An Exploration of the Common Content Knowledge of High School Mathematics Teachers

By Bansilal, Sarah; Brijlall, Deonarain et al. | Perspectives in Education, March 2014 | Go to article overview

An Exploration of the Common Content Knowledge of High School Mathematics Teachers


Bansilal, Sarah, Brijlall, Deonarain, Mkhwanazi, Thokozani, Perspectives in Education


Introduction

In South Africa, many studies suggest that mathematics teachers struggle with the content that they teach. I n fact, studies point to the teachers' poor content knowledge as one of the reasons for South African learners' poor results in both national and international assessments (CDE, 2011; Mji & Makgato, 2006). Hugo, Wedekind and Wilson (2010) reported on a study of teaching and learning mathematics in primary schools in KwaZulu-Natal. They found that none of the teachers were able to achieve 100% for the test on the curriculum that they were teaching, and 24% of the respondents got less than 50%. On average, only 47% managed to get each test item correct. Spaull (2011), in his analysis of the Southern and Eastern Africa Consortium for Monitoring Educational Quality (SAQMEQ) 2010 results, revealed that the top 5% of Grade 6 learners (559 students) scored higher marks on the same mathematics test than the bottom 12.5% of Grade 6 educators (62 teachers) in the sample.

Most studies about mathematics teachers' content knowledge in South Africa have been reported in terms of primary school teachers (Hugo et al., 2010; Spaull, 2011) and there are no studies with specific details of what FET mathematics teachers are struggling with. In this study, we attempt to scratch the surface of this issue by investigating the content knowledge of 253 Grade 12 mathematics teachers from various regions in KwaZulu-Natal.

The purpose of this study is to explore the teachers' understanding of the concepts of quadratic equations, patterns, functions (hyperbolic and quadratic), aspects of calculus and linear programming. With this purpose in mind, we formulated the research question: How do Grade 12 mathematics teachers perform on Grade 12 mathematics test items? We hope that the results of this study will add to the knowledge of what mathematics teachers know and understand about the content they teach.

The formal two-year upgrading programme that the teachers were enrolled in was the Advanced Certificate in Education in Mathematics in the Further Education and Training band (ACE: Maths FET). The programme consisted of eight modules, two of which were generic education modules that all ACE students in the Faculty of Education studied. There were four mathematics content modules which focused on probability and statistics; geometry, trigonometry and measurement; differential calculus and integral calculus. These modules were intended to deepen the teachers' content knowledge by including some topics from school mathematics, but also going beyond what was required in the classroom and could be seen as what Ball, Thames and Phelps (2008) call horizon knowledge. This is an 'awareness of how mathematical topics are related over the span of mathematics included in the curriculum' (Ball et al., 2008: 403). Horizon knowledge enables teachers to make decisions about how to teach concepts to their school learners. The programme also included two pedagogic content modules.

Literature review and theoretical framework

Wu (2005: 9) argues that often 'a well-intentioned pedagogical decision in the classroom can be betrayed by faulty content knowledge'; thus, emphasising the importance of content knowledge in the teaching situation. Bansilal (2012b) focused on a teacher's poor mathematics content knowledge and found that the teacher's explanations were often incoherent and illogical. The teacher's poor understanding of the concepts of ratio and number resulted in her missing some key ideas and presenting convoluted explanations that involved circular reasoning, which made no sense to her learners. In another South African study an author explored links between the pedagogic content knowledge (PCK) and classroom practice in a calculus class at a university (Brijlall, 2011; Brijlall & Isaac, 2011). The data revealed that there was a strong link between PCK and classroom practice.

Many researchers agree that professional development programmes should include a focus on content knowledge and pedagogical content knowledge (Adler, Slominsky & Reed, 2002; Peressini, Borko, Romagnano, Knuth & Willis, 2004; Kriek & Grayson, 2009; Ono & Ferreira, 2010; Bansilal & Rosenberg, 2011). …

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