The Effect of a Corequisite Instructional Model on Undergraduate Achievement in First-Order Ordinary Differential Equations: A Quasi-Experimental Study

Undergraduate students often struggle with first-order ordinary differential equations (ODEs) due to unresolved gaps in their prerequisite algebra and calculus skills. This study examined whether a corequisite instructional model one that reinforces foundational competencies concurrently with, rather than prior to, advanced content, improves undergraduate achievement and affective outcomes in first-order ODEs. A quasi-experimental pretest–posttest design with a non-equivalent control group was used with 60 Mathematics Education undergraduates (30 experimental, 30 control) enrolled in an ODE course. The Corequisite Diagnostic Test (CDT), the Ordinary Differential Equations Achievement Test (ODE-AT), and the Student Learning Perception Questionnaire (SLPQ) were used to collect data, which were analyzed with descriptive statistics, Pearson correlation, independent-samples t-tests, and analysis of covariance (ANCOVA). Prerequisite competence in algebraic manipulation, function interpretation, differentiation, and integration correlated significantly with ODE achievement in both groups, with integration (r = .72) and differentiation (r = .67) showing the strongest associations. After controlling for CDT pretest scores, students who received the corequisite intervention achieved significantly higher ODE-AT posttest scores than those receiving conventional instruction, F(1, 57) = 43.69, p < .001, η²p = .432, with adjusted posttest means of 74.3 and 62.1, respectively. The experimental group also reported significantly stronger self-efficacy, confidence, attitudes, and engagement on the SLPQ (all p < .001). These findings indicate that embedding just-in-time prerequisite support directly within ODE instruction produces measurable gains in both achievement and learner confidence, offering a practicable, theory-grounded alternative to standalone developmental mathematics courses for advanced undergraduate content. Implications for classroom practice and curriculum design in undergraduate mathematics programmes were discussed.

Corequisite Instruction; Ordinary Differential Equations; Prerequisite Competencies; Undergraduate Mathematics Education; Cognitive Load; Self-Efficacy

1. Artigue, M. (2011). Learning and teaching pre-calculus and calculus. In Second international handbook of mathematics education (pp. 511–542). Springer. [Google Scholar] [Crossref]

2. Ashcraft, M. H., & Kirk, E. P. (2001). The relationships among working memory, math anxiety, and performance. Journal of Experimental Psychology: General, 130(2), 224–237. [Google Scholar] [Crossref]

3. Bandura, A. (1997). Self-efficacy: The exercise of control. W. H. Freeman. [Google Scholar] [Crossref]

4. Bloom, B. S. (1968). Learning for mastery. Evaluation Comment, 1(2), 1–12. [Google Scholar] [Crossref]

5. Borji, V., & Martínez-Planell, R. (2020). On students' understanding of implicit differentiation based on APOS theory. Educational Studies in Mathematics, 105(2), 163–179. [Google Scholar] [Crossref]

6. Brunner, E. J., Dougherty, S. M., & Reback, R. (2025). The effects of high school remediation on long-run outcomes (CESifo Working Paper No. 11908). CESifo. [Google Scholar] [Crossref]

7. Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum Associates. [Google Scholar] [Crossref]

8. Cook, T. D., & Campbell, D. T. (1979). Quasi-experimentation: Design and analysis issues for field settings. Houghton Mifflin. [Google Scholar] [Crossref]

9. Daugherty, M. K., Johnston, M., & Tsai, H.-Y. S. (2017). Corequisite models in mathematics gateway courses. Journal of Developmental Education, 40(3), 18–25. [Google Scholar] [Crossref]

10. Dogan-Dunlap, H. (2006). Lack of set theory relevant prerequisite knowledge. International Journal of Mathematical Education in Science and Technology, 37(4), 401–410. [Google Scholar] [Crossref]

11. Eccles, J. S., & Wigfield, A. (2002). Motivational beliefs, values, and goals. Annual Review of Psychology, 53, 109–132. [Google Scholar] [Crossref]

12. Fraenkel, J. R., Wallen, N. E., & Hyun, H. H. (2023). How to design and evaluate research in education (10th ed.). McGraw-Hill. [Google Scholar] [Crossref]

13. Goriely, Z. (2023). British mathematical reformers in the nineteenth century: Motivations and methods. British Journal for the History of Mathematics, 38(2), 159–167. [Google Scholar] [Crossref]

14. Guskey, T. R. (2022). Implementing mastery learning (3rd ed.). Corwin. [Google Scholar] [Crossref]

15. Hassan, O. (2022). Classroom applicability of Bloom's mastery learning as perceived by teachers. Humanika: Kajian Ilmiah Mata Kuliah Umum, 22(1), 65–76. [Google Scholar] [Crossref]

16. Hattie, J., & Timperley, H. (2007). The power of feedback. Review of Educational Research, 77(1), 81–112. [Google Scholar] [Crossref]

17. Hodara, M., & Jaggars, S. S. (2014). An examination of the impact of accelerating community college students' progression through developmental education. Journal of Higher Education, 85(2), 246–276. [Google Scholar] [Crossref]

18. Honicke, T., & Broadbent, J. (2016). The influence of academic self-efficacy on academic performance: A systematic review. Educational Research Review, 17, 63–84. [Google Scholar] [Crossref]

19. Hyland, D., van Kampen, P., & Nolan, B. C. (2018). Outcomes of a service teaching module on ODEs for physics students. International Journal of Mathematical Education in Science and Technology, 49(5), 743–758. [Google Scholar] [Crossref]

20. Ishak, Ardiana, Bakar, M. T., & Saputra, L. R. (2025). Analysis of students' learning obstacles in the differential equations course reviewed from their problem-solving ability. Al-Jabar: Jurnal Pendidikan Matematika, 16(1), 1–12. [Google Scholar] [Crossref]

21. Kashyap, U., & Mathew, S. (2017). Corequisite model: An effective strategy for remediation in freshmen-level quantitative reasoning course. Journal of STEM Education: Innovations and Research, 18(2), 23–29. [Google Scholar] [Crossref]

22. Logue, A. W., Douglas, D., & Watanabe-Rose, M. (2019). Corequisite mathematics remediation: Results over time and in different contexts. Educational Evaluation and Policy Analysis, 41(3), 294–315. [Google Scholar] [Crossref]

23. Mangarin, R. A., & Caballes, D. O. (2024). Difficulties in learning mathematics: A systematic review. International Journal of Research and Scientific Innovation, 11(9), 401–405. [Google Scholar] [Crossref]

24. Martirosyan, N. M., Saxon, D. P., Skidmore, S. T., & Kelly, B. (2025). Corequisite developmental mathematics: Faculty input on challenges and positive outcomes. Journal of College Academic Support Programs, 7(1), 9–20. [Google Scholar] [Crossref]

25. Mokher, C. G., & Park-Gaghan, T. J. (2025). How academic preparation shapes college students' own success and the success of their peers in corequisite courses: Evidence from Texas. AERA Open, 11, 1–19. [Google Scholar] [Crossref]

26. Oyelami, B. O. (2024). Solutions of first-order differential equations and applications. In Ordinary differential equations and applications I: With Maple examples. Bentham Science Publishers. [Google Scholar] [Crossref]

27. Pajares, F. (1996). Self-efficacy beliefs in academic settings. Review of Educational Research, 66(4), 543–578. [Google Scholar] [Crossref]

28. Ramirez, G., Gunderson, E. A., Levine, S. C., & Beilock, S. L. (2013). Math anxiety, working memory, and math achievement in early elementary school. Journal of Cognition and Development, 14(2), 187–202. [Google Scholar] [Crossref]

29. Ran, F. X., & Lin, Y. (2022). The effects of corequisite remediation: Evidence from a statewide reform in Tennessee. Educational Evaluation and Policy Analysis, 44(3), 458–484. [Google Scholar] [Crossref]

30. Rasmussen, C. L. (2001). New directions in differential equations: A framework for interpreting students' understandings and difficulties. Journal of Mathematical Behavior, 20(1), 55–87. [Google Scholar] [Crossref]

31. Sanabria, T., Penner, A., & Domina, T. (2020). Failing at remediation? College remedial course-taking, failure and long-term student outcomes. Research in Higher Education, 61(4), 459–484. [Google Scholar] [Crossref]

32. Schneider, M., & Simonsmeier, B. A. (2025). How does prior knowledge affect learning? A review of 16 mechanisms and a framework for future research. Learning and Individual Differences, 122, Article 102744. [Google Scholar] [Crossref]

33. Scott-Clayton, J., & Rodriguez, O. (2014). Development, discouragement, or diversion? New evidence on the effects of college remediation. Education Finance and Policy, 9(4), 4–45. [Google Scholar] [Crossref]

34. Sweller, J. (1988). Cognitive load during problem solving: Effects on learning. Cognitive Science, 12(2), 257–285. [Google Scholar] [Crossref]

35. Sweller, J. (2024). Cognitive load theory and individual differences. Learning and Individual Differences, 110, Article 102423. [Google Scholar] [Crossref]

36. Sweller, J., & Cooper, G. A. (1985). The use of worked examples as a substitute for problem solving in learning algebra. Cognition and Instruction, 2(1), 59–89. [Google Scholar] [Crossref]

37. Sweller, J., van Merriënboer, J. J. G., & Paas, F. (2019). Cognitive architecture and instructional design: 20 years later. Educational Psychology Review, 31(2), 261–292. [Google Scholar] [Crossref]

38. Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Harvard University Press. [Google Scholar] [Crossref]

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