Fraction or division? Conceptual misunderstandings in early fraction instruction in elementary school

DOI: https://doi.org/10.34007/jdm.v7i1.2883
Lia Ardiansari(1), Ayubu Ismail Ngao(2), Helma Mustika(3),


(1) Universitas Panca Marga, Probolinggo, Jawa Timur, Indonesia, 67271
(2) Mkwawa University College of Education, Iringa, Tanzania, 51111
(3) STKIP Insan Madani, Airmolek, Riau, Indonesia, 29352

Abstract


Many elementary students encounter difficulties in comprehending fractions conceptually and frequently confuse them with basic division operations. This persistent misconception is partially attributed to the manner in which fractions are introduced in early-grade textbooks, which often employ simplified narratives and visual contexts—such as dividing apples or coloring shapes—that obscure the distinction between “a part of a whole” and “a result of division.” This study investigated the impact of such textbook content and classroom practices on these misunderstandings. Employing a qualitative research approach, the study involved two second-grade teachers and 55 students (aged 7–8 years) and integrated content analysis of a widely utilized second-grade mathematics textbook, diagnostic assessments, and interviews. The analysis revealed that fractions are frequently depicted as division outcomes (e.g., 1:4 = 1/4), thereby reinforcing procedural thinking and impeding students’ capacity to grasp the abstract nature of fractions. The study concludes that effective early fraction instruction necessitates the incorporation of diverse representations and explicit differentiation between fractions and division. It is recommended that educators utilize multiple representations and precise mathematical language to facilitate students’ conceptual comprehension.

Keywords


Conceptual misconceptions; elementary mathematics; fraction understanding; textbook analysis; visual representation

Full Text:

PDF
DOI: https://doi.org/10.34007/jdm.v7i1.2883

References


Adelia, V., Putri, R. I. I., & Zulkardi. (2025). From parts to wholes: Investigating fraction division through partitioning strategies. Jurnal Pendidikan Matematika, 19(2), 241–254. https://doi.org/10.22342/mej.v19i2.pp241-254

Aldianisa, E. T., Huda, N., & Effendi-Hsb, M. H. (2021). Analisis miskonsepsi siswa dalam menyelesaikan soal pecahan berdasarkan kerangka kerja asimilasi dan akomodasi di MTsN 4 Kerinci. Jurnal Cendekia: Jurnal Pendidikan Matematika, 5(3), 2141–2151. https://doi.org/10.31004/cendekia.v5i3.737

Aliustao?lu, F., Tuna, A., & Biber, A. Ç. (2018). The misconceptions of sixth grade secondary school students on fractions. International Electronic Journal of Elementary Education, 10(5), 591–599. https://iejee.com/index.php/IEJEE/article/view/512

Andriatna, R. (2025). Exploring students’ concept images of fractions: A hermeneutic phenomenology study. Indonesian Journal of Science and Mathematics Education, 8(1), 54–65. https://doi.org/10.24042/ijsme.v8i1.23753

Ardiansari, L., Sahrul, M., & Herdiyanti, S. (2024). Zoom in: Exploring perceptions of the multiplication symbol (×) up close. Jurnal Didaktik Matematika, 5(2), 127–146. https://doi.org/10.34007/jdm.v5i2.2281

Ba?türk, S. (2024). Teaching fractions in middle school: The case of mathematics teachers’ perceptions. In A. Kabadayi & M. Özcan (Eds.), New researches in education sciences (pp. 9–40). Livre de Lyon. https://doi.org/10.5281/zenodo.10870626

Björklund, C., van den Heuvel-Panhuizen, M., & Kullberg, A. (2020). Research on early childhood mathematics teaching and learning. ZDM Mathematics Education, 52, 607–619. https://doi.org/10.1007/s11858-020-01177-3

Braithwaite, D. W., & Siegler, R. S. (2023). A unified model of arithmetic with whole numbers, fractions, and decimals. Psychological Review, 131(2), 431–455. https://doi.org/10.1037/rev0000440

Braun, V., & Clarke, V. (2006). Using thematic analysis in psychology. Qualitative Research in Psychology, 3(2), 77–101.

Creswell, J. W., & Creswell, J. D. (2017). Research design: Qualitative, quantitative, and mixed methods approaches (5th ed.). SAGE Publications.

Isnawan, M. G., Suryadi, D., & Turmudi. (2022). How secondary students develop the meaning of fractions? A hermeneutic phenomenological study. Beta: Jurnal Tadris Matematika, 15(1), 1–19. https://doi.org/10.20414/betajtm.v15i1.496

Kalra, P. B., Hubbard, E. M., & Matthews, P. G. (2020). Taking the relational structure of fractions seriously: Relational reasoning predicts fraction knowledge in elementary school children. Contemporary Educational Psychology, 62, Article 101896. https://doi.org/10.1016/j.cedpsych.2020.101896

Kieren, T. E. (1980). Five faces of mathematical knowledge building. Department of Secondary Education, University of Alberta.

Lamon, S. J. (2007). Rational numbers and proportional reasoning: Toward a theoretical framework. In F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 629–668). Information Age Publishing.

Lamon, S. J. (2012). Teaching fractions and ratios for understanding: Essential content knowledge and instructional strategies for teachers (3rd ed.). Routledge. https://doi.org/10.4324/9780203803165

Lee, H.-J., & Boyadzhiev, I. (2020). Underprepared college students’ understanding of and misconceptions with fractions. International Electronic Journal of Mathematics Education, 15(3), Article em0583. https://doi.org/10.29333/iejme/7835

Mulligan, J., & Mitchelmore, M. (2016). Pattern and structure mathematics awareness program (PASMAP): Book one—Foundation and Year 1. Australian Council for Educational Research.

Park, S., & Esposito, A. G. (2024). Rational number representation, math anxiety, and algebra performance in college students. Cognitive Development, 69, Article 101417. https://doi.org/10.1016/j.cogdev.2024.101417

Petit, M. M., Laird, R. E., Ebby, C. B., & Marsden, E. L. (2010). A focus on fractions: Bringing research to the classroom(1st ed.). Routledge.

Petit, M. M., Laird, R. E., Ebby, C. B., & Marsden, E. L. (2022). A focus on fractions: Bringing mathematics education research to the classroom (3rd ed.). Routledge.

Pitta-Pantazi, D., Christou, C., & Pittalis, M. (2020). Number teaching and learning. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 645–654). Springer. https://doi.org/10.1007/978-3-030-15789-0_122

Ramadianti, W., Priatna, N., & Kusnandi. (2019). Misconception analysis of junior high school students in interpreting fraction. Journal for the Education of Gifted Young Scientists, 7(4), 1159–1173. https://doi.org/10.17478/jegys.631567

Sharp, C. A. (2003). Qualitative research and evaluation methods (3rd ed.). Evaluation Journal of Australasia, 3(2), 60–61. https://doi.org/10.1177/1035719X0300300213

Turan, E., Van den Broe, D., Peters, E., De Smedt, B., & Torbeyns, J. (2026). Effects of a mathematical language intervention on mathematical development in preschool dual language learners. Learning and Instruction, 102, 19–38. https://doi.org/10.1016/j.learninstruc.2025.102269

Van de Walle, J. A., Karp, K. S., Bay-Williams, J. M., Wray, J. A., & Brown, E. T. (2020). Developing measurement concepts. In Elementary and middle school mathematics: Teaching developmentally. Pearson.

Watt, S. J., Locke, J., & Fesenmyer, A. (2025). Developing understanding of fraction magnitude among sixth graders with math difficulties. Learning Disabilities Research & Practice, 40(4), 341–364. https://doi.org/10.1177/09388982251341364

Xu, C., Burr, S. D. L., McNally-Edwards, N., McShane, C., Wan, L., & Judith. (2024). A holistic investigation of fraction learning: Examining the hierarchy of fraction skills, misconceptions, mathematics anxiety and response confidence. Journal of Cognitive Psychology, 36(7), 815–833. https://doi.org/10.1080/20445911.2024.2388907




DOI: https://doi.org/10.34007/jdm.v7i1.2883

Refbacks

  • There are currently no refbacks.


Journal of Didactic Mathematics

Mahesa Research Center