers that the learners intend to pursue. According to Shulman (1986), subject matter knowledge refers to the amount and the organisation of knowledge per se in the mind of the teacher. He states that “this content knowledge of the teacher must at least be equal to that of his or her colleagues” (Shulman, 1986, p. 9). The research review of teacher learning conducted by Darling-Hammond (2009), stressed the importance of content knowledge from teachers’ reports showing that their knowledge and skills and their practice changed when they received professional development that was coherent, focused on content knowledge and involved in active teacher learning.
In South Africa, there is evidence that subject content knowledge is a crucial aspect of any professional development programme (Venkat & Spaull 2014; Pournara, Hodgen & Pillay 2015). These South African studies on teachers’ mathematical knowledge establish findings that many teachers in South Africa lack subject content knowledge. Another group of authors state that in initial teacher education there has been too much focus on general teaching methods and too little on the underpinning conceptual knowledge that needs to be taught (Hofmeyr & Hall, 1995; Taylor & Vinjevold, 1999 and Parker & Adler, 2005). As a result, in 2001, the government restructured teacher education; the teacher training colleges were incorporated into Higher Education system. Professor Kader Asmal’s (the former Minister of Education) comments on quality give us one of the reasons for the restructuring of teacher education. He says, “Quality and subject content knowledge which was seen in relation to the National Teacher Education Audit highlighted the poor quality of education in the colleges”
(Parker & Adler, 2005, p. 69). In relation to the restructuring of teacher education, Parker and Adler (2005) also state that teacher educators are positioned to redefine knowledge and practices for teacher education and to re-insert disciplined and disciplinary inquiry into teacher preparation programmes.
With regard to the subject knowledge that Commerce teachers need to know, Maistry (1998) in a study of Economics teaching in secondary schools, states that the nature of school Economics knowledge is determined by the demands found in Economics courses in Higher Education Institutions and in the workplace. The reason for this link, between school studies and what follows, is to “enable learners to further their studies inter alia, education, macro- economics, economic development, international economics, public sector economics, environmental economics, economic history, monetary economics, ecometrics, business cycles and forecasting, journalism, transport economics, economics doctrines and systems
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and related social studies” (Department of Education, 2005, p.10). In relation to this broad scope, Commerce teachers were previously expected to use knowledge of their discipline to make choices about what content is appropriate for the learners and how best to pace and organise teaching and learning (Department of Education, 2005). This was in line with OBE.
However, in Curriculum and Assessment Policy Statement (CAPS), the current South African curriculum, teachers have no choice about the selection of the content as they have to follow the CAPS document.
In terms of Mathematics content knowledge, Krauss and Blum (2012) contend that the content knowledge for Mathematics is not treated extensively in the literature. Krauss and Blum (2012) argue that Shulman’s description of content knowledge does not specify the relationship between subject matter of the school curriculum and a broad basis of university- related knowledge. In relation to subject matter knowledge, Grossman (1990) argues that this includes knowledge of the content of a subject area, as well as knowledge of the substantive and syntactic structures of the discipline. Knowledge of the content refers to major concepts within a field and the relationships among them (Grossman, 1990, p. 6). For example, there are concepts such as wants and needs in Business Studies. In this context, needs are things that you cannot live without, such as shelter. On the other hand, wants (such as a cell phone) are things that you can live without. Grossman (1990) goes on to say that the substantive structures of a discipline refer to the various paradigms within a field that affect both how the field is organized and the questions that guide further inquiry. For example, the field of school Mathematics in South Africa is organized into three sections, algebra, geometry and trigonometry. The syntactic structures of a discipline in the subject matter knowledge;
“includes an understanding of the canons of evidence and proof within the discipline, or how claims are evaluated by members of the discipline” (Grossman, 1990, p 6). Grossman (1990) maintains that knowledge of the structure of a discipline is important because without the knowledge structures, teachers may misrepresent both the content and the nature of the discipline.
In relation to Mathematics, several scholars such as Ball, Thames and Phelps (2008) and Ben-Peretz (2011) critique Shulman’s (1987) categorization of teacher knowledge, saying that it focused on knowledge structures rather than knowledge construction. These authors argue that different set of concepts are required for the subject matter knowledge in Mathematics. Grossman’s (1990) components of subject matter knowledge also seem to be insufficient to conceptualize Mathematics subject matter knowledge because Mathematics
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involves numerical constructions rather than logical structures. In elaborating Shulman’s (1987) content knowledge, Ball, Thames and Phelps (2008) break down the subject matter knowledge into three categories that describe the different aspects of teacher knowledge that are relevant to Mathematics. These categories are shown in the following Figure 8:
Figure 8: Ball, Thames and Phelps (2008) Components of Subject Matter Knowledge in Mathematics
Common Content Knowledge (CCK). According to Ball et al. (2008), CCK is not specific to teaching but it is a subject-specific knowledge needed to solve mathematics problems. An example of CCK in algebra is 20×10 = 200. These authors contend that this knowledge is critical for teachers because it is difficult to teach what you do not know yourself.
Specialised Content Knowledge. (SCK) is described as Mathematical knowledge and skills unique to teaching (Ball et al., 2008, p. 400). Ball et al. (2008) contend that teachers need to have a specialized understanding of, for example, how ( can be expanded.
Furthermore, Ball et al. (2008) also state that SCK enables the teachers to understand learners’ strategies and sources of error better. According to Ball et al. (2008), SCK also includes knowledge of representing mathematical procedures and ideas using pictures and manipulatives. The understanding of learners’ strategies and error is in line with Grossman and Shulman’s notion of pedagogical content knowledge (PCK).
Horizon Content knowledge is described as an awareness of how Mathematics topics are related over the span of Mathematics included in the curriculum (Ball et al., 2008, p.403).
Subject Matter Knowledge (SMK)
Common Content Knowledge (CCK)
Specialized Content
Knowledge (SCK)
Horizon Content Knowledge (HCK)
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For example, algebra teachers need to understand how exponents relate to polynomials and how to work with rational expressions (Ball et al., 2008, p. 403). Furthermore, the horizon content knowledge includes curriculum knowledge because teachers draw from the curriculum to articulate a familiarity with the structure of the Mathematics curriculum (Hurrell, 2013, p. 58). For example, the syntactic structures of a discipline Grade 10 Mathematics teacher needs the knowledge of the curriculum to know how the Mathematics he or she teaches is related to the grade 11 Mathematics in order to set the foundation for the learners.