Analyzing Pre-service Primary Mathematics Teachers’ Skills to Determine Errors in Problems Posed by Students

Author :  

Year-Number: 2014-Volume 6, Issue 3
Language : null
Konu : null

Abstract

In the study, it was aimed to determine the skills of pre-service elementary mathematics teachers in identifying the errors which the middle school third grade students made in addition of proper fractions. The study was conducted with 64 pre-service teachers studying as senior students in the department of Elementary Mathematics Teaching. In the process of data collecting, third grade students were applied a Problem Posing Test. Error Determination Test, which has six problem statements about addition operation with fractions, was applied to pre-service elementary mathematics teachers. The pre-service teachers were asked to identify and explain the errors in the problem sentences. The results of the study show that the pre-service teachers experienced difficulty in identifying the errors and made different errors in explaining the errors.

Keywords

Abstract

In the study, it was aimed to determine the skills of pre-service elementary mathematics teachers in identifying the errors which the middle school third grade students made in addition of proper fractions. The study was conducted with 64 pre-service teachers studying as senior students in the department of Elementary Mathematics Teaching. In the process of data collecting, third grade students were applied a Problem Posing Test. Error Determination Test, which has six problem statements about addition operation with fractions, was applied to pre-service elementary mathematics teachers. The pre-service teachers were asked to identify and explain the errors in the problem sentences. The results of the study show that the pre-service teachers experienced difficulty in identifying the errors and made different errors in explaining the errors.

Keywords


  • Abu-Elwan, R. (2002). Effectiveness of problem posing strategies on prospective mathematics teachers’ problem solving performance. Journal of Science and Mathematics Education, 25(1), 56-69.

  • 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. http://dx.doi.org/10.1177/0022487108324554

  • Ball, D. L., Lubienski, S. T. & Mewborn, D. S. (2001). Research on teaching mathematics: The unsolved problem of teachers’ mathematical knowledge. In V. Richardson (Ed.), Handbook of research on teaching (4th ed., pp. 433-456). New York: Macmillan.

  • Charalambous, C. Y., Delaney, S., Hsu, H. Y. & Mesa, V. (2010). A comparative analysis of the addition and subtraction of fractions in textbooks from three countries. Mathematical Thinking and Learning, 12, 117– 151. http://dx.doi.org/10.1080/10986060903460070

  • Chick, H. L. & Baker, M. K. (2005). Investigating teacher’s responses to student misconceotions. In Chick, H. L. & Vincent, J. L. (Eds.). Proceedings of the 29 th conference of the international group for the psychology of mathematics education (Vol.2, pp. 249-256). Melbourne: PME.

  • Crespo, S. (2003). Learning to pose mathematical problems: Exploring changes in preservice teachers’ practices. Educational Studies in Mathematics, 52, 243–270. http://dx.doi.org/10.1023/A:1024364304664

  • Darley, J. W. (2005). Ninth grader’s interpretations and use of contextualized models of fractions and algebraic properties: A classroom-based approach Unpublished doctoral dissertation. University of South Carolina.

  • Dickerson, V. M. (1999). The impact of problem posing instruction on the mathematical problem solving achievement of seventh graders. Unpublished doctoral dissertation. University of Emory, Atlanta.

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

  • Flores, E., Escudero, D.I. & Carrillo, J. (2012). A theoretical review of specialised content Knowledge. Paper presented at the meeting of Eighth Congress of European Research in Mathematics Education (CERME 8), Antalya, Turkey.

  • Fuller, R. A. (1996). Elementary teachers’ pedagogical content knowledge of mathematics. Paper presented at the Mid-Western Educational Research Association Conference,Chicago.

  • Gonzales, N. A. (1998). A blueprint for problem posing. School Science and Mathematics, 94(2), 78- 85. http://dx.doi.org/10.1111/j.1949-8594.1994.tb12295.x

  • Goos, M. (2013) Knowledge for teaching secondary school mathematics: What counts?. International Journal of Mathematical Education in Science and Technology, 44(7), 972-983. http://dx.doi.org/10.1080/0020739X.2013.826387

  • Hill, H. C., Rowan, B. & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371–406. http://dx.doi.org/10.3102/00028312042002371

  • Işık, C. (2011). İlköğretim matematik öğretmeni adaylarının kesirlerde çarpma ve bölmeye yönelik kurdukları problemlerin kavramsal analizi. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 41, 231-243.

  • Işık, C. & Kar, T. (2012a). 7. sınıf öğrencilerinin kesirlerde toplama işlemine kurdukları problemlerin analizi. İlköğretim Online, 11(4), 1021-1035.

  • Işık, C. ve Kar, T. (2012b). Matematik dersinde problem kurmaya yönelik öğretmen görüşleri üzerine nitel bir çalışma. Milli Eğitim Dergisi, 194, 199-215.

  • Işık, C., Kar, T., Işık, A. & Güler, G. (2012). İlköğretim matematik öğretmeni adaylarının kesirlerde toplama işlemine yönelik kurulan problemlerdeki hataları belirleyebilme becerileri. Türk Bilgisayar ve Matematik Eğitimi Dergisi, 3(3), 161-182.

  • Işık, C., Öcal, T. & Kar, T. (2013). Analysis of pre-service elementary teachers’ pedagogical content knowledge in the context of problem posing. Paper presented at the meeting of Eighth Congress of European Research in Mathematics Education (CERME 8), Antalya, Turkey.

  • Kılıç, Ç. (2013). Pre-Service primary teachers’ free problem-posing performances in the context of fractions: An example from turkey. The Asia-Pacific Education Researcher, 1-10. http://dx.doi.org/10.1007/s40299013-0073-1

  • Kulm, G. (2008). Teachers’ mathematics knowledge. School Science and Mathematics, 108, 2-3. http://dx.doi.org/10.1111/j.1949-8594.2008.tb17933.x

  • Lin, C. Y. (2010). Web-based instruction on preservice teachers’ knowledge of fraction operations. School Science and Mathematics, 110(2), 59-70. http://dx.doi.org/10.1111/j.1949-8594.2009.00010.x

  • Luo, F. (2009). Evaluating the effectiveness and insights of preservice elementary teachers’ abilities to construct word problems for fraction multiplication. Journal of Mathematics Education, 2(1), 83-98.

  • Ma, L. (2010). Knowing and teaching elementary mathematics: Teachers' understanding of fundamental mathematics in China and the United States. Newyork, NJ: Lawrence Erlbaum Associates.

  • McAllister, C. J. & Beaver, C. (2012). Identification of error types in preservice teachers' attempts to create fraction story problems for specified operations. School Science and Mathematics 112(2), 88-98. http://dx.doi.org/10.1111/j.1949-8594.2011.00122.x

  • Mcmillan, H. J. & Schumacher, S. (2010). Research in education. Boston, USA: Pearson Education.

  • Milli Eğitim Bakanlığı[MEB], (2009). İlköğretim matematik dersi 1-5. Sınıflar öğretim programı. Ankara: Devlet Kitapları Müdürlüğü.

  • Milli Eğitim Bakanlığı[MEB], (2009). İlköğretim matematik dersi 6-8. Sınıflar öğretim programı ve kılavuzu. Ankara: Devlet Kitapları Müdürlüğü.

  • Milli Eğitim Bakanlığı[MEB], (2013). Ortaokul matematik dersi (5, 6, 7 ve 8. Sınıflar) öğretim programı. Ankara: MEB Basımevi.

  • Newton, K. J. (2008). An extensive analysis of preservice elementary teachers’ knowledge of fractions. American Educational Research Journal, 45(4), 1080-1110. http://dx.doi.org/10.3102/0002831208320851

  • Özmantar, M. F. ve Bingölbali, E. (2009). Sınıf öğretmenleri ve matematiksel zorlukları. Gaziantep Üniversitesi Sosyal Bilimler Dergisi, 8(2), 401-427.

  • Redmond, A. & Utley, J. (2007). Prospective elementary teachers understanding of and attitudes towards the division of fractions. Paper presented at the Research Council on Mathematics Learning Annual Convention, Oklahoma City.

  • Rizvi, N. F. & Lawson, M. J. (2007). Prospective teachers’ knowledge: Concept of division. International Education Journal, 8(2), 377-392.

  • Rizvi, N. F. (2004). Prospective teachers’ ability to pose word problems. Retrived from http://ecommons.aku.edu/cgi/viewcontent.cgi?article=1048&context=pakistan_ied_pdck

  • Stoyanova, E. (1998). Problem posing in mathematics classrooms. In A. McIntosh, & N. Ellerton (Eds.), Research in mathematics education: A contemporary perspective (pp.164-185). Perth: MASTEC Publication.

  • Ticha, M. & Hospesova, A. (2009). Problem posing and development of pedagogical content knowledge in pre-service teacher training. Paper presented at the meeting of CERME 6, Lyon, France.

  • Toluk-Uçar, Z. (2009). Developing pre-service teachers understanding of fractions through problem posing. Teaching and Teacher Education, 25(1), 166-175. http://dx.doi.org/10.1016/j.tate.2008.08.003

  • Toluk-Uçar, Z. (2011). Öğretmen adaylarının pedagojik içerik bilgisi: Öğretimsel açıklamalar. Türk Bilgisayar ve Matematik Eğitimi Dergisi, 2(2), 87-102.

  • Ward, J. & Thomas, G. (2007). What do teachers know about fractions? In findings from the New Zealand numeracy development projects (pp. 128–138). Wellington: Learning Media.

  • Zembat, İ. Ö. (2007). Working on the same problem-Concepts; with the usual subjects- pre-service elementary teachers. İlköğretim Online, 6(2), 305-312.

                                                                                                                                                                                                        
  • Article Statistics