THE MIDDLE SCHOOL MATHEMATICS TEACHERS’ SUBJECT MATTER KNOWLEDGE: THE CONTEXT OF DIVISION OF FRACTIONS

Reyhan Tekin Sitrava

Abstract


In this study, the middle school mathematics teachers’ knowledge of division of fractions was investigated through the strategies that they proposed and the problems that they posed for division of fractions. The data was collected from 22 middle school mathematics teachers through the task and semi-structured interviews. The data of this case study was analyzed by content analysis approach. According to the findings, 5 alternative strategies were proposed by 22 teachers to divide fractions. Among these strategies, the most commonly used was invert and multiply strategy and the least are converting fractions into decimal and converting to equation. In relation to the problems that the teachers posed, the findings revealed that more than half of the teachers could not propose appropriate problems. In other words, the teachers had difficulty in generating an appropriate story problem to illustrate division of fractions. These results and implications are discussed and the recommendations are presented in accordance with the findings of the study.

 

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teacher knowledge, subject matter knowledge, division of fractions, alternative strategies, problem posing

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Ball, D. L. (1990a). The mathematical understanding that prospective teachers to teacher education. Elementary School Journal, 90, 449-466.

Ball, D. L. (1990b). Prospective elementary and secondary teachers’ understanding of division. Journal of Research in Mathematics Education, 21, 132-144.

Ball, D. L., Hill, H. C., & Bass, H. (2005). Knowing mathematics for teaching: Who knows mathematics well enough to teach third grade, and how can we decide? American Educator, 29(3), 14–46.

Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59 (5), 389- 407.

Boaler, J. & Staples, M. (2008) Creating mathematical futures through an equitable teaching approach: The case of Railside school. Teachers College Record, 110(3), 608–645.

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, 194–222.

Borko, H. & Putnam, R. T. (1996). Learning to teach. In R. Calfee & D. Berliner (Eds.), Handbook of educational psychology (pp. 673–725). New York: Macmillan.

Carreño, E., Ribeiro, C. M., & Climent, N. (2013). Specialized and horizon content knowledge–Discussing prospective teachers knowledge on polygons. In Proceedings of the Eight Congress of European Mathematics Education (pp. 2966-2975).

Castro-Rodríguez, E., Pitta-Pantazi, D., Rico, L., & Gómez, P. (2016).Prospective teachers‘ understanding of the multiplicative part-whole relationship of fraction. Educational Studies in Mathematics,92(1), 129-146.

Cohen, D., Raudenbush, S., & Ball, D. (2003) Resources, instruction, and research. Educational Evaluation and Policy Analysis, 25(2), 1–24.

Contreras, J. M., Batanero, C., Díaz, C., & Fernandes, J. A. (2011). Prospective teachers’ common and specialized knowledge in a probability task. In Seventh Congress of the European Society for Research in Mathematics Education (pp. 766-775). European Society for Research in Mathematics Education.

Creswell, J. W. (2007). Qualitative inquiry and research design: Choosing among five approaches (2nd ed.). Thousand Oaks, California: Sage Publications, Inc.

English, L. D. (1998). Children's problem posing within formal and informal contexts. Journal for Research in Mathematics Education, 29(1) 83-106. Doi: 10.2307/749719.

Even, R. (1990). Subject-matter knowledge for teaching and the case of functions. International Journal of Mathematics Education in Science and Technology, 14, 293-305.

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.

Even, R., & Tirosh, D. (1995). Subject-matter knowledge and knowledge about students as sources of teacher presentations of the subject-matter. Educational Studies in Mathematics, 29(1), 1-20.

Fendel, D. M. (1987). Understanding the structure of elementary school mathematics. Allyn & Bacon.

Fennema, E., & Franke, M. L. (1992). Teachers' knowledge and its impact. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 147-164). New York: Macmillan.

Fennema, E., Carpenter, T. P., Franke, M. L., Levi, L., Jacobs, V. R., & Empson, S. B. (1996). A longitudinal study of learning to use children’s thinking in mathematics instruction. Journal for Research in Mathematics Education, 27(4), 403–434.

Franke, M. L., Kazemi, E., & Battey, D. (2007). Mathematics teaching and classroom practice. Second handbook of research on mathematics teaching and learning, 1(1), 225-256.

Hill, H. C., Schilling, S., & Ball, D. L., (2004). Developing measures of teachers' mathematics knowledge for teaching. Elementary School Journal, 105(1), 1130.

Hu, H. W., & Hsiao, W. Y. (2013). Developing pre-service teachers’ understanding in division of fractions by using TPACK. In Society for Information Technology & Teacher Education International Conference (pp. 4801-4805). Association for the Advancement of Computing in Education (AACE).

Huang, R., & Kulm, G. (2012). Prospective middle grade mathematics teachers’ knowledge of algebra for teaching. The Journal of Mathematical Behavior, 31(4), 417-430.

Isiksal, M. (2006). A study on pre-service elementary mathematics teachers‟ subject matter knowledge and pedagogical content knowledge regarding the multiplication and division of fractions. Unpublished doctoral dissertation, Middle East Technical University, Turkey.

Lin, P. J. (2004). Supporting teachers on designing problem-posing tasks as a tool of assessment to understand students' mathematical learning. In Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education. (Vol. 3, pp. 257-2644). Norway: Bergen.

Livy, S., & Vale, C. (2011). First year pre-service teachers' mathematical content knowledge: Methods of solution to a ratio question. Mathematics Teacher Education and Development, 13(2), 22-43.

Ma, L. (1999). Knowing and Teaching Elementary Mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum.

Magnusson, S., Krajcik, J., & Borko, H. (1999). Nature, sources and development of pedagogical content knowledge for science teaching. In J. Gess-Newsome & N. G. Lederman (Eds.), Examining pedagogical content knowledge: The construct and its implications for science education (pp. 95-132). Boston: Kluwer.

Merriam, S. B. (2009). Qualitative research: A guide to design and implementation. San Francisco: Jossey-Bass.

Mewborn, D. (2003). Teaching, teachers’ knowledge, and their professional development. In J. Kilpatrick, W. G. Martin, & D. Schifter (Eds.), Research companion to principles and standards for school mathematics (pp. 45–52). Reston, VA: NCTM.

Ministry of National Education (MoNE) (2018). Matematik dersi öğretim programı (İlkokul ve Ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. sınıflar) [Primary and middle school grades 1 to 8]. Ankara, Turkey: Author.

National Council of Teacher of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.

National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. Reston, VA: Author.

Olanoff, D., Lo, J. J., & Tobias, J. (2014). Mathematical content knowledge for teaching elementary mathematics: A focus on fractions. The Mathematics Enthusiast, 11(2), 267-310.

Pino-Fan, L., Godino, J. D., Font, V., & Castro, W. F. (2013). Prospective teacher's specialized content knowledge on derivative. In Proceedings of the Eighth Congress of the European Society for Research in Mathematics Education (pp. 3195-3205).

Rowland, T., Huckstep, P., &Thwaites, A. (2005). Elementary teachers‟ mathematics subject knowledge: The Knowledge Quartet and the case of Naomi. Journal of Mathematics Teacher Education, 8(3), 255-281.

Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14.

Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19-28.

Son, J., & Crespo, S. (2009). Prospective teachers’ reasoning about students’ non-traditional strategies when dividing fractions. Journal of Mathematics Teacher Education, 12(4), 236–261.

Stein, M. K. & Lane, S. (1996) Instructional tasks and the development of student capacity to think and reason: An analysis of the relationship between teaching and learning in a reform mathematics project. Educational Research and Evaluation, 2(1), 50–80.

Stein, M. K., Remillard, J. & Smith, M. S. (2007) How curriculum influences student learning. In F. K. Lester (ed.), Second Handbook of Research on Mathematics Teaching and Learning, 319–36, Charlotte, NC: Information Age Publishing.

Stoyanova, E. (2003). Extending students' understanding of mathematics via problem posing. Australian Mathematics Teacher, 59(2), 32-40.

Strauss, A., & Corbin, J. (1990). Basics of qualitative research. Sage publications.

Tirosh, D. (2000). Enhancing prospective teacher’ knowledge of children’s conceptions: The case of division of fractions. Journal for Research in Mathematics Education, 31(1), 5-25.

Tirosh, D., & Graeber, A. (1991). The effect of problem type and common misconceptions on preservice elementary teachers’ thinking about division. School Science and Mathematics, 91, 157-163.

Ticha, M., & Hošpesova, A. (2009, January). Problem posing and development of pedagogical content knowledge in prospective teacher training. In meeting of CERME (Vol. 6, pp. 1941-1950). Doi: 10.1007/978-1-4614-6258-3_21.

Van de Walle, J. A., Karp, K. S., Bay-Williams, J. M. (2013). Elementary and middle school mathematics: Teaching developmentally (8th ed.). Boston, MA: Pearson.

Wahyu, K., Amin, S.M., & Lukito, A. (2017). Motivation cards to support students’ understanding on fraction divisions. International Journal on Emerging Mathematics Education, 1(1), 99-120.




DOI: http://dx.doi.org/10.46827/ejes.v0i0.2362

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