Session Information
24 SES 09, Issues in Mathematics Teacher Education II
Paper Session
Contribution
Mathematics is a field that is composed of abstract concepts, which are found to be very hard to grasp by many school children. In this sense, dealing with concrete representations of abstract mathematical concepts is essential for children if they are to develop an understanding of those concepts. The use of concrete models in teaching and learning mathematics has been taken attention by the researchers and educators for years. Van de Walle (2007) defined a model as any object, picture, or drawing that represents the concepts or onto which the relationship for that concept can be imposed. Sowell (1989) defined a concrete model learning environment as students worked directly with materials under the supervision of a treatment administrator. Considerable studies have supported the idea that using concrete models enhance learning of mathematics (Moyer, 2001; Silver, 2009; Sowell, 1989; Suydam & Higgins, 1977). The strongest theoretical arguments in favor of concrete models were developed by Piaget (1971), Bruner (1960), and Dienes (1969). Each theoretician represented the cognitive view points of learning and they suggested proper use of concrete models in mathematics classrooms (Post, 1981). However, there are also other studies that suggested concrete models are not always necessarily more effective than traditional methods (Clements, 1999; Fennema, 1972; Van de Walle, 2007). The main reason of possible ineffectiveness of models is quality of instruction. Therefore, teachers have an important role on the effectiveness of instruction with concrete models (Moyer, 2001; Post, 1981; Suydam & Higgins, 1977).
Until recently, the national mathematics curriculum in Turkey did not have recommendations for the use of concrete models in mathematics instruction. The recent curriculum reform in Turkey, however, emphasized the use of concrete models in the teaching of mathematics (Ministry of National Education, 2004). In such a context, teachers’ role becomes critical, since they play an important role in the quality of mathematics instruction at the school level. Most of the preservice mathematics teaches in Turkey have almost no experience in the use of concrete models as learners of mathematics. In this sense, preparing preservice teachers to meaningfully use concrete models in Turkish schools is an important issue. Moreover, based on research from several countries, teachers’ usage of models is generally problematic (Moyer, 2001; Puncher, 2008;Van de Walle, 2007). In this sense, it is critical to investigate future mathematics teachers’ views about concrete models for understanding the reasons of ineffective use of models, or worse, possible disuse.
One important factor on teachers’ use of instructional strategies is their beliefs and views (Moyer, 2001). In this respect, as future practitioners, preservice teachers are critical stakeholders to study about their views and beliefs. Therefore, the primary purpose of the study was to investigate preservice mathematics teachers’ views about using concrete models in the mathematics classrooms.
Method
Expected Outcomes
References
Clements, D. H. (1999). Concrete manipulatives, concrete ideas. Contemporary Issues in Early Childhood, 1(1), 45-60. Fennema, E. (1972). The relative effectiveness of a symbolic and a concrete model in learning a selected mathematical principle. Journal for Research in Mathematics Education, 3(4), 233-238. Ministry of National Education (MNE). (2004). İlköğretim matematik dersi öğretim programı [Elementary school mathematics curriculum]. Ankara: Ministry of National Education. Moyer, S. P. (2001). Are we having fun yet? How teachers use manipulatives to teach mathematics. Educational Studies in Mathematics, 47, 175-197. Post, T. (1981). The Role of Manipulative Materials in the Learning of Mathematical Concepts. In Selected Issues in Mathematics Education (pp. 109-131). Berkeley, CA: National Society for the Study of Education and National Council of Teachers of Mathematics, McCutchan Publishing Corporation. Puncher, L., Taylor, A., O’Donnell, B., & Fick, K. (2008). Teacher learning and mathematics manipulatives: A collective case study about teacher use of manipulatives in elementary and middle school mathematics lessons. School Science and Mathematics 108(7), 313-325. Silver, E. A., Mesa, V. M., Morris, K. A., Star, J., & Benken, B. M. (2009). Teaching mathematics for understanding: An analysis of lessons submitted by teachers seeking NBPTS certification. American Educational Research Journal,46(2), 501-531. Sowell, E. J. (1989). Effects of manipulative materials in mathematics instruction. Journal for Research in Mathematics Education, 20(5), 499-505. Suydam, M., & Higgins. J. (1977). Activity-based learning in elementary school mathematics. Reston, Virginia: NCTM. Van de Walle, J. A. (2007). Elementary and middle school mathematics: Teaching developmentally (6th ed.). Boston, MA: Pearson /Allyn and Bacon.
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