Session Information
24 SES 07 A, Issues in Mathematics Teacher Education I
Paper Session
Contribution
Many research studies have documented that the mathematical understanding preservice teachers bring from schooling and university mathematics courses was inadequate for teaching primary school mathematics (Ball, 1990a, 1990b; Even, 1993; Ma, 1999; Tirosh, 2000; Toluk Uçar, 2009). In these studies, while preservice teachers generally knew how to carry out a procedure, they could not produce mathematical explanation for the underlying meaning. To become a mathematics teacher preservice teachers need to develop profound subject matter knowledge, pedagogical content knowledge and knowledge of students’ cognition (Shulman, 1986; Ball, 1990a; Carpenter, Fennema and Franke, 1997; Ma, 1999). These three types of knowledge should be considered as parts of a larger system on which teacher rely on as they plan and implement instruction (Verschafel, Janssens, and Janssens, 2005). Moreover, Borko, Eisenhart, Brown, Underhill, Jones and Agard (1992) argue that subject-matter knowledge and pedagogical content knowledge are central to the task of subject matter teaching. Subject-matter knowledge includes mastery of the key facts, concepts, principles and explanatory frameworks, procedures, problem solving techniques and strategies in mathematics. What is critical in this knowledge type is the level of teachers’ understanding of mathematics (Ball, 1990a; Borko et al., 1992; Ma, 1999). According to Ball (1990a), teachers’ knowledge of concepts and procedures should be correct; they should understand the underlying principles and meanings, and teachers must appreciate and understand the connections among mathematical ideas. Pedagogical content knowledge or subject specific pedagogical knowledge, which depends on subject matter knowledge (McDiarmid, Ball, and Anderson, 1989), consists of knowledge of ways of representing and explaining mathematics to make it understandable, and knowledge of students’ cognition (preconceptions, misconceptions, and conceptions). Knowledge of representation and knowledge of students mathematical thinking are two main components of this knowledge type. To highlight the dependence of pedagogical content knowledge on subject-matter knowledge, several researcher argue that to produce a conceptually correct representation, teacher must have an understanding of the they are representing (McDiarmid, Ball, and Anderson, 1989; Borko et al., 1992; Ma, 1999). Agreeing fully with this argument that to become a mathematics teacher preservice teachers need to develop extensive subject-matter background in order to develop pedagogical content knowledge. The present study focuses on the preservice teachers’ mathematics knowledge and the explanations they produce. The purpose of this study was to investigate the nature of explanations they provide for mathematical situations and the knowledge of these mathematical situations.
Method
Expected Outcomes
References
Ball, D. L. (1990a). The mathematical understandings that prospective teachers bring to teacher education. The Elementary School Journal, 90(4), 449–466. Ball, D. L. (1990b). Prospective elementary and secondary teachers’ understanding of division. Journal for Research in Mathematics Education, 21(2), 132–144. Borko, H., Eisenhart, M., Brown, C. A., Underhill, R. G., Jones, D., & Agard, P. C. (1992). Learning to Teach Hard Mathematics: Do Novice Teachers and Their Instructors Give up Too Easily? Journal for Research in Mathematics Education, 23(3), 194-222. Carpenter, T. P., Fennema, E., and Franke, M. L. (1996). Cognitively Guided Instruction: A Knowledge Base for Reform in Mathematics Instruction. The Elementary School Journal, 97(1), 3–20. Even, R. (1993). Subject-matter knowledge and pedagogical content knowledge: Prospective secondary teachers and the function concept. Journal for Research in Mathematics Education, 24(2), 94–116. Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Erlbaum. McDiarmid, G. W., Ball, D. L., & Anderson, C. (1989). Why Staying One Chapter Ahead Doesn't Really Work: Subject-Specific Pedagogy. In M. C. Reynolds (Ed.), Knowledge Base for the Beginning Teacher (pp. 193-205). Elmsford, NY: Pergamon Press. Shulman, L. S. (1986). Those Who Understand: Knowledge Growth in Teaching. Educational Researcher, 15(2), 4-14. Tirosh, D. (2000). Enhancing prospective teachers’ knowledge of children’s conceptions: The case of division of fractions. Journal for Research in Mathematics Education, 31(1), 5–25. Toluk-Uçar, Z. (2009). Developing pre-service teachers understanding of fractions through problem posing. Teaching and Teacher Education, 25(1), 166–175. Verschaffel, L., Janssens, S., & Janssen, R. (2005). The development of mathematical competence in Flemish pre-service elementary school teachers. Teaching and Teacher Education, 21, 49–63.
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