Journal of Education and Practice www.iiste.org ISSN 2222-1735 (Paper) ISSN 2222-288X (Online) Vol.5, No.25, 2014 117 Mathematics Teachers’ Ability to Investigate Students’ Thinking Processes About Some Algebraic Concepts Elisha Habila Zuya Department of Science Education, Modibbo Adama University of Technology, Yola, Adamawa State, Nigeria E-mail:elishazuya2@gmail.com Abstract The study investigated Mathematics teachers’ ability to evaluate students’ thinking process about some algebraic concepts. The study involved 156 Mathematics teachers randomly selected from some Public Secondary Schools in Bauchi State, Nigeria. Open ended questionnaire was used to collect data from the participants. The teachers were required to respond in detail to the questions asked. The research design was a qualitative one and expository method was used in the analysis of the data collected. It was revealed that, though the teachers showed some success in understanding the students’ errors and misconceptions, great majority of them could not assess students’ thinking process. The study also revealed that most of the teachers were unable to ask competent questions that could help in evaluating the students’ thinking process. Another important finding was the difficulty the teachers themselves had in understanding the problem situations, and hence asked irrelevant questions or make irrelevant statements. It was suggested that training workshops be organized for the teachers to improve their subject matter knowledge about the concepts studied. Keywords: Ability, Thinking process, Algebraic concepts 1. Introduction The mathematics teacher is a necessary component in the reform of teaching and learning mathematics. The possession of various structures of knowledge by teachers indicates the kind of teachers they might be. And talking about teachers’ knowledge brings to mind the concept of pedagogical content knowledge of teachers. Tanisli and Kose (2013) asked, “What should teachers know?” They noted that the answer can be explained through the concept of pedagogical content knowledge. According to them, pedagogical content knowledge is defined as “the ways of representing and formulating the subject that makes it comprehensive to others”. They maintained that pedagogical content knowledge is a kind of knowledge that reveals a teacher’s meaningful and effective ways of teaching. Chick and Baker (2005) quoted Graeber as saying “an understanding of common students’ misconceptions, and effective strategies to help students avoid them, are important aspects of mathematics pedagogical content knowledge”. Pedagogical content knowledge is the subject-matter knowledge that teachers have and it consists of many components. According to Shulman (1987) pedagogical content knowledge has seven components, among which include subject-matter knowledge, knowledge of students, knowledge of curriculum and knowledge of educational purposes. Tamir (1988) categorized pedagogical content knowledge into four components: knowledge of understanding students; knowledge of teaching methods, knowledge of measurement and evaluation and knowledge of curriculum. Grossman (1990) also identified four components of pedagogical content knowledge as: knowledge of strategies and representations for teaching particular topics; knowledge of students’ understanding, conceptions and misconceptions of these topics; knowledge and beliefs about the purposes of teaching particular topics; and knowledge of curriculum materials available for teaching. In the same vein, Fennema and Franke (1992) categorized mathematics teachers’ pedagogical content knowledge under four categories, and one of which is knowledge of students. Shulman (1986) and Park and Oliver (2008) placed knowledge of students in the centre of pedagogical content knowledge, and it is viewed as one of the key components. Knowledge of students is described as a teacher’s knowledge of student’s procedural and conceptual knowledge, students’ thinking processes, learning styles, difficulties and misconceptions in the process of learning a subject. Several scholars in mathematics education (e.g. Carpenter, Fennema, Peterson & Carey, 1988; An, Kulm & Wu, 2004; Chick & Baker, 2005; Chick, Baker, Pham & Cheng, 2006) have conducted studies about in- service and pre-service teachers’ knowledge of students in many subject areas. The findings of these studies indicated that mathematics teachers and pre-service mathematics teachers have incomplete and inadequate knowledge of students in general. Carpenter, Fennema, Peterson and Carey (1988) pointed out that teachers’ knowledge of students is necessary for effective teaching. It goes without saying then that mathematics teachers’ knowledge of students is important in teacher education. A study conducted by Tanisli and Kose (2013) revealed that students’ background knowledge, the concepts which they have difficulty in understanding and their misconceptions are different from teachers’ expectations and predictions about them. Similarly, in a study carried out by Asquith, Stephens, Knuth and Alibali (2007), the findings revealed that mathematics teachers’ knowledge of students about the concept of