Mathematical Critical Thinking Profiles of Seventh-Grade Students in Solving Fraction Problems within Realistic Mathematics Education Contexts

Neli Neli; Siti Suprihatiningsih

doi:10.31949/dm.v8i2.18102

Authors

Neli Neli Universitas Katolik Santo Agustinus Hippo, Indonesia
Siti Suprihatiningsih Universitas Katolik Santo Agustinus Hippo, Indonesia

DOI:

https://doi.org/10.31949/dm.v8i2.18102

Abstract

This study investigates seventh-grade students’ mathematical critical thinking profiles in solving fraction problems involving different denominators within Realistic Mathematics Education (RME) contexts. A qualitative multiple-case descriptive design was employed involving 18 students who completed contextual essay-based mathematical tasks, with six students purposively selected for in-depth semi-structured interviews representing high-, medium-, and low-ability categories. Data were collected through written tasks and interview protocols developed according to Ennis’s five critical thinking indicators: interpretation, analysis, evaluation, inference, and explanation. Data analysis followed an interactive qualitative approach involving data reduction, data display, and conclusion verification. The findings revealed substantial variation in students’ mathematical critical thinking across indicators and ability categories. High-level students demonstrated relatively systematic and coherent reasoning processes, whereas medium- and low-level students exhibited fragmented reasoning characterized by procedural uncertainty and conceptual difficulties. Interpretation emerged as the most accessible indicator, while inference and explanation represented the most challenging dimensions. Additive misconception was identified as the most dominant conceptual difficulty, particularly among low-level students, indicating broader weaknesses in fraction understanding rather than isolated procedural errors. Furthermore, the findings suggest that mathematical critical thinking indicators function as interconnected dimensions, where difficulties occurring during earlier reasoning stages frequently coincided with limitations in subsequent processes. This study contributes to mathematics education literature by providing a multidimensional understanding of students’ mathematical critical thinking through the integration of written responses and interview data. The findings highlight the importance of instructional practices emphasizing conceptual understanding, reflective reasoning, and meaningful mathematical contexts.

Keywords:

Mathematical critical thinking, Fractions, Realistic Mathematics Education, Additive misconception, Critical thinking indicators

Downloads

Download data is not yet available.

References

Ahmad, M., & Wilkins, S. (2025). Purposive sampling in qualitative research: A framework for the entire journey. Qualitative and Quantitative, 59, 1461–1479. https://doi.org/10.1007/s11135-024-02022-5

Aldila Afriansyah, E., Herman, T., Turmudi, T., & Afgani Dahlan, J. (2021). Critical thinking skills in mathematics. Journal of Physics: Conference Series, 1778(1), Article 012013. https://doi.org/10.1088/1742-6596/1778/1/012013

Ames, H., Glenton, C., & Lewin, S. (2019). Purposive sampling in a qualitative evidence synthesis: A worked example from a synthesis on parental perceptions of vaccination communication. BMC Medical Research Methodology, 19, Article 26. https://doi.org/10.1186/s12874-019-0665-4

Amir, F., Firdaus, F. M., & Pada, A. (2024). How does realistic mathematics learning shape learners' problem solving and critical thinking skills? Al-Ishlah: Jurnal Pendidikan, 16(3), 3588–3602. https://doi.org/10.35445/alishlah.v16i3.5101

Astuti, M. D., Warmi, A., & Effendi, K. N. S. (2026). Students’ mathematical critical thinking processes in solving algebraic problems: A qualitative analysis based on Watson–Glaser indicators. Didactical Mathematics, 8(1), 29–44. https://doi.org/10.31949/dm.v8i1.16564

Bikner-Ahsbahs, A., Knipping, C., & Presmeg, N. (2015). Approaches to qualitative research in mathematics education. Advances in Mathematics Education. Springer. https://doi.org/10.1007/978-94-017-9181-6

Cahyaningsih, U., & Nahdi, D. S. (2021). The effect of realistic mathematics education on elementary students’ critical thinking skills. Journal of Physics: Conference Series, 1764(1), Article 012127. https://doi.org/10.1088/1742-6596/1764/1/012127

Derry, J. (2017). An introduction to inferentialism in mathematics education. Mathematics Education Research Journal, 29, 403–418. https://doi.org/10.1007/s13394-017-0193-7

DeWolf, M., & Vosniadou, S. (2015). The representation of fraction magnitudes and the whole number bias reconsidered. Learning and Instruction, 37, 39–49. https://doi.org/10.1016/j.learninstruc.2014.07.002

Ennis, R. H. (2015). Critical thinking: A streamlined conception. In M. Davies & R. Barnett (Eds.), The Palgrave handbook of critical thinking in higher education (pp. xx–xx). Palgrave Macmillan. https://doi.org/10.1057/9781137378057_2

González-Forte, J. M., Fernández, C., Van Hoof, J., et al. (2023). Incorrect ways of thinking about the size of fractions. International Journal of Science and Mathematics Education, 21, 2005–2025. https://doi.org/10.1007/s10763-022-10338-7

Hurrell, D. (2021). Conceptual knowledge or procedural knowledge or conceptual knowledge and procedural knowledge: Why the conjunction is important to teachers. Australian Journal of Teacher Education, 46(2), 57–71. https://doi.org/10.3316/informit.757709794375494

Jablonka, E. (2020). Critical thinking in mathematics education. In S. Lerman (Ed.), Encyclopedia of mathematics education. Springer. https://doi.org/10.1007/978-3-030-15789-0_35

Jordan, N. C., Resnick, I., Rodrigues, J., Hansen, N., & Dyson, N. (2017). Delaware longitudinal study of fraction learning: Implications for helping children with mathematics difficulties. Journal of Learning Disabilities, 50(6), 621–630. https://doi.org/10.1177/0022219416662033

Kania, N., Kusumah, Y. S., Dahlan, J. A., Nurlaelah, E., Gürbüz, F., & Bonyah, E. (2024). Constructing and providing content validity evidence through the Aiken’s V index based on experts’ judgments of the instrument to measure mathematical problem-solving skills. REiD (Research and Evaluation in Education), 10(1). https://doi.org/10.21831/reid.v10i1.71032

Koh, K., Chapman, O., Gierus, B., et al. (2025). Assessment of higher-level mathematical thinking skills: A scoping review. ZDM Mathematics Education, 57, 665–678. https://doi.org/10.1007/s11858-025-01695-y

Lamon, S. J. (2012). Ratio and proportion: Children's cognitive and metacognitive processes. In Rational Numbers (pp. 131–156). Routledge. https://doi.org/10.4324/9780203052624-9

Lestari, R., Prahmana, R. C. I., Chong, M. S. F., & Shahrill, M. (2023). Developing realistic mathematics education-based worksheets for improving students' critical thinking skills. Infinity Journal, 12(1), 69–84. https://doi.org/10.22460/infinity.v12i1.p69-84

Miles, M. B., Huberman, A. M., & Saldaña, J. (2014). Qualitative data analysis: A methods sourcebook (3rd ed.). SAGE Publications.

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. https://doi.org/10.1207/s15326985ep4001_3

Norqvist, M. (2018). The effect of explanations on mathematical reasoning tasks. International Journal of Mathematical Education in Science and Technology, 49(1), 15–30. https://doi.org/10.1080/0020739X.2017.1340679

Pfannkuch, M., Wild, C. J., & Regan, M. (2014). Students’ difficulties in practicing computer-supported statistical inference: Some hypothetical generalizations from a study. In T. Wassong, D. Frischemeier, P. Fischer, R. Hochmuth, & P. Bender (Eds.), Using tools for learning mathematics and statistics (pp. xx–xx). Springer Spektrum. https://doi.org/10.1007/978-3-658-03104-6_28

Primadoni, A. B., Kusumawati, D., & Muslim, R. I. (2025). Profiles of elementary students’ fraction conceptual understanding across collaboration ability levels: A qualitative inquiry. Jurnal Elementaria Edukasia, 8(4), 736–747. https://doi.org/10.31949/jee.v8i4.16396

Said, A. M., & Lukmana, D. A. (2020). Mathematical critical thinking abilities of middle school students in Tidore based on gender and background. International Journal of Trends in Mathematics Education Research, 3(2), 81–88. https://doi.org/10.33122/ijtmer.v3i2.172

Sari, D. R. (2020). The analysis of mathematical critical thinking skills of students in junior high school. In Proceedings of the International Conference on Progressive Education (ICOPE 2019) (pp. 123–126). Atlantis Press. https://doi.org/10.2991/assehr.k.200323.103

Schutte, B. G., Bayram, D., Vennix, J., & van der Veen, J. (2026). Scaffolding for challenge-based learning in sustainability education: A multiple-case study. Sustainability, 18(7), Article 3273. https://doi.org/10.3390/su18073273

Seidouvy, A., & Schindler, M. (2020). An inferentialist account of students’ collaboration in mathematics education. Mathematics Education Research Journal, 32, 411–431. https://doi.org/10.1007/s13394-019-00267-0

Simpson, A., & Haltiwanger, L. (2017). “This is the first time I’ve done this”: Exploring secondary prospective mathematics teachers’ noticing of students’ mathematical thinking. Journal of Mathematics Teacher Education, 20, 335–355. https://doi.org/10.1007/s10857-016-9352-0

Streefland, L. (2012). Fractions: A realistic approach. In Rational Numbers (pp. 289–325). Routledge. https://doi.org/10.4324/9780203052624-18

Sutarni, S., Sutama, S., Prayitno, H. J., Sutopo, A., & Laksmiwati, P. A. (2024). The development of realistic mathematics education-based student worksheets to enhance higher-order thinking skills and mathematical ability. Infinity Journal, 13(2), 285–300. https://doi.org/10.22460/infinity.v13i2.p285-300

Tambunan, E. T., & Mahmudi, A. (2024). The improvement of students’ mathematical critical thinking skills and learning motivation through contextual teaching and learning. Formatif: Jurnal Ilmiah Pendidikan MIPA, 14(1). http://dx.doi.org/10.30998/formatif.v14i1.21634

Tambunan, H., & Naibaho, T. (2019). Performance of mathematics teachers to build students' high-order thinking skills (HOTS). Journal of Education and Learning (EduLearn), 13(1), 111–117. https://doi.org/10.11591/edulearn.v13i1.11218

Williams, E. N., & Morrow, S. L. (2009). Achieving trustworthiness in qualitative research: A pan-paradigmatic perspective. Psychotherapy Research, 19(4–5), 576–582. https://doi.org/10.1080/10503300802702113

Xu, C., Di Lonardo Burr, S., McNally-Edwards, N., McShane, C., Wan, L., & Wylie, J. (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

Ye, A., Resnick, I., Hansen, N., Rodrigues, J., Rinne, L., & Jordan, N. C. (2016). Pathways to fraction learning: Numerical abilities mediate the relation between early cognitive competencies and later fraction knowledge. Journal of Experimental Child Psychology, 152, 242–263. https://doi.org/10.1016/j.jecp.2016.08.001

Yilmaz, A., & Kostur, M. (2021). Rethinking principles of school mathematics during the COVID-19 pandemic: A multiple-case study on higher education courses related to teaching mathematics. International Electronic Journal of Mathematics Education, 16(3), Article em0653. https://doi.org/10.29333/iejme/11103

Yohannes, A., & Chen, H. L. (2024). The effect of flipped realistic mathematics education on students’ achievement, mathematics self-efficacy and critical thinking tendency. Education and Information Technologies, 29, 16177–16203. https://doi.org/10.1007/s10639-024-12502-8

Zuhaida, A., Zuhri, M. K., & Ayyubi, S. H. Y. A. (2022). Analysis of students’ critical thinking skills through science, technology, engineering and mathematics (STEM) approach. AIP Conference Proceedings, 2600(1), Article 070023. https://doi.org/10.1063/5.0112996