Bayesian Growth Curve Modelling of Student Academic Trajectories: The Impact of Individual-Level Characteristics and Implications for Education Policy
Abstract
:1. Introduction
1.1. Theoretical Framework
1.1.1. Human Capital Theory
1.1.2. Tinto’s Model of Student Integration
1.2. Reviewed Literature
1.3. Research Questions
- Do individual-level characteristics (AP scores, Grade 12 mathematics marks, school quintile, and credits passed) have a statistically significant influence on students’ academic performance in the BSc Actuarial Science programme?
- Do socioeconomic factors, such as school quintile, have a statistically significant influence on academic performance in the BSc Actuarial Science programme?
- What is the relationship between the number of credits passed and students’ academic performance in the BSc Actuarial Science programme?
- Is there significant unobserved heterogeneity in student performance that varies across modules, and what are the implications for admission policies, curriculum development, and student support services in higher education?
1.4. Hypotheses
- Higher Grade 12 mathematics marks are positively associated with improved academic performance in the BSc Actuarial Science programme.
- Students from higher socioeconomic backgrounds (as proxied by school quintile) will exhibit better academic performance than those from lower socioeconomic backgrounds.
- The number of credits passed during the academic year is positively associated with students’ final marks in the programme.
- There is significant unobserved heterogeneity in student performance due to individual factors not captured by the included covariates, and this unobserved heterogeneity varies across modules.
2. Materials and Methods
2.1. Research Design
2.2. Participants
2.3. Data Collection
2.4. Analytical Approach
- Fixed effects: These were included to estimate the direct relationships between covariates (e.g., AP scores and Grade 12 mathematics marks) and academic outcomes;
- Random effects: These were included to capture unobserved heterogeneity at both the student and module levels, allowing for individual differences in starting performance and growth trajectories.
2.5. Data Analysis
3. Results
3.1. Impact of Individual-Level Characteristics on Academic Performance
3.2. Student Academic Performance Trajectories over Time
3.3. Unobserved Heterogeneity in Student Performance
“Is there significant unobserved heterogeneity in student performance that can be attributed to random effects at the student and module levels?”
3.4. Model Adequacy and Posterior Predictive Check
4. Discussion
5. Conclusions
5.1. Educational Implications
5.2. Limitations
5.3. Recommendations
- Higher education institutions should place a stronger emphasis on Grade 12 mathematics marks during the admission process and consider introducing bridging programmes for students who need additional mathematical preparation. This would ensure that students entering demanding programmes are adequately prepared;
- Policies aimed at reducing educational inequalities should be strengthened. These include increasing access to quality education in under-resourced schools and expanding financial aid and mentorship opportunities for disadvantaged students;
- Universities should implement continuous academic engagement strategies, including frequent formative assessments, peer tutoring, and academic advising, to ensure students remain on track throughout their studies;
- Support services personnel should work closely with the faculty and students to offer targeted interventions that address emotional, psychological, and motivational challenges. This should involve regular mental health check-ins, counselling, and workshops on personal development alongside academic tutoring.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
- Methkal, Y.; Algani, A. Role, need and benefits of mathematics in the development of society. J. Math. Educ. Teach. Pract. 2022, 3, 23–29. [Google Scholar]
- Li, Y.; Schoenfeld, A.H. Problematizing teaching and learning mathematics as “ given ” in STEM education. Int. J. STEM Educ. 2019, 6, 44. [Google Scholar] [CrossRef]
- Mosia, M.; Egara, F.O. Predictors of student success in mathematics: Hierarchical bayesian approach. Int. J. Appl. Eng. Technol. 2024, 6, 59–72. [Google Scholar]
- Mosia, M.; Montso, T.; Egara, F.O. Leveraging Amartya Sen’s capability approach for advancing mathematics teacher development: A data-driven perspective. Int. J. Appl. Eng. Technol. 2024, 6, 10–26. [Google Scholar]
- Mabena, N.; Mokgosi, P.N.; Ramapela, S.S. Factors contributing to poor Learner performance in mathematics: A case of selected schools in Mpumalanga Province, South Africa. Probl. Educ. 21st Century 2021, 79, 451–466. [Google Scholar] [CrossRef]
- Robbins, J.K.; Herzog, L.; King, K.; Snyder, A.W.; Sume, N.; Gangiah, J. Math matters: From the basics to problem solving in a South African township. Behav. Soc. Issues 2024, 33, 364–390. [Google Scholar] [CrossRef]
- McCarthy, J.; Oliphant, R. Mathematics Outcomes in South African Schools. What Are the Facts? What Should be Done? 2013. Available online: https://www.cde.org.za/wp-content/uploads/2018/07/Mathematics-outcomes-in-South-African-schools-what-are-the-facts-what-should-be-done-CDE-Report.pdf (accessed on 22 September 2024).
- Ngwenya, T.; Chaba, P. Mathematics education in South African schools (grades 1–12): A systems dynamics approach from an engineering education perspective. Proc. Int. Conf. Ind. Eng. Oper. Manag. 2024. [Google Scholar] [CrossRef]
- van Staden, S.; Graham, M.A.; Harvey, J.C. An analysis of timss 2015 science reading demands. Perspect. Educ. 2020, 8, 285–302. [Google Scholar] [CrossRef]
- England, D. Actuarial Science Overview. Available online: https://www.iwu.edu/math/actuarialscienceoverview-derekengland.pdf (accessed on 11 October 2024).
- Promislow, S.D. Fundamentals of Actuarial Mathematics, 2nd ed.; John Wiley & Sons, Ltd.: Hoboken, NJ, USA, 2011; ISBN 9780470684115. [Google Scholar]
- Simelane, B.; Engelbrecht, J. Measuring the mathematical maturity of students in an academic development programme. Int. J. Res. Undergrad. Math. Educ. 2024, 10, 577–606. [Google Scholar] [CrossRef]
- Nimy, E.; Mosia, M. Modelling student retention in tutorial classes with uncertainty—A Bayesian approach to predicting attendance-based retention. Educ. Sci. 2024, 14, 830. [Google Scholar] [CrossRef]
- Munir, J.; Faiza, M.; Jamal, B.; Daud, S.; Iqbal, K. The impact of socio-economic status on academic achievement. J. Soc. Sci. Rev. 2023, 3, 695–705. [Google Scholar] [CrossRef]
- Spaull, N.; Kotze, J. Starting behind and staying behind in South Africa. The case of insurmountable learning deficits in mathematics. Int. J. Educ. Dev. 2015, 41, 13–24. [Google Scholar] [CrossRef]
- Nimy, E.; Mosia, M.; Chibaya, C. Identifying at-risk students for early intervention—A probabilistic machine learning approach. Appl. Sci. 2023, 13, 3869. [Google Scholar] [CrossRef]
- Becker, G.S. Human Capital: A Theoretical and Empirical Analysis, with Special Reference to Education; University of Chicago Press: Chicago, IL, USA, 1964. [Google Scholar]
- Tinto, V. Dropout from higher education: A theoretical synthesis of recent research. Rev. Educ. Res. 1975, 45, 89–125. [Google Scholar] [CrossRef]
- Molontay, R.; Nagy, M. How to improve the predictive validity of a composite admission score? A case study from Hungary. Assess. Eval. High. Educ. 2023, 48, 419–437. [Google Scholar] [CrossRef]
- Edwards, D.; Friedman, T.; Pearce, J. Same admissions tools, different outcomes: A critical perspective on predictive validity in three undergraduate medical schools. BMC Med. Educ. 2013, 13, 173. [Google Scholar] [CrossRef] [PubMed]
- Sole, M.A. Streamlining time spent in alternative developmental mathematics pathways: Increasing access to college-level mathematics courses by altering placement procedures. J. Math. Educ. Teach. Coll. 2020, 11, 43–54. [Google Scholar] [CrossRef]
- Brunner, M.; Keller, U.; Wenger, M.; Fischbach, A.; Lüdtke, O. Between-school variation in students’ achievement, motivation, affect, and learning strategies: Results from 81 countries for planning group-randomized trials in education. J. Res. Educ. Eff. 2018, 11, 452–478. [Google Scholar] [CrossRef]
- McCall, M.S.; Hauser, C.; Cronin, J.; Kingsbury, G.G.; Houser, R. Achievement Gaps: An Examination of Differences in Student Achievement and Growth. Full Report. Northwest Evaluation Association. 2006. Available online: https://eric.ed.gov/?id=ED498429 (accessed on 18 September 2024).
- Burns, S.M. Predicting academic progression for student registered nurse anesthetists. AANA J. 2011, 79, 193–201. [Google Scholar]
- Harding, M.M. Efficacy of progression testing in predicting nursing student academic success. J. Nurs. Educ. Pract. 2012, 2, 137–140. [Google Scholar] [CrossRef]
- Lowis, M.; Castley, A. Factors affecting student progression and achievement: Prediction and intervention. A two-year study. Innov. Educ. Teach. Int. 2008, 45, 333–343. [Google Scholar] [CrossRef]
- Pike, G.R.; Robbins, K.R. Using panel data to identify the effects of institutional characteristics, cohort characteristics, and institutional actions on graduation rates. Res. High. Educ. 2020, 61, 485–509. [Google Scholar] [CrossRef]
- Sánchez, T.; Gilar-Corbi, R.; Castejón, J.L.; Vidal, J.; León, J. Students’ evaluation of teaching and their academic achievement in a higher education institution of Ecuador. Front. Psychol. 2020, 11, 233. [Google Scholar] [CrossRef]
- Umbach, P.D.; Tuchmayer, J.B.; Clayton, A.B.; Smith, K.N. Transfer student success: Exploring community college, university, and individual predictors. Community Coll. J. Res. Pract. 2019, 43, 599–617. [Google Scholar] [CrossRef]
- Gajderowicz, L.G.; Mehta, R.; Rosokha, K.; Zou, J.; Grossman, J.; Smith, C.E. Practice Makes Better: Quantifying Grade Benefits of Study. arXiv 2023, arXiv:2301.02927. Available online: https://arxiv.org/abs/2301.02927 (accessed on 6 August 2024).
Covariate | M | SE | 95% CI (Lower, Upper) |
---|---|---|---|
AP Score (β1) | 0.10 | 0.06 | [−0.03, 0.22] |
Grade 12 Math (β2) | 0.42 | 0.03 | [0.37, 0.49] |
School Quintile (β3) | 1.69 | 0.19 | [1.33, 2.07] |
Credits Passed (β4) | 0.15 | 0.01 | [0.14, 0.16] |
Random Effect | Minimum | 1st Quartile | Median | Mean | 3rd Quartile | Maximum |
---|---|---|---|---|---|---|
Student Intercepts | −0.08 | −0.04 | −0.00 | −0.01 | 0.02 | 0.04 |
Student Slopes | −4.02 | −3.53 | −3.04 | −2.45 | −1.66 | −0.28 |
Module Intercepts | −1.96 | −0.08 | 0.18 | 0.00 | 0.34 | 0.78 |
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |
© 2025 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Mosia, M.; Egara, F.O.; Nannim, F.; Basitere, M. Bayesian Growth Curve Modelling of Student Academic Trajectories: The Impact of Individual-Level Characteristics and Implications for Education Policy. Appl. Sci. 2025, 15, 1426. https://doi.org/10.3390/app15031426
Mosia M, Egara FO, Nannim F, Basitere M. Bayesian Growth Curve Modelling of Student Academic Trajectories: The Impact of Individual-Level Characteristics and Implications for Education Policy. Applied Sciences. 2025; 15(3):1426. https://doi.org/10.3390/app15031426
Chicago/Turabian StyleMosia, Moeketsi, Felix O. Egara, Fadip Nannim, and Moses Basitere. 2025. "Bayesian Growth Curve Modelling of Student Academic Trajectories: The Impact of Individual-Level Characteristics and Implications for Education Policy" Applied Sciences 15, no. 3: 1426. https://doi.org/10.3390/app15031426
APA StyleMosia, M., Egara, F. O., Nannim, F., & Basitere, M. (2025). Bayesian Growth Curve Modelling of Student Academic Trajectories: The Impact of Individual-Level Characteristics and Implications for Education Policy. Applied Sciences, 15(3), 1426. https://doi.org/10.3390/app15031426