Research Article
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The Views of Elementary Mathematics Teachers about Using Problem Posing for Addition of Fractions

Year 2013, Volume: 2 Issue: 1, 27 - 46, 19.03.2016

Tuğrul Kar Cemalettin Işık

Abstract

The identification of the viewpoints of teachers on problem posing and their views on the
application process may contribute to studies to be conducted for eliminating the
shortcomings that might appear. Within this scope, this study aims at identifying the
viewpoints of elementary mathematics teachers on problem posing method for addition of
fractions and the application process of this method in the classroom. The study was
conducted with the participation of ten elementary school mathematics teachers working in
the Erzurum county center during the spring semester of the 2011-2012 academic year.
Case study method that is among the qualitative research approaches was used in the study.
The data were collected using three open-ended questions about problem posing. The
obtained data were analyzed by using the categorical analysis technique of the content
analysis type. The study findings suggested that, generally, teachers had positive
viewpoints on the inclusion of problem posing for addition operations with fractions.
However, they had a limited understanding of the problem posing application in a
classroom environment.

Keywords

Elementary mathematics teachers problem posing fractions addition of fractions

References

  • Abu-Elwan, R. (1999). The development of mathematical problem posing skills for prospective middle school teachers. In A. Rogerson (Ed.) Proceedings of theInternational conference on Mathematical Education into the 21st Century: Social Challenges, Issues and Approaches, (Vol. II, pp. 1-8), Cairo Egypt.
  • Abu-Elwan, R. (2002). Effectiveness of problem posing strategies on prospective mathematics teachers’ problem solving performance. Journal of Science and Mathematics Education in S.E. Asia, 25(1), 56-69.
  • Akay, H. (2006). Problem kurma yaklaşımı ile yapılan matematik öğretiminin öğrencilerin akademik başarısı, problem çözme becerisi ve yaratıcılığı üzerindeki etkisinin incelenmesi (Yayınlanmamış Doktora Tezi). Gazi Üniversitesi, Ankara.
  • Akay, H., & Boz, N. (2008). Prospective teachers’ views about problem-posing activities. Procedia Social and Behavioral Sciences, 1, 1192–1198.
  • Akay, H., & Boz, N. (2010). The effect of problem posing oriented analyses-II course on the attitudes toward mathematics and mathematics self-efficacy of elementary prospective mathematics teachers. Australian Journal of Teacher Education, 35(1), 59-75.
  • Amato, A. S. (2005). Developıng students’ understandıng of the concept of fractıons as numbers. Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education, Australia.
  • Barlow, A. T., & Cates, J. M. (2010). The impact of problem posing on elementary teachers' beliefs about mathematics and mathematics teaching. School Science and Mathematics, 106(2), 64-73.
  • Barlow, A. T., & Drake, J. M. (2008). Division by a fraction: Assessing understanding through problem writing. Teaching Children Mathematics, 13, 326-332.
  • Brown, S. I., & Walter, M. I. (1993). Problem posing in mathematics education. In S. I. Brown & M. I. Walter (Eds.), Problem posing: Reflection and applications (pp. 16-27). Hillsdale, NJ: Lawrence Erlbaum Associates.
  • Bulgar, S. (2003). Children's sense-making of division of fractions. The Journal of Mathematical Behavior, 20, 319-334.
  • Cai, J., & Hwang, S. (2002). Generalized and generative thinking in US and Chinese students’ mathematical problem solving and problem posing. Journal of Mathematical Behavior, 21, 401–421.
  • Cankoy, O., & Darbaz, S. (2010). Effect of a problem posing based problem solving instruction on understanding problem. Hacettepe University Journal of Education, 38, 11-24.
  • Christou, C., Mousoulides, N., Pittalis, M., Pitta-Pantazi, D., & Sriraman, B. (2005). An empirical taxonomy of problem posing processes. ZDM, 37(3), 149 – 158.
  • Corbin, J. M., & Strauss, A. C. (2007). Basics of qualitative research: Techniques and procedures for developing grounded theory. Thousand Oaks, CA: Sage Publication.
  • Crespo, S., & Sinclair, N. (2008). What makes a problem mathematically interesting? Inviting prospective teachers to pose better problems. Journal Mathematics Teacher Education, 11, 395–415.
  • Crespo, S. (2003). Learning to pose mathematical problems: Exploring changes in preservice teachers’ practices. Educational Studies in Mathematics, 52, 243–270.
  • Cunningham, R. (2004). Problem posing: an opportunity for increasing student responsibility. Mathematics and Computer Education, 38(1), 83-89.
  • Dede, Y., & Yaman, S. (2005). Investigation of prospective teachers’ mathematical problem posing and problem solving skills. Eurasian Journal of Educational Research, 18, 236– 252.
  • 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.
  • Dooren, W. V., Verschaffel, L., & Onghena, P. (2002). The impact of preservice teachers’ content knowledge on their evaluation of students’ strategies for solving arithmetic and algebra words problems. Journal for Research in Mathematics Education, 33(5), 319- 351.
  • English, L. D., & Halford, G. S. (1995). Mathematics education: Models and processes. New Jersey: Lawrence Erlbaum Associates.
  • English, L. D. (1997). The development of fifth-grade children’s problem-posing abilities. Educational Studies in Mathematics, 34, 183-217.
  • English, L. D. (1998). Children’s problem posing within formal and informal contexts. Journal for Research in Mathematics Education, 29(1), 83-106.
  • English, L. D. (2003). Problem posing in elementary curriculum. In F. Lester, & R. Charles (Eds.), Teaching mathematics through problem solving. Reston, Virginia: National Council of Teachers of Mathematics.
  • Fennema, E., & Franke, M. (2006). Teachers’ knowledge and its impact. In Grouws, D.A. (Ed). Handbook of Research on Mathematics Teaching and Learning (p.147-164), Reston, VA: NCTM.
  • Gonzales, N. A. (1998). A blueprint for problem posing. School Science and Mathematics, 94(2), 78- 85.
  • Hasemann, K. (1981). On difficulties with fractions. Educational Studies in Mathematics 12, 71-87.
  • Herman, J., Ilucova, L., Kremsova, V., Pribyl, J., Ruppeldtova, J., Simpson, A., Stehlikova, N., Sulista, M., & Ulrychova, M. (2004). Images of fractions as process and images of fractions in processes. Proceedings of the 28th Conference of the International Group of the Psychology of Mathematics Education, Bergen.
  • 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.
  • 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., Işık, A., & Kar, T. (2011). Öğretmen adaylarının sözel ve görsel temsillere yönelik kurdukları problemlerin analizi. Pamukkale Üniversitesi Eğitim Fakültesi Dergisi, 39- 49.
  • Işık, C., & Kar, T. (2012a) The Analysis of the Problems Posed by the Preservice Teachers About Equations.Australian Journal of Teacher Education, 37(9), 92-113.
  • Işık, C., & Kar, T. (2012b). 7. sınıf öğrencilerinin kesirlerde toplama işlemine kurdukları problemlerin analizi. İlköğretim Online, 11(4), 1021-1035. [Online]: http://ilkogretim- online.org.tr adresinden 12.09.2012 tarihinde edinilmiştir.
  • Işık, C. & Kar, T. (2012c). Matematik Dersinde Problem Kurmaya Yönelik Öğretmen Görüşleri Üzerine Nitel Bir Çalışma. Milli Eğitim Dergisi, 194, 199-215.
  • Işık, C., Kar, T., Işık, A. & Albayrak, M. (2012). İlköğretim 6. sınıf öğrencilerinin doğal sayılarda kalanlı bölme işlemine yönelik problem kurma ve çözme becerilerinin araştırılması. 11. Ulusal Sınıf Öğretmenliği Eğitimi Sempozyumu, Rize.
  • Kar, T., Özdemir, E., İpek, A. S., & Albayrak, M. (2010). The relation between the problem posing and problem solving skills of prospective elementary mathematics teachers. Social and Behavioral Sciences, 2, 1577–1583.
  • Kerslake, D. (1986). Fractions: Children ’s strategies and errors. A report of the strategies and errors in secondary mathematics project. Windsor, England: NFER-Nelson.
  • Knott, L. (2010). Problem posing from the foundations of mathematics. TMME, 7, 413-432.
  • Kulm, G. (2008). Teachers’ mathematics knowledge. School Science and Mathematics, 108, 2-3.
  • Lavy, I., & Shriki, A. (2007). Problem posing as a means for developing mathematical knowledge of prospective teachers. Paper presented at the meeting of 31st Conference of the International Group for the Psychology of Mathematics Education, Seoul.
  • Leung, S. S. (1993). The relation of mathematical knowledge and creative thinking to the mathematical problem posing of prospective elementary school teachers on tasks differing in numerical information content (Unpublished doctoral dissertation). Pittsburg.
  • Lowrie, T. (2002). Young children posing problems: the influence of teacher intervention on the type of problems children pose. Mathematics Education Research Journal,14(2), 87-98.
  • Luft, J. A., & Gillian, H. R. (2007). Capturing Science Teachers’ Epistemological Beliefs:
  • The Development of the Teacher Beliefs Interview. Electronic Journal of Science
  • Education, 11(2), 38-63.
  • 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.
  • Mack, N. K. (1995). Confounding whole-number and fraction concepts when building on informal knowledge. Journal for Research in Mathematics Education, 26(5), 422-441.
  • 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.
  • National Council of Teachers of Mathematics (NCTM). (2000). Principles and Standard for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
  • 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.
  • Nicolaou, A. A., & Philippou, G. N. (2007). Efficacy beliefs, problem posing, and mathematics achievement. Focus on Learning Problems in Mathematics, 29(4), 48-70.
  • 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. http://www.cimt.plymouth.ac.uk/Journal/rizvi.pdf adresinden 17.10.2011 tarihinde alınmıştır.
  • Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1-22.
  • Siegler, R. S. (2003). Implications of cognitive science research for mathematics education. In Kilpatrick, J., Martin, W. B., & Schifter, D. E. (Eds.), A research companion to principles and standards for school mathematics (pp. 219-233). Reston, VA: National Council of Teachers of Mathmatics.
  • Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19–28.
  • Silver, E. A., & Cai, J. (1996). An analysis of arithmetic problem posing by middle school students. Journal for Research in Mathematics Education, 27, 521–539.
  • Silver, E. A., & Cai, J. (2005). Assessing students’ mathematical problem posing.
  • Teaching Children Mathematics, 12(3), 129-135.
  • Smith, M. (2000). Redefining success in mathematics teaching and learning. Mathematics Teaching in the Middle School, 5(6), 378-386.
  • Stickles, P. R. (2006). An analysis of secondary and middle school teachers’ mathematical problem posing (Unpublished doctoral dissertation). University of Indiana, Bloomington.
  • 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.
  • Stoyanova, E., & Ellerton, N. F. (1996). A framework for research into students’ problem posing. In P. Clarkson (Ed.), Technology in Mathematics Education (pp.518–525). Melbourne: Mathematics Education Research Group of Australasia.
  • Ticha, M., & Hošpesová, A. (2009). Problem posing and development of pedagogical content knowledge in pre-service teacher training. Paper presented at the meeting of CERME 6, Lyon.
  • Toluk-Uçar, Z. (2009). Developing pre-service teachers understanding of fractions through problem posing, Teaching and Teacher Education, 25, 166–175.
  • Whiten, D. J. (2004). Building a mathematical community through problem posing. In R. N. Rubenstein & G. W. Bright (Eds.), Perspectives on the teaching of mathematics: Sixty- sixth yearbook (pp. 129-140). Reston, VA: National Council of Teachers of Mathematics.
  • Yıldırım, A., & Şimşek, H. (2008). Sosyal bilimlerde nitel araştırma yöntemleri, Ankara, Seçkin Yayıncılık.
  • Yuan, X., & Sriraman, B. (2010). An exploratory study of relationshıps between students’ creativity and mathematical problem-posing abilities. In B.Sriraman, K. Lee (eds.), The Elements of Creativity and Giftedness in Mathematics, xx–xy.
  • Zakaria, E., & Ngah, N. (2011). A preliminary analysis of students’ problem-posing ability and its relationship to attitudes towards problem solving. Research Journal of Applied Sciences, Engineering and Technology, 3(9), 866-870.

İlköğretim Matematik Öğretmenlerinin Kesirlerde Toplama İşleminde Problem Kurmayı Kullanmaya İlişkin Görüşleri

Year 2013, Volume: 2 Issue: 1, 27 - 46, 19.03.2016

Tuğrul Kar Cemalettin Işık

Abstract

Öğretmenlerin problem kurmaya yönelik bakış açıları ve uygulama sürecine yönelik görüşlerinin belirlenmesi ortaya çıkabilecek eksikliklerin giderilmesine yönelik yapılabilecek çalışmalara katkı sağlayabilecektir. Bu bağlamda çalışmada, ilköğretim matematik öğretmenlerinin kesirlerde toplama işleminde problem kurma yöntemine ve bu yöntemin uygulama sürecine yönelik görüşlerinin belirlenmesi amaçlanmıştır. Çalışma, 2011-2012 eğitim-öğretim yılı bahar döneminde Erzurum il merkezinde görev yapan on ilköğretim matematik öğretmeni ile yürütülmüştür. Çalışmada, nitel araştırma yaklaşımları içerisinde yer alan durum çalışması yöntemi kullanılmıştır. Veriler üç açık-uçlu sorudan oluşan görüşme formu kullanılarak toplanmıştır. Elde edilen veriler, içerik analiz türleri içerisinde yer alan kategorisel analiz tekniği kullanılarak çözümlenmiştir. Çalışmanın bulguları genel olarak öğretmenlerin kesirlerde toplama işlemine yönelik problem kurmaya yer verilmesi noktasında olumlu görüşlere sahip olduklarını buna karşın problem kurmanın ders ortamlarında uygulanmasına yönelik sınırlı bir anlayışa sahip olduklarını ortaya koymuştur.

Keywords

İlköğretim matematik öğretmenleri problem kurma kesirler kesirlerde toplama

References

  • Abu-Elwan, R. (1999). The development of mathematical problem posing skills for prospective middle school teachers. In A. Rogerson (Ed.) Proceedings of theInternational conference on Mathematical Education into the 21st Century: Social Challenges, Issues and Approaches, (Vol. II, pp. 1-8), Cairo Egypt.
  • Abu-Elwan, R. (2002). Effectiveness of problem posing strategies on prospective mathematics teachers’ problem solving performance. Journal of Science and Mathematics Education in S.E. Asia, 25(1), 56-69.
  • Akay, H. (2006). Problem kurma yaklaşımı ile yapılan matematik öğretiminin öğrencilerin akademik başarısı, problem çözme becerisi ve yaratıcılığı üzerindeki etkisinin incelenmesi (Yayınlanmamış Doktora Tezi). Gazi Üniversitesi, Ankara.
  • Akay, H., & Boz, N. (2008). Prospective teachers’ views about problem-posing activities. Procedia Social and Behavioral Sciences, 1, 1192–1198.
  • Akay, H., & Boz, N. (2010). The effect of problem posing oriented analyses-II course on the attitudes toward mathematics and mathematics self-efficacy of elementary prospective mathematics teachers. Australian Journal of Teacher Education, 35(1), 59-75.
  • Amato, A. S. (2005). Developıng students’ understandıng of the concept of fractıons as numbers. Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education, Australia.
  • Barlow, A. T., & Cates, J. M. (2010). The impact of problem posing on elementary teachers' beliefs about mathematics and mathematics teaching. School Science and Mathematics, 106(2), 64-73.
  • Barlow, A. T., & Drake, J. M. (2008). Division by a fraction: Assessing understanding through problem writing. Teaching Children Mathematics, 13, 326-332.
  • Brown, S. I., & Walter, M. I. (1993). Problem posing in mathematics education. In S. I. Brown & M. I. Walter (Eds.), Problem posing: Reflection and applications (pp. 16-27). Hillsdale, NJ: Lawrence Erlbaum Associates.
  • Bulgar, S. (2003). Children's sense-making of division of fractions. The Journal of Mathematical Behavior, 20, 319-334.
  • Cai, J., & Hwang, S. (2002). Generalized and generative thinking in US and Chinese students’ mathematical problem solving and problem posing. Journal of Mathematical Behavior, 21, 401–421.
  • Cankoy, O., & Darbaz, S. (2010). Effect of a problem posing based problem solving instruction on understanding problem. Hacettepe University Journal of Education, 38, 11-24.
  • Christou, C., Mousoulides, N., Pittalis, M., Pitta-Pantazi, D., & Sriraman, B. (2005). An empirical taxonomy of problem posing processes. ZDM, 37(3), 149 – 158.
  • Corbin, J. M., & Strauss, A. C. (2007). Basics of qualitative research: Techniques and procedures for developing grounded theory. Thousand Oaks, CA: Sage Publication.
  • Crespo, S., & Sinclair, N. (2008). What makes a problem mathematically interesting? Inviting prospective teachers to pose better problems. Journal Mathematics Teacher Education, 11, 395–415.
  • Crespo, S. (2003). Learning to pose mathematical problems: Exploring changes in preservice teachers’ practices. Educational Studies in Mathematics, 52, 243–270.
  • Cunningham, R. (2004). Problem posing: an opportunity for increasing student responsibility. Mathematics and Computer Education, 38(1), 83-89.
  • Dede, Y., & Yaman, S. (2005). Investigation of prospective teachers’ mathematical problem posing and problem solving skills. Eurasian Journal of Educational Research, 18, 236– 252.
  • 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.
  • Dooren, W. V., Verschaffel, L., & Onghena, P. (2002). The impact of preservice teachers’ content knowledge on their evaluation of students’ strategies for solving arithmetic and algebra words problems. Journal for Research in Mathematics Education, 33(5), 319- 351.
  • English, L. D., & Halford, G. S. (1995). Mathematics education: Models and processes. New Jersey: Lawrence Erlbaum Associates.
  • English, L. D. (1997). The development of fifth-grade children’s problem-posing abilities. Educational Studies in Mathematics, 34, 183-217.
  • English, L. D. (1998). Children’s problem posing within formal and informal contexts. Journal for Research in Mathematics Education, 29(1), 83-106.
  • English, L. D. (2003). Problem posing in elementary curriculum. In F. Lester, & R. Charles (Eds.), Teaching mathematics through problem solving. Reston, Virginia: National Council of Teachers of Mathematics.
  • Fennema, E., & Franke, M. (2006). Teachers’ knowledge and its impact. In Grouws, D.A. (Ed). Handbook of Research on Mathematics Teaching and Learning (p.147-164), Reston, VA: NCTM.
  • Gonzales, N. A. (1998). A blueprint for problem posing. School Science and Mathematics, 94(2), 78- 85.
  • Hasemann, K. (1981). On difficulties with fractions. Educational Studies in Mathematics 12, 71-87.
  • Herman, J., Ilucova, L., Kremsova, V., Pribyl, J., Ruppeldtova, J., Simpson, A., Stehlikova, N., Sulista, M., & Ulrychova, M. (2004). Images of fractions as process and images of fractions in processes. Proceedings of the 28th Conference of the International Group of the Psychology of Mathematics Education, Bergen.
  • 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.
  • 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., Işık, A., & Kar, T. (2011). Öğretmen adaylarının sözel ve görsel temsillere yönelik kurdukları problemlerin analizi. Pamukkale Üniversitesi Eğitim Fakültesi Dergisi, 39- 49.
  • Işık, C., & Kar, T. (2012a) The Analysis of the Problems Posed by the Preservice Teachers About Equations.Australian Journal of Teacher Education, 37(9), 92-113.
  • Işık, C., & Kar, T. (2012b). 7. sınıf öğrencilerinin kesirlerde toplama işlemine kurdukları problemlerin analizi. İlköğretim Online, 11(4), 1021-1035. [Online]: http://ilkogretim- online.org.tr adresinden 12.09.2012 tarihinde edinilmiştir.
  • Işık, C. & Kar, T. (2012c). Matematik Dersinde Problem Kurmaya Yönelik Öğretmen Görüşleri Üzerine Nitel Bir Çalışma. Milli Eğitim Dergisi, 194, 199-215.
  • Işık, C., Kar, T., Işık, A. & Albayrak, M. (2012). İlköğretim 6. sınıf öğrencilerinin doğal sayılarda kalanlı bölme işlemine yönelik problem kurma ve çözme becerilerinin araştırılması. 11. Ulusal Sınıf Öğretmenliği Eğitimi Sempozyumu, Rize.
  • Kar, T., Özdemir, E., İpek, A. S., & Albayrak, M. (2010). The relation between the problem posing and problem solving skills of prospective elementary mathematics teachers. Social and Behavioral Sciences, 2, 1577–1583.
  • Kerslake, D. (1986). Fractions: Children ’s strategies and errors. A report of the strategies and errors in secondary mathematics project. Windsor, England: NFER-Nelson.
  • Knott, L. (2010). Problem posing from the foundations of mathematics. TMME, 7, 413-432.
  • Kulm, G. (2008). Teachers’ mathematics knowledge. School Science and Mathematics, 108, 2-3.
  • Lavy, I., & Shriki, A. (2007). Problem posing as a means for developing mathematical knowledge of prospective teachers. Paper presented at the meeting of 31st Conference of the International Group for the Psychology of Mathematics Education, Seoul.
  • Leung, S. S. (1993). The relation of mathematical knowledge and creative thinking to the mathematical problem posing of prospective elementary school teachers on tasks differing in numerical information content (Unpublished doctoral dissertation). Pittsburg.
  • Lowrie, T. (2002). Young children posing problems: the influence of teacher intervention on the type of problems children pose. Mathematics Education Research Journal,14(2), 87-98.
  • Luft, J. A., & Gillian, H. R. (2007). Capturing Science Teachers’ Epistemological Beliefs:
  • The Development of the Teacher Beliefs Interview. Electronic Journal of Science
  • Education, 11(2), 38-63.
  • 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.
  • Mack, N. K. (1995). Confounding whole-number and fraction concepts when building on informal knowledge. Journal for Research in Mathematics Education, 26(5), 422-441.
  • 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.
  • National Council of Teachers of Mathematics (NCTM). (2000). Principles and Standard for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
  • 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.
  • Nicolaou, A. A., & Philippou, G. N. (2007). Efficacy beliefs, problem posing, and mathematics achievement. Focus on Learning Problems in Mathematics, 29(4), 48-70.
  • 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. http://www.cimt.plymouth.ac.uk/Journal/rizvi.pdf adresinden 17.10.2011 tarihinde alınmıştır.
  • Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1-22.
  • Siegler, R. S. (2003). Implications of cognitive science research for mathematics education. In Kilpatrick, J., Martin, W. B., & Schifter, D. E. (Eds.), A research companion to principles and standards for school mathematics (pp. 219-233). Reston, VA: National Council of Teachers of Mathmatics.
  • Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19–28.
  • Silver, E. A., & Cai, J. (1996). An analysis of arithmetic problem posing by middle school students. Journal for Research in Mathematics Education, 27, 521–539.
  • Silver, E. A., & Cai, J. (2005). Assessing students’ mathematical problem posing.
  • Teaching Children Mathematics, 12(3), 129-135.
  • Smith, M. (2000). Redefining success in mathematics teaching and learning. Mathematics Teaching in the Middle School, 5(6), 378-386.
  • Stickles, P. R. (2006). An analysis of secondary and middle school teachers’ mathematical problem posing (Unpublished doctoral dissertation). University of Indiana, Bloomington.
  • 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.
  • Stoyanova, E., & Ellerton, N. F. (1996). A framework for research into students’ problem posing. In P. Clarkson (Ed.), Technology in Mathematics Education (pp.518–525). Melbourne: Mathematics Education Research Group of Australasia.
  • Ticha, M., & Hošpesová, A. (2009). Problem posing and development of pedagogical content knowledge in pre-service teacher training. Paper presented at the meeting of CERME 6, Lyon.
  • Toluk-Uçar, Z. (2009). Developing pre-service teachers understanding of fractions through problem posing, Teaching and Teacher Education, 25, 166–175.
  • Whiten, D. J. (2004). Building a mathematical community through problem posing. In R. N. Rubenstein & G. W. Bright (Eds.), Perspectives on the teaching of mathematics: Sixty- sixth yearbook (pp. 129-140). Reston, VA: National Council of Teachers of Mathematics.
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There are 71 citations in total.

Details

Primary Language Turkish
Journal Section Articles
Authors

Tuğrul Kar

Cemalettin Işık

Publication Date March 19, 2016
Published in Issue Year 2013Volume: 2 Issue: 1

Cite

APA Kar, T., & Işık, C. (2016). İlköğretim Matematik Öğretmenlerinin Kesirlerde Toplama İşleminde Problem Kurmayı Kullanmaya İlişkin Görüşleri. Cumhuriyet Uluslararası Eğitim Dergisi, 2(1), 27-46.
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