Undergraduate students’ mathematical reasoning in numeracy-based tasks: A Rasch model approach
Keywords:
mathematical reasoning, numeracy problems, Rasch model, undergraduate studentsAbstract
Mathematical reasoning is essential in higher education because it enables students to formulate conjecture, generalize patterns, and justify. This study examined undergraduate students’ mathematical reasoning, operationalized through conjecturing, generalizing, and justifying, in two numeracy tasks. A purposive sample of 185 mathematics education students from the first, third and fifth semesters at a State University in Kediri, Indonesia, participated in the study. Responses were scored using an analytic rubric and analyzed with the Rasch model to estimate item difficulty and person ability, evaluate item fit and reliability, and examine Differential Item Functioning (DIF) across gender, Grade Point Average (GPA), and semester level. The results indicated that conjecturing and justifying were the most challenging aspects for students, while evidence of generalizing was relatively limited. Rasch analysis verified the instrument’s validity and reliability, with all items satisfying fit requirements, while DIF analysis indicated no significant demographic bias. However, observed patterns suggested that female students tended to be more systematic and accurate, male students were generally more flexible but less consistent, and students with higher GPAs displayed stronger logical reasoning. These findings highlight the importance of instructional strategies that intentionally foster mathematical reasoning and suggest future research involving multiple institutions and longitudinal designs.
References
Adelia, V., Putri, R. I. I., & Zulkardi. (2024). A systematic literature review: How do we support students to become numerate? International Journal of Evaluation and Research in Education, 13(2), 842–851. https://doi.org/10.11591/ijere.v13i2.26299
Agustyaningrum, N., Kusmayadi, T. A., & Riyadi. (2019). Student’s conjecturing ability in mathematical problem solving. Journal of Physics: Conference Series, 1188(1), 012031. https://doi.org/10.1088/1742-6596/1188/1/012031
Andrews-Larson, C., Johnson, E., Peterson, V., & Keller, R. (2021). Doing math with mathematicians to support pedagogical reasoning about inquiry-oriented instruction. Journal of Mathematics Teacher Education, 24(2), 127–154. https://doi.org/10.1007/s10857-019-09450-3
Aryadoust, V., Ng, L. Y., & Sayama, H. (2021). A comprehensive review of Rasch measurement in language assessment: Recommendations and guidelines for research. Language Testing, 38(1), 6–40. https://doi.org/10.1177/0265532220927487
Bond, T. G., Yan, Z., & Heene, M. (2020). Applying the Rasch model: Fundamental measurement in the human sciences. Routledge. https://doi.org/10.4324/9780429030499
Boone, W. J. (2016). Rasch analysis for instrument development: Why, when, and how? CBE—Life Sciences Education, 15(4). https://doi.org/10.1187/cbe.16-04-0148
Brečka, P., Valentová, M., & Lančarič, D. (2022). The implementation of critical thinking development strategies into technology education: The evidence from Slovakia. Teaching and Teacher Education, 109, 103555. https://doi.org/10.1016/j.tate.2021.103555
Carvalho, R. G. G. (2016). Gender differences in academic achievement: The mediating role of personality. Personality and Individual Differences, 94, 54–58. https://doi.org/10.1016/j.paid.2016.01.011
Case, J., & Speer, N. (2021). Calculus students’ deductive reasoning and strategies when working with abstract propositions and calculus theorems. PRIMUS, 31(2), 184–201. https://doi.org/10.1080/10511970.2019.1660931
Clarke, J. (2024). Mathematical meaning construction in language, tables, and images: The potential utility of language proficiency development in numeracy teaching. Critical Studies in Teaching and Learning, 12(1), 56–74. https://doi.org/10.14426/cristal.v12i1.800
Darta, D., & Saputra, J. (2018). Indicators that influence prospective mathematics teachers’ representational and reasoning abilities. Journal of Physics: Conference Series, 948(1), 012053. https://doi.org/10.1088/1742-6596/948/1/012053
Edwards, A., & Alcock, L. (2010). Using Rasch analysis to identify uncharacteristic responses to undergraduate assessments. Teaching Mathematics and its Applications, 29(4), 165–175. https://doi.org/10.1093/teamat/hrq008
Ellis, A., Özgür, Z., & Reiten, L. (2022). From empirical to structural reasoning: Shifts in students’ justifications in mathematics. Journal of Mathematical Behavior, 66, 100940. https://doi.org/10.1016/j.jmathb.2021.100940
Galligan, L. (2013). A systematic approach to embedding academic numeracy at university. Higher Education Research and Development, 32(5), 734–747. https://doi.org/10.1080/07294360.2013.777038
Geiger, V., Goos, M., & Forgasz, H. (2015). A rich interpretation of numeracy for the 21st century: A survey of the state of the field. ZDM Mathematics Education, 47(4), 531–548. https://doi.org/10.1007/s11858-015-0708-1
Hamidah, D., Susiswo, S., H, H., A, Z., & Osman, S. (2025). Exploring the mathematical reasoning skills across different levels of prospective mathematics teachers: a mixed-methods investigation. Mathematics Education Journal, 19(2), 389–412. https://doi.org/10.22342/mej.v19i2.pp389-412
Hamidah, D., Susiswo, S., Susanto, H., & Osman, S. (2025). Prospective mathematics teachers’ mathematization competencies in solving word problems. Jurnal Ilmiah Ilmu Terapan Universitas Jambi, 9(3), 894–908. https://doi.org/10.22437/jiituj.v9i3.33211
Hasanah, S. I., Tafrilyanto, C. F., & Aini, Y. (2019). Mathematical reasoning: The characteristics of students’ mathematical abilities in problem solving. Journal of Physics: Conference Series, 1188(1), 012057. https://doi.org/10.1088/1742-6596/1188/1/012057
Herbert, S., & Williams, G. (2023). Eliciting mathematical reasoning during early primary problem solving. Mathematics Education Research Journal, 35(1), 77–103. https://doi.org/10.1007/s13394-021-00376-9
Jain, P., & Rogers, M. (2019). Numeracy as critical thinking. Adults Learning Mathematics: An International Journal, 14(1), 20–31. https://www.alm-online.net/images/ALM/journals/almij-volume14-1-june2019.pdf
Jeannotte, D., & Kieran, C. (2017). A conceptual model of mathematical reasoning for school mathematics. Educational Studies in Mathematics, 96(1), 1–16. https://doi.org/10.1007/s10649-017-9761-8
Joachin-Arizmendi, I., Espinoza, E. L., Carballo, A. M., & Reyna-Hernández, G. (2024). Diagnostic study of mathematical reasoning in novice university students. International Electronic Journal of Mathematics Education, 19(3), 0788. https://doi.org/10.29333/iejme/14862
Kadarisma, G., Nurjaman, A., Sari, I. P., & Amelia, R. (2019). Gender and mathematical reasoning ability. Journal of Physics: Conference Series, 1157(4), 042109. https://doi.org/10.1088/1742-6596/1157/4/042109
Li, J., Faisal, E., & Al Hariri, A. (2022). Numbers for boys and words for girls? Academic gender stereotypes among Chinese parents. Sex Roles, 87(9–10), 475–489. https://doi.org/10.1007/s11199-022-01298-0
Lunardon, M., Cerni, T., & Rumiati, R. I. (2022). Numeracy gender gap in STEM higher education: The role of neuroticism. Frontiers in Psychology, 13, 856405. https://doi.org/10.3389/fpsyg.2022.85640
Luo, M., Sun, D., Zhu, L., & Yang, Y. (2021). Evaluating scientific reasoning ability: Student performance and the interaction effects between grade level, gender, and academic achievement level. Thinking Skills and Creativity, 40, 100820. https://doi.org/10.1016/j.tsc.2021.100820
Minnigh, T. L., & Coyle, T. R. (2023). Gender differences in self-efficacy partially explain the female underprediction effect. Journal of Research in Personality, 104, 104214. https://doi.org/10.1016/j.jrp.2023.104214
Nurdiansah, I., Rahardjo, S., & Susiswo. (2024). Exploring students’ mathematical generalization ability in problem solving. Journal of Physics: Conference Series, 2600(1), 012035. https://doi.org/10.1088/1742-6596/2600/1/012035
OECD. (2022). PISA 2022 Mathematics Framework. https://pisa2022-maths.oecd.org/
Paradesa, R. (2018). Students’ ability in generalization of mathematical pattern. Infinity Journal, 7(1), 21–30. https://doi.org/10.22460/infinity.v7i1.p21-30
Purnomo, H., Sa'dijah, C., Hidayanto, E., Sisworo, P., H, & Anwar, L. (2022). Development of instrument numeracy skills test of minimum competency assessment (MCA) in Indonesia. International Journal of Instruction, 15(3), 635–648. https://doi.org/10.29333/iji.2022.15335a
Qirom, M., & Nurlaelah, E. (2023). Rasch model: Analysing the items quality of mathematics higher-order thinking skill instrument. Jurnal Pendidikan dan Pembelajaran, 30(1), 11–20. https://doi.org/10.17977/um047v30i12023p011
Ramadhani, R., Saragih, S., & Napitupulu, E. E. (2022). Exploration of students’ statistical reasoning ability in the context of ethnomathematics: A study of the Rasch model. Mathematics Teaching Research Journal, 14(1), 138–168.
Riwayani, Istiyono, E., Supahar, Perdana, R., & Soeharto. (2024). Analyzing students’ statistical literacy skills based on gender, grade, and educational field. International Journal of Evaluation and Research in Education, 13(2), 842–851. https://doi.org/https://doi.org/10.11591/ijere.v13i2.26299
Rohati, R., Kusumah, Y. S., & Kusnandi, K. (2023). Exploring students’ mathematical reasoning behavior in junior high schools: A grounded theory. Education Sciences, 13(3), 252. https://doi.org/10.3390/educsci13030252
Rokhima, W. A., Kusmayadi, T. A., & Fitriana, L. (2019). Mathematical reasoning of student in senior high school based on gender differences. Journal of Physics: Conference Series, 1318(1), 012092. https://doi.org/10.1088/1742-6596/1318/1/012092
Rosyadi, A. A. P., Sa'dijah, C., Susiswo, S., & Rahardjo, S. (2022). Critical thinking of prospective mathematics teachers: What are the errors in argumentation? Multicultural Education, 8(3), 80–90. https://doi.org/10.5281/zenodo.7348010
Rubianti, N. S., Usodo, B., & Subanti, S. (2022). The difference of mathematical reasoning between male and female students. AIP Conference Proceedings, 2566(1), 030005. https://doi.org/10.1063/5.0117121
Rusdi, M., Fitaloka, O., Basuki, F. R., & Anwar, K. (2020). Mathematical communication skills based on cognitive styles and gender. International Journal of Evaluation and Research in Education, 9(4), 847–856. https://doi.org/10.11591/ijere.v9i4.20497
Suanto, H., Mulyana, T., & Prasetyo, H. (2023, 2023). Analysis of students’ mathematical reasoning instrument using Rasch model Proceedings of the International Conference on Education, Social Sciences and Humanities (ICoESSE 2023, https://doi.org/10.2991/978-2-494069-55-8_18
Subanji, N., T, R., D, & Purnomo, H. (2021). The statistical creative framework in descriptive statistics activities. International Journal of Instruction, 14(2), 591–608. https://doi.org/10.29333/iji.2021.14233a
Suherman, S., & Vidákovich, T. (2022). Tapis patterns in the context of ethnomathematics to assess students’ creative thinking in mathematics: A Rasch measurement. Mathematics Teaching Research Journal, 14(4), 56–79.
Tariq, V. N., Qualter, P., Roberts, S., & Barnes, L. (2013). Mathematical literacy in undergraduates: Role of gender, emotional intelligence, and emotional self-efficacy. International Journal of Mathematical Education in Science and Technology, 44(7), 1010–1029. https://doi.org/10.1080/0020739X.2013.783632
Vos, H., Marinova, M., Léon, S. C., Sasanguie, D., & Reynvoet, B. (2023). Gender differences in young adults’ mathematical performance: Examining the contribution of working memory, math anxiety, and gender-related stereotypes. Learning and Individual Differences, 102, 102255. https://doi.org/10.1016/j.lindif.2022.102255
Wrigley-Asante, C., Ackah, C. G., & Frimpong, L. K. (2023). Gender differences in academic performance of students studying STEM subjects at the University of Ghana. SN Social Sciences, 3(6), 91. https://doi.org/10.1007/s43545-023-00834-5
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