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Are Pre-service Elementary Teachers able to Pose Problems for the Subtraction of Fractions?

Year 2018, Volume 5, Issue 2, 94 - 105, 01.10.2018

Abstract

The purpose of this study is to examine whether or not pre-service elementary teachers are able to pose appropriate problems for the subtraction of fractions, if not, to determine the types of errors made in their posed problems. A qualitative research method was used in this study and the data were collected from 83 pre-service elementary teachers in the spring 2017 academic semester of a public university in Turkey using a Problem Posing Test. The test consisted of four items related to the subtraction of fractions given in number sentences. Findings showed that most of the pre-service elementary teachers could not appropriately pose problems and made distinct types of errors. It was found that the two most common errors were failing to include subtraction in the question root and expressing the subtrahend fraction as a certain amount of the minuend fraction. Teacher educators can integrate problem posing activities in their courses to give pre-service teachers opportunities to pose problems

References

  • 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.
  • Bailey, D. H., Hoard, M. K., Nugent, L., & Geary, D. C. (2012). Competence with fractions predicts gains in mathematics achievement. Journal of Experimental Child Psychology, 113(3), 447-455.
  • Barlow, A. T., & Cates, J. M. (2006). The impact of problem posing on elementary teachers’ beliefs about mathematics and mathematics teaching. School Science and Mathematics, 106(2), 64–73.
  • Brown, S. I., & Walter, M. I. (1993). Problem posing: Reflection and application. Hillsdale, NJ: Erlbaum.
  • Brown, S. I., & Walter, M. I. (2005). The art of problem posing. Mahwah, NJ: Lawrence Erlbaum.
  • Carraher, D. W. (1996). Learning about fractions. In L. P. Steffe and P. Nesher, (Eds.), Theories of Mathematical Learning (pp. 241–266). Mahwah, NJ: Lawrence Erlbaum.
  • Cathcart, W. G., Pothier, V. M., Vance, T. H., & Bezuk, N. S. (2003). Learning mathematics in elementary and middle schools. (3rd Ed.) River, N.J: Merrill/Prentice Hall.
  • Charalambous, C. Y. (2007). Developing and testing a scale for measuring students’ understanding of fractions. Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education 2, 105-112.
  • Charalambous, C. Y., & Pitta-Pantazi, D. (2006). Drawing on a theoretical model to study students’ understandings of fractions. Educational Studies in Mathematics, 64(3), 293-316.
  • Christou, C., Mousoulides, N., Pittalis, M., Pitta-Pantazi, D., & Sriraman, B. (2005). An empirical taxonomy of problem posing process. ZDM-The International Journal on Mathematics Education, 37(3), 149-158.
  • Crespo, S., & Sinclair, N. (2008). What makes a problem mathematically interesting? Inviting prospective teachers to pose better problems. Journal of Mathematics Teacher Education, 11(5), 395–415.
  • Hecht, S. A. (1998). Toward an information-processing account of individual differences in fraction skills. Journal of Educational Psychology, 90(3), 545-559.
  • Johnston, J., & Ahtee, M. (2006). Comparing primary student teachers’ attitudes, subject knowledge and pedagogical content knowledge needs in a physics activity. Teaching and Teacher Education, 22(4), 503-512.
  • Kar, T., & Isik, C. (2014). Analyzing problems posed by seventh grade middle school students for subtraction operation with fractions. Elementary Education Online, 13(4), 1223-1239.
  • Kieren, T. E. (1993). Rational and fractional numbers: From quotient fields to recursive understanding. In T. P. Carpenter, E. Fennema, & T. A. Romberg (Eds.), Rational Numbers: An Integration of Research (pp. 49–84). Hillsdale, NJ: Lawrence Erlbaum.
  • Kilic, C. (2013a). Pre-service primary teachers’ free problem-posing performances in the context of fractions: An example from Turkey. The Asia-Pacific Education Researcher, 22(4), 677-686.
  • Kilic, Ç. (2013b). Sınıf öğretmeni adaylarının farklı problem kurma durumlarında sergilemiş oldukları performansın belirlenmesi [Determining the performances of pre-service primary school teachers in problem posing situations]. Educational Sciences: Theory & Practice, 13(2), 1195–1211.
  • Kilpatrick, J. (1987). Problem formulating: where do good problems come from? In A. H. Schoenfeld (Ed.), Cognitive science and mathematics education (pp. 123-147). Hillsdale, NJ: Lawrence Erlbaum.
  • Lamon, S. J. (1999). Teaching fractions and ratios for understanding: Essential content knowledge and instructional strategies for teachers. Mahwah, NJ: Lawrence Erlbaum.
  • 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. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum.
  • 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.
  • Ministry of National Education [MoNE]. (2018). Mathematics program for elementary and middle school. Ankara: Devlet Kitapları Müdürlüğü.
  • National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.
  • National Council of Teachers of Mathematics. (1991). Professional standards for teaching mathematics. Reston, VA: National Council of Teachers of Mathematics.
  • National Council of Teachers of Mathematics. (2000). Principles and Standards for School Mathematics. Reston, VA: Author.
  • Newton, K. J., Willard, C., & Teufel, C. (2014). An examination of the ways that students with learning disabilities solve fraction computation problems. The Elementary School Journal, 115(1), 1–21.
  • Ni, Y., & Zhou, Y. D. (2005). Teaching and learning fraction and rational numbers: The origins and implications of whole number bias. Educational Psychologist, 40(1), 27–52.
  • Pantziara, M., & Philippou, G. (2012). Levels of students’ “conception” of fractions. Educational Studies in Mathematics, 79(1), 61-83.
  • Rizvi, N. F. (2004). Prospective teachers’ ability to pose word problems. International Journal for Mathematics Teaching and Learning, 12, 1-22.
  • Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19-28.
  • Silver, E. A., & Cai, J. (2005). Assessing students’ mathematical problem posing. Teaching Children Mathematics, 12(3), 129- 135.
  • Silver, E. A., Kilpatrick, J., & Schlesinger, B. (1990). Thinking through mathematics: Fostering inquiry and communication in mathematics classrooms. New York: The College Board.
  • Stoyanova, E., & Ellerton, N. F. (1996). A framework for research into students’ problem posing in school mathematics. In P. Clarkson, (Ed.), Technology in mathematics education (pp.518-525). Melbourne: Mathematics Education Research Group of Australasia.
  • Toluk-Ucar, Z. (2009). Developing pre-service teachers understanding of fractions through problem posing. Teaching and Teacher Education, 25(1), 166-175.

Are Pre-service Elementary Teachers able to Pose Problems for the Subtraction of Fractions?

Year 2018, Volume 5, Issue 2, 94 - 105, 01.10.2018

Abstract

References

  • 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.
  • Bailey, D. H., Hoard, M. K., Nugent, L., & Geary, D. C. (2012). Competence with fractions predicts gains in mathematics achievement. Journal of Experimental Child Psychology, 113(3), 447-455.
  • Barlow, A. T., & Cates, J. M. (2006). The impact of problem posing on elementary teachers’ beliefs about mathematics and mathematics teaching. School Science and Mathematics, 106(2), 64–73.
  • Brown, S. I., & Walter, M. I. (1993). Problem posing: Reflection and application. Hillsdale, NJ: Erlbaum.
  • Brown, S. I., & Walter, M. I. (2005). The art of problem posing. Mahwah, NJ: Lawrence Erlbaum.
  • Carraher, D. W. (1996). Learning about fractions. In L. P. Steffe and P. Nesher, (Eds.), Theories of Mathematical Learning (pp. 241–266). Mahwah, NJ: Lawrence Erlbaum.
  • Cathcart, W. G., Pothier, V. M., Vance, T. H., & Bezuk, N. S. (2003). Learning mathematics in elementary and middle schools. (3rd Ed.) River, N.J: Merrill/Prentice Hall.
  • Charalambous, C. Y. (2007). Developing and testing a scale for measuring students’ understanding of fractions. Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education 2, 105-112.
  • Charalambous, C. Y., & Pitta-Pantazi, D. (2006). Drawing on a theoretical model to study students’ understandings of fractions. Educational Studies in Mathematics, 64(3), 293-316.
  • Christou, C., Mousoulides, N., Pittalis, M., Pitta-Pantazi, D., & Sriraman, B. (2005). An empirical taxonomy of problem posing process. ZDM-The International Journal on Mathematics Education, 37(3), 149-158.
  • Crespo, S., & Sinclair, N. (2008). What makes a problem mathematically interesting? Inviting prospective teachers to pose better problems. Journal of Mathematics Teacher Education, 11(5), 395–415.
  • Hecht, S. A. (1998). Toward an information-processing account of individual differences in fraction skills. Journal of Educational Psychology, 90(3), 545-559.
  • Johnston, J., & Ahtee, M. (2006). Comparing primary student teachers’ attitudes, subject knowledge and pedagogical content knowledge needs in a physics activity. Teaching and Teacher Education, 22(4), 503-512.
  • Kar, T., & Isik, C. (2014). Analyzing problems posed by seventh grade middle school students for subtraction operation with fractions. Elementary Education Online, 13(4), 1223-1239.
  • Kieren, T. E. (1993). Rational and fractional numbers: From quotient fields to recursive understanding. In T. P. Carpenter, E. Fennema, & T. A. Romberg (Eds.), Rational Numbers: An Integration of Research (pp. 49–84). Hillsdale, NJ: Lawrence Erlbaum.
  • Kilic, C. (2013a). Pre-service primary teachers’ free problem-posing performances in the context of fractions: An example from Turkey. The Asia-Pacific Education Researcher, 22(4), 677-686.
  • Kilic, Ç. (2013b). Sınıf öğretmeni adaylarının farklı problem kurma durumlarında sergilemiş oldukları performansın belirlenmesi [Determining the performances of pre-service primary school teachers in problem posing situations]. Educational Sciences: Theory & Practice, 13(2), 1195–1211.
  • Kilpatrick, J. (1987). Problem formulating: where do good problems come from? In A. H. Schoenfeld (Ed.), Cognitive science and mathematics education (pp. 123-147). Hillsdale, NJ: Lawrence Erlbaum.
  • Lamon, S. J. (1999). Teaching fractions and ratios for understanding: Essential content knowledge and instructional strategies for teachers. Mahwah, NJ: Lawrence Erlbaum.
  • 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. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum.
  • 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.
  • Ministry of National Education [MoNE]. (2018). Mathematics program for elementary and middle school. Ankara: Devlet Kitapları Müdürlüğü.
  • National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.
  • National Council of Teachers of Mathematics. (1991). Professional standards for teaching mathematics. Reston, VA: National Council of Teachers of Mathematics.
  • National Council of Teachers of Mathematics. (2000). Principles and Standards for School Mathematics. Reston, VA: Author.
  • Newton, K. J., Willard, C., & Teufel, C. (2014). An examination of the ways that students with learning disabilities solve fraction computation problems. The Elementary School Journal, 115(1), 1–21.
  • Ni, Y., & Zhou, Y. D. (2005). Teaching and learning fraction and rational numbers: The origins and implications of whole number bias. Educational Psychologist, 40(1), 27–52.
  • Pantziara, M., & Philippou, G. (2012). Levels of students’ “conception” of fractions. Educational Studies in Mathematics, 79(1), 61-83.
  • Rizvi, N. F. (2004). Prospective teachers’ ability to pose word problems. International Journal for Mathematics Teaching and Learning, 12, 1-22.
  • Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19-28.
  • Silver, E. A., & Cai, J. (2005). Assessing students’ mathematical problem posing. Teaching Children Mathematics, 12(3), 129- 135.
  • Silver, E. A., Kilpatrick, J., & Schlesinger, B. (1990). Thinking through mathematics: Fostering inquiry and communication in mathematics classrooms. New York: The College Board.
  • Stoyanova, E., & Ellerton, N. F. (1996). A framework for research into students’ problem posing in school mathematics. In P. Clarkson, (Ed.), Technology in mathematics education (pp.518-525). Melbourne: Mathematics Education Research Group of Australasia.
  • Toluk-Ucar, Z. (2009). Developing pre-service teachers understanding of fractions through problem posing. Teaching and Teacher Education, 25(1), 166-175.

Details

Primary Language English
Journal Section Research Article
Authors

Sümeyra DOĞAN COŞKUN This is me
Eskisehir Osmangazi University, Eskisehir, TURKEY

Publication Date October 1, 2018
Published in Issue Year 2018, Volume 5, Issue 2

Cite

Bibtex @ { ojer594922, journal = {Osmangazi Journal of Educational Research}, eissn = {2651-4206}, address = {Osmangazi Journal of Educational Research (OJER) Eskişehir Osmangazi Üniversitesi Eğitim Bilimleri Enstitüsü Meşelik Yerleşkesi 26480 Eskişehir /TURKEY}, publisher = {Eskişehir Osmangazi University}, year = {2018}, volume = {5}, number = {2}, pages = {94 - 105}, title = {Are Pre-service Elementary Teachers able to Pose Problems for the Subtraction of Fractions?}, key = {cite}, author = {Doğan Coşkun, Sümeyra} }
APA Doğan Coşkun, S. (2018). Are Pre-service Elementary Teachers able to Pose Problems for the Subtraction of Fractions? . Osmangazi Journal of Educational Research , 5 (2) , 94-105 . Retrieved from https://dergipark.org.tr/en/pub/ojer/issue/47234/594922
MLA Doğan Coşkun, S. "Are Pre-service Elementary Teachers able to Pose Problems for the Subtraction of Fractions?" . Osmangazi Journal of Educational Research 5 (2018 ): 94-105 <https://dergipark.org.tr/en/pub/ojer/issue/47234/594922>
Chicago Doğan Coşkun, S. "Are Pre-service Elementary Teachers able to Pose Problems for the Subtraction of Fractions?". Osmangazi Journal of Educational Research 5 (2018 ): 94-105
RIS TY - JOUR T1 - Are Pre-service Elementary Teachers able to Pose Problems for the Subtraction of Fractions? AU - SümeyraDoğan Coşkun Y1 - 2018 PY - 2018 N1 - DO - T2 - Osmangazi Journal of Educational Research JF - Journal JO - JOR SP - 94 EP - 105 VL - 5 IS - 2 SN - -2651-4206 M3 - UR - Y2 - 2023 ER -
EndNote %0 Osmangazi Journal of Educational Research Are Pre-service Elementary Teachers able to Pose Problems for the Subtraction of Fractions? %A Sümeyra Doğan Coşkun %T Are Pre-service Elementary Teachers able to Pose Problems for the Subtraction of Fractions? %D 2018 %J Osmangazi Journal of Educational Research %P -2651-4206 %V 5 %N 2 %R %U
ISNAD Doğan Coşkun, Sümeyra . "Are Pre-service Elementary Teachers able to Pose Problems for the Subtraction of Fractions?". Osmangazi Journal of Educational Research 5 / 2 (October 2018): 94-105 .
AMA Doğan Coşkun S. Are Pre-service Elementary Teachers able to Pose Problems for the Subtraction of Fractions?. OJER. 2018; 5(2): 94-105.
Vancouver Doğan Coşkun S. Are Pre-service Elementary Teachers able to Pose Problems for the Subtraction of Fractions?. Osmangazi Journal of Educational Research. 2018; 5(2): 94-105.
IEEE S. Doğan Coşkun , "Are Pre-service Elementary Teachers able to Pose Problems for the Subtraction of Fractions?", Osmangazi Journal of Educational Research, vol. 5, no. 2, pp. 94-105, Oct. 2018