Session Information
10 SES 05 B, Research on Values, Beliefs and Understandings in Teacher Education
Paper Session
Contribution
According to mathematicians, angle is a multifaceted concept (Keiser 2004; Mitchelmore, & White 2000). Because of angle’s multifaceted structure, defining it from one single point of view is very difficult (Mitchelmore & White 2000; Keiser 2004). Therefore, in the literature, there are different definitions for angle. The definitions that have mathematical grounds have classified into three particular classes: an amount of turning about a point between two lines; a pair of rays with a common end-point; and the region formed by the intersection of two half-planes (Mitchelmore, & White, 2000). Another classification of the definitions has been made based on physical properties of angle. In that classification, there are two definitions: static definition and dynamic definition (Clements, & Burns, 2000; Close, 1982; Kieran, 1986; Mitchelmore, & White, 2000). While the static definition defines angle as a part of the plane included between two rays meeting at their endpoints, the dynamic definition defines as the amount of rotation necessary to bring one of its rays to the other ray without moving out of the plane (Kieran, 1986). In the literature, there isn’t any common definition and any single interpretation of the angle concept. The similar problem exists when perceptions of students and teachers about the concept are considered (Clements, & Battista, 1989; Keiser, 2004; Mitchelmore, & White, 2000).
Even though the concept of angle is one of the most basic concepts in geometry, there are difficulties even for teachers (Mitchelmore, & White, 2000; Keiser, 2004). When education policies of different countries are analyzed, it can be concluded that mathematics teachers are expected to have a deep understanding of mathematical knowledge and also they are expected to use this knowledge effectively while teaching the concepts (Australian Education Council, 1991; MNE, 2008; NCTM, 2000). It is obvious that it’s not possible to teach angle concept effectively without having clear understanding of the definition of angle. If teachers have misconception about a concept, it’s hard for them to understand students’ misconceptions about it and to create solutions to eliminate their misconceptions (Fennema, & Franke, 1992). Specifically, in geometry education, if the natural development of geometrical thinking and its internal structure are well understood by teachers, it can be expected that overcoming students’ difficulties and finding solutions to them will be easy (Durmus, Toluk, & Olkun, 2002). Teacher education programs should take this issue into the consideration. Because of that reason, it is important to facilitate learning environments in which pre-service mathematics teachers experience different conceptualizations of angle concept and might develop a clear understanding of angle so that they can help their students understand this concept properly. In this respect, as future practitioners, pre-service teachers are critical stakeholders to study about their understandings on angle concept. Silfverberg & Joutsenlahti (2010) investigated Finnish pre-service primary school and subject teachers’ interpretations of angle concept. From international perspective, it is worthy to investigate this concept for pre-service mathematics teachers in Turkey. Therefore, our study aims to investigate pre-service mathematics teachers’ perceptions about the meaning of angle concept.
Method
Expected Outcomes
References
Australian Education Council (1991). A National Statement on Mathematics for Australian Schools: Curriculum Corporation, Melbourne. Clements, D.H., & Battista, M.T. (1989). Learning of geometric concepts in a Logo environment, Journal for Research in Mathematics Education 20, 450–467. Clements, D. H., & Burns, B. A. (2000). Students' development of strategies for turn and angle measure. Educational Studies in Mathematics, 41(1), 31. Close, G.S. (1982). Children’s understanding of angle at the primary/secondary transfer stage. London: Polytechnic of the South Bank. Durmus, S., Toluk, Z., Olkun, S. (2002). Matematik ögretmenligi 1. sinif ögrencilerinin geometri alan bilgi düzeylerinin tespiti, düzeylerin gelistirilmesi için yapilan arastirma ve sonuçlari. V. Ulusal Fen Bilimleri ve Matematik Egitimi Kongresi, Ankara. Fennema, E., & Franke, M. (1992). Teachers’ knowledge and its impact in: D.A. Grouws (Ed) Handbook of Research on Mathematics Teaching and Learning, New York: Macmillan Publishing. Keiser, J. M. (2004). Struggles with developing the concept of angle: Comparing sixth-grade students' discourse to the history of the angle concept, Mathematical Thinking and Learning 6, 285–306. Kieran, C. (1986). LOGO and the notion of angle among fourth and sixth grade children. In L. Burton and C. Hoyles (Eds.), Proceedings of the 10th International Conference on the Psychology of Mathematics Education, London, pp. 99–104. Mitchelmore M. C., & White, A. P. (2000). Development of angle concepts by progressive abstraction and generalization, Educational Studies in Mathematics 41, 209–238. Ministry of National Education [MNE]. (2008). Matematik Öğretmeni Özel Alan Yeterlikleri, Retrieved December 27, 2010, from http://otmg.meb.gov.tr/alanmatematik.htmlMEB 2008. National Council of Teachers of Mathematics [NCTM] (2000). Curriculum and evaluation standards for school mathematics. Reston, VA: NCTM. Silfverberg, H., & Joutsenlahti, J. (2010). Prospective class and subject teachers’ interpretations of the meaning of the concept of a plane angle. The European Conference on Educational Research 2010, Helsinki.
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