Fraction Models Used by Primary School Teachers

Adem Doğan, Neşe Işık Tertemiz

Abstract


Fractions and anything related to fractions are among the mathematics subjects that are challenging for primary school students to comprehend probably due to the fact that fractions have multiple meanings in different circumstances. Primary school teachers could overcome this challenge using various fraction models to facilitate students’ understanding the concept of fraction. With this in mind, the current study aimed to reveal the fraction models used by these teachers when teaching fractions. Accordingly, those used by 14 teachers were analyzed to see whether the meaning of fraction differs depending on the models used. This qualitative study adopted the single case research model. The data were collected from primary school teachers through a semi-structured interview form and descriptively analyzed. The study has concluded that the cluster model, the area model, and the length model are the most preferred models by the teachers and that their choice of models in teaching fractions differs across the sub-constructs of fractions.


Keywords


Primary school teacher, mathematics education, fractions, sub-construct, fraction models

Full Text:

PDF

References


Behr, M., Harel, G., Post, T., & Lesh, R. (1993). Rational numbers: Toward a semantic analysis-emphasis on the operator construct. In T. Carpenter, E. Fennema, T. Ramberg (Eds.), Rational numbers: An integration of research (pp. 13-47). Hillsdale, New Jersey: Lawrence Erlbaum.

Bright, G. W., Behr, M. J., Post, T. R., & Wachsmuth, I. (1988). Identifying fractions on number lines. Journal for Research in Mathematics Education, 19(3), 215-232.

Charalambous, C. Y., & Pitta-Pintazi, D. (2005). Revisiting a theoretical model on fractions: implications for teaching and research. In Chick, H. L. & Vincent, J. L. (Ed.), Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education, (pp. 233-240).

Charalambous, C. Y., & Pitta-Pantazi, D. (2007). Drawing on a theoretical model to study students’ understandings of fractions. Educational Studies in Mathematics, 64(3), 293-316. Doi:10.1007/s10649-006-9036-2

Clarke, D., Roche, A., & Mitchell, A. (2011). One-to-one student interviews provide powerful insights and clear focus for the teaching of fractions in the middle years. In J. Way & J. Bobis (Eds.), Fractions: Teaching for understanding (pp. 23-31). Australia: Australian Association of Mathematics Teachers.

Clarke, D., Roche, A., & Mitchell, A. (2011). One-to-one student interviews provide powerful insights and clear focus for the teaching of fractions in the middle years. J. Way, J. Bobis. Fractions: Teaching for understanding 23-31. Australia: Australian Association of Mathematics Teachers.

Creswell, J. W. (2013). Research design: Qualitative, quantitative, and mixed methods approaches. Thousand Oaks, CA: Sage.

Cramer, K. A., & Whitney, S. (2010). Learning rational number concepts and skills in elementary classrooms: Translating research to the elementary classroom. In D. V. Lambdin, & F. K. Lester (Eds.), Teaching and learning mathematics: Translating research to the elementary classroom (pp. 15-22). NCTM, Virginia: Reston.

Cramer, K., & Henry, A. (2002). Using manipulative models to build number sense for addition of fractions. In B. Litwiller & G. Bright (Eds.), Yearbook of Making sense of fractions, ratios, and proportions, (pp. 41-48). NCTM, Virginia: Reston.

Cramer, K., Wyberg, T., & Leavitt, S. (2008). The role of representations in fraction addition and subtraction. Mathematics teaching in the middle school, 13(8), 490.

Çelik, B., & Çiltaş, A. (2015). Investigation of the teaching process of 5th grade-fractions subject in terms of mathematical models. Bayburt Faculty of Education Journal, 10(1), 180-204.

Doğan, A., & Işık-Tertemiz, N. (2019). Investigating primary school teachers’ knowledge towards meanings of fractions. International Education Studies, 12(6), (pp.56-74). Doi:10.5539/ies.v12n6p56

Doğan, A., & Tertemiz, N. (2018). Examination of knowledge levels of primary school teacher candidates to fractional meanings. The Journal of Academic Social Science, 6(68), 580-597. Doi:10.16992/ASOS.13582

Gökkurt, B., Soylu, Y., & Demir, Ö. (2015). The investigation of middle school mathematics

teachers' views on the difficulty levels of posed problems. Necatibey Eğitim Fakültesi Elektronik Fen ve Matematik Eğitimi Dergisi, 9(2)1-25.

Işık, C., & Kar, T. (2012). İlköğretim matematik öğretmeni adaylarının kesirlerde bölmeye yönelik kurdukları problemlerde hata analizi [Error analysis of the problems established by fractions of elementary mathematics teacher candidates]. Kuram ve Uygulamada Eğitim Bilimleri, 12(3), 2289-2309.

Kadhi, T. (2005). Online assessment: A study of the validation and implementation of a formative online diagnostic tool in developmental mathematics for college students. Doctoral Dissertation, Office of Graduate Studies of Texas A&M University, Texas.

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). Mahwah, New Jersey: Lawrence Erlbaum.

Leymun, Ş. O., Odabaşı, H. F., & Yurdakul, I. K. (2017). The importance of case study research in educational settings. Journal of Qualitative Research in Education, 5(3), 367-385.

Merriam, S. B. (2013). Nitel araştırma desen ve uygulama için bir rehber (S. Turan, Çev. Ed.). Ankara: Nobel.

Miles, M. B., Huberman, A. M., & Saldana, J. (1984). Qualitative data analysis: A sourcebook. London: SAGE.

Olkun, S. &Toluk, Z. (2003). Matematik öğretimi [Mathematics teaching]. Ankara; Anı.

Olkun, S., & Toptaş, V. (2007). Resimli matematik terimleri sözlüğü [Illustrated math glossary]. Ankara: Maya.

Pantziara, M., & Philippou, G. (2012). Levels of students' "conception" of fractions. Educational Studies in Mathematics, 79, 61-83.

Patton, M. Q. (2014). Nitel araştırma yöntemleri, beş yaklaşıma göre nitel araştırma ve araştırma deseni. Çeviri Ed. M. Bütün & S.B. Demir) Ankara: Siyasal Kitabevi.

Pesen, C. (2008). Students’ learning difficulties and misconceptions in pointing the fractions on the number line. İnönü University Faculty of Education Journal, 9(15), 157-168.

Post, T., Cramer, K., Harel, G., Kiernen, T., & Lesh, R. (1998). Research on rational number, ratio and proportionality. Proceedings of the Twentieth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, 20(1), 89-93.

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

Toluk-Uçar, Z. (2011). Öğretmen adaylarının pedagojik içerik bilgisi: Öğretimsel açıklamalar [Pre-service teachers’ pedagogic content knowledge: Instructional explanations]. Turkish Journal of Computer and Mathematics Education, (2), 87-102.

Toptaş, V., Han, B., & Akın, Y. (2017). Sınıf öğretmenlerinin kesirlerin farklı anlam ve modelleri konusunda görüşlerinin incelenmesi. Sakarya Üniversitesi Eğitim Fakültesi Dergisi, (33), 49-67.

Van De Walle, J. E., (1989). Elementary school mathematics. New York: Longman.

Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. W. (2014). İlkokul ve ortaokul matematiği: Gelişimsel yaklaşımla öğretim [Primary and secondary mathematics: Teaching with developmental approach] (7. Baskı). (Çev. S. Durmuş). Ankara: Nobel.

Yıldırım, A., & Şimşek, H. (2013). Sosyal bilimlerde nitel araştırma yöntemleri [Qualitative research methods in social sciences]. Ankara: Seçkin.


Refbacks

  • There are currently no refbacks.




Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

 ISSN: 1305-3515