Ozlem Ozcakir Sumen


Whole-half-quarter are important mathematical concepts that form the basis of fractions and should be well understood for advancing mathematical topics. The aim of this study is to determine the primary school students' abstraction levels of whole-half-quarter concepts according to RBC theory. The participants of the study are six students (8 age group) from the second grade of primary school. The data of the research which is a case study were collected through worksheets and semi-structured interviews. The data obtained from interviews were analyzed by qualitative data analysis steps. The abstraction levels of students were evaluated according to RBC theory. As a result of the study, it was seen that many of the students could not abstract the whole, half and quarter concepts. It was determined that difficulties of students to abstract the whole-half-quarter concepts resulted from reasons such as not understanding the half and quarter concepts, not being able to divide the whole into two equal parts, not being able to divide one dimensional shapes into half and quarter, generalizing dividing into quarter as putting a "+", not being able to divide into four equal parts for quarter.


Abstraction; Fractions; Mathematics Education; RBC Theory; Whole-Half-Quarter Concepts

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Alacac?, C. (2010). Ö?rencilerin kesirler konusundaki kavram yan?lg?lar?. In E. Bingölbali ve M. F. Özmantar (Eds). ?lkö?retimde kar??la??lan matematiksel zorluklar ve çözüm önerileri, (p. 63-94), Ankara: Pegem Akademi.

Baykul, Y. (2011). ?lkö?retimde matematik ö?retimi (10. Bask?). Ankara: Pegem Akademi.

Bikner-Ahsbahs, A. (2004). Towards the emergence of constructing mathematical meanings. Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, 2, 119-126.

Bikner-Ahsbahs, A. (2019). The research pentagon: A diagram with which to think about research. In Compendium for Early Career Researchers in Mathematics Education (pp. 153-180). Springer, Cham.

Brown, G., & Quinn, R.J. (2006). Algebra students' difficulty with fractions: An error analysis. Australian Mathematics Teacher, 62(4), 28-40.

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.

Cramer, K.A., Post, T.R., & Delmas, R.C. (2002). Initial fraction learning by fourth-and fifth-grade students: A comparison of the effects of using commercial curricula with the effects of using the rational number project curriculum. Journal for Research in Mathematics Education, 33(2), 111-144.

Creswell, J.W. (2013). Nitel ara?t?rma yöntemleri, be? yakla??ma göre nitel ara?t?rma ve ara?t?rma deseni (3. bask?dan çeviri). Çev. Ed: M. Bütün, S. B. Demir. Ankara: Siyasal Kitabevi.

Dooley, T. (2007). Construction of knowledge by primary pupils: The role of whole-class interaction. In Proceedings of CERME, 5, 1658-1668.

Dreyfus, T. (2007). Processes of abstraction in context the nested epistemic actions model. Retrieved from

Dreyfus, T., Hadas, N., Hershkowitz, R. & Schwarz, B. (2006). Mechanisms for consolidating knowledge constructs. Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education. Prague, Czech Republic.

Dreyfus, T., Hershkowitz, R., & Schwarz, B. (2001). Abstraction in context II: The case of peer interaction. Cognitive Science Quarterly, 1(3/4), 307-368.

Dreyfus, T., & Tsamir, P. (2004). Ben's consolidation of knowledge structures about infinite sets. The Journal of Mathematical Behavior, 23(3), 271-300.

Erbilgin, E., ?ahin, B., & Ar?kan, S. (2017). Pasta dilimlerinin fiyat? ne kadar?. Journal of Inquiry Based Activities, 5(1), 34-47.

Gilboa, N., Kidron, I., & Dreyfus, T. (2019). Constructing a mathematical definition: the case of the tangent. International Journal of Mathematical Education in Science and Technology, 50(3), 421-446.

Guler, H.K., & Gurbuz, M.C. (2018). Construction process of the length of [cube root of 2] by paper folding. International Journal of Research in Education and Science, 4(1), 121-135.

Halverscheid, S. (2008). Building a local conceptual framework for epistemic actions in a modelling environment with experiments. ZDM Mathematics Education, 40(2), 225-234.

Hershkowitz, R., Schwarz, B., & Dreyfus, T., (2001). Abstraction in context: epistemic actions. Journal for Research in Mathematics Education, 32(2), 195-222.

Kaplan, A., ??leyen, T., & Öztürk, M. (2011). The misconceptions in ratio and proportion concept among 6th grade students. Kastamonu Education Journal, 19(3), 953-968.

Kidron, I., & Dreyfus, T. (2009). Justification, enlightenment and the explanatory nature of proof. In Proceedings of the ICMI Study 19 Conference: Proof and proving in mathematics education, 1, 244-249.

Merriam, S.B. (2013). Nitel ara?t?rma desen ve uygulama için bir rehber (3. bask?dan çeviri). Çev. Ed: S. Turan. Ankara: Nobel Yay?nc?l?k.

Monaghan, J., & Ozmantar, M.F. (2006). Abstraction and consolidation. Educational Studies in Mathematics, 62(3), 233-258.

National Ministry of Education. (2018). Matematik dersi ö?retim program? (?lkokul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. s?n?flar). Retrieved from

Olkun, S. & Toluk, Z. (2003). Matematik ö?retimi. Ankara: An? Yay?nc?l?k.

Ozmantar, M.F., & Monaghan, J. (2007). A dialectical approach to the formation of mathematical abstractions. Mathematics Education Research Journal, 19(2), 89-112.

Schwarz, B., Dreyfus, T., Hadas, N. & Hershkowitz, R. (2004). Teacher guidance of knowledge construction. Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education. Bergen, Norway.

Sowder, J., & Wearne, D. (2006). What do we know about eighth – grade achievement? Mathematics Teaching in the Middle School, 11(6), 285-293.

Stafylidou, S., & Vosniadou, S. (2004). The development of students’ understanding of the numerical value of fractions. Learning and Instruction, 14(5), 503-518.

Temur, Ö.D. (2015). Opinions of teachers of fourth and fifth grade about teaching fractions: A phenomenograhic research. Dumlup?nar Üniversitesi Sosyal Bilimler Dergisi, 29.

Van de Walle, J.A., Karp, K.S. & Bay Williams, J.M. (2012). ?lkokul ve ortaokul matemati?i geli?imsel yakla??mla ö?retim (Yedinci bask?dan çeviri, S. Durmu? Çev. Ed.). Ankara: Nobel Yay?nc?l?k.



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Journal on Mathematics Education
Doctoral Program on Mathematics Education
Faculty of Teacher Training and Education, Universitas Sriwijaya
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