Academic journal article Perspectives in Education

Perspectives on Pre-Service Teacher Knowledge for Teaching Early Algebra

Academic journal article Perspectives in Education

Perspectives on Pre-Service Teacher Knowledge for Teaching Early Algebra

Article excerpt

Introduction and rationale

Mathematics results at both primary and secondary level in South Africa continue to reflect poorly on the system, learners and teachers. A study by Carnoy and Chisholm (2008), which investigates factors contributing to low levels of mathematics achievement in South African primary schools, found some evidence to suggest that high-quality mathematics teaching is related positively to learner achievement. Although the sample of 40 schools is relatively small, the study results support claims that larger gains in learner achievement are related to teaching by those who know more about the subject and how to teach it. The results of this study highlight teacher knowledge as an important factor in learner achievement, in addition to the learner- and curriculum-related factors focused on previously.

The work of pre-service teacher education is to prepare effective teachers of mathematics with strong content knowledge, which includes both subject matter knowledge and pedagogical content knowledge. This research is part of a more extensive study on understanding the links between pre-service teachers' developing mathematical content knowledge and the teaching and learning of early algebra. In this study, the expression 'early algebra' includes algebraic reasoning and algebra- related instruction with learners in the primary school (Carraher & Schliemann, 2007). The inclusion of algebra thinking in the early grades, or early algebra as it is also called, gives learners the opportunity to experience and develop conceptual understanding of algebra from the outset. Early algebra can help to prepare learners for more complex mathematics, to cultivate habits of mind that attend to the 'deeper underlying structure of mathematics' and to improve their algebra understanding (Blanton & Kaput, 2005: 412).

This paper looks at one pre-service teacher's knowledge demonstrated in teaching early algebra. Teacher knowledge can be defined in different ways and this research focuses on two conceptual perspectives: the Knowledge Quartet (KQ) (Rowland & Turner, 2009) and Mathematical Knowledge for Teaching (MKfT) frameworks (Ball, Thames & Phelps, 2008). Both draw from the work of Shulman (1986) who identified content-specific knowledge as subject matter knowledge, pedagogical content knowledge and curriculum knowledge.

The use of different perspectives to understand mathematics and the work of teaching is not new and has been elaborated in different ways (Ball, Charalambous, Thames & Lewis, 2009; Even, 2009; Rowland & Turner, 2009). However, the purpose of this paper is to consider one lesson through these two different theoretical lenses which lead to different interpretations of the same lesson (Even, 2009). Thus, the study intends to examine the differences between the inferences using each framework, and to reflect on how they may help us to make better sense of the knowledge needed for teaching early algebra.

Theoretical perspectives

The Knowledge Quartet (KQ)

Turner and Rowland (2008) describe the Knowledge Quartet as an empirically based conceptual framework for classifying ways in which pre-service student teachers' subject matter knowledge and pedagogical content knowledge come into play in the classroom. It can be used to identify and analyse mathematical content knowledge 'enacted' in teaching and to provide a structure for reflection and discussions of lessons (Turner & Rowland, 2008). On the basis of an investigation of mathematical content knowledge of pre-service teachers in England and Wales, Rowland, Thwaites, Huckstep and Turner (2009) suggest that mathematical content knowledge is a complex combination of different types of knowledge that interact with one another and can be seen more easily in the act of teaching.

The KQ model is an elaboration of the earlier work of Shulman (1986) and responds and updates the work of Fennema and Franke (1992) by suggesting ways in which teachers' subject matter knowledge relates to their pedagogical content knowledge, and how their actions in the classroom are informed by their knowledge (Goulding & Petrou, 2008). …

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