Distributional Inequality in Mathematics Achievement: Quantile Regression Evidence from Low-Performing Secondary Schools in Ghana

Authors

  • Prince Hamid Armah

Keywords:

mathematics achievement; quantile regression; expectancy–value theory; motivation

Abstract

This study examines how demographic, family, motivational and contextual factors are associated with mathematics achievement across the achievement distribution among students in low-performing public Senior High Schools in Ghana. Using a cross-sectional survey of 725 final-year students, of whom 418 listwise-complete cases were retained for the main ordinary least squares and quantile models, the study estimates quantile regression at the 25th, 50th, and 75th conditional quantiles and interprets the findings through family capital theory and expectancy-value theory. Results show clear heterogeneity across achievement levels. Mathematics self-confidence is a strong positive correlate at the median and upper quantiles, classroom engagement is negatively associated with achievement at the lower and median quantiles, and regional disadvantage is most evident among lower-achieving students in the Middle Belt. The findings show that mean-based estimates can mask important differences across achievement levels and support a distribution-sensitive understanding of mathematics achievement inequality in under-resourced school settings.

https://doi.org/10.26803/ijlter.25.5.12

References

Agyei, E. A., Annim, S. K., Acquah, B. Y. S., Sebu, J., & Agyei, S. K. (2024). Education infrastructure inequality and academic performance in Ghana. Heliyon, 10(14), e34041. https://doi.org/10.1016/j.heliyon.2024.e34041

Alorki, I., Tahiru, A. W., & Tahiru, R. (2024). Exploring impact of student attitude, parental involvement, and teacher competence on mathematics performance in selected schools in Northern Ghana. Journal of Mathematics and Science Teacher, 4(1), em056. https://doi.org/10.29333/mathsciteacher/14251

Amponsah, M. O., Milledzi, E. Y., Ampofo, E. T., & Gyambrah, M. (2018). Relationship between parental involvement and academic performance of senior high school students: The case of Ashanti Mampong Municipality of Ghana. American Journal of Educational Research, 6(1), 1–8. https://doi.org/10.12691/education-6-1-1

Appiah, J. B., Arthur, Y. D., Boateng, F. O., & Akweittey, E. (2023). Teacher-student relationship and students’ mathematics achievement: Mediating roles of students’ perception of mathematics, students’ self-efficacy, and cooperative learning strategies. Journal of Mathematics and Science Teacher, 3(2), em041. https://doi.org/10.29333/mathsciteacher/13193

Ayebale, L., Habaasa, G., & Tweheyo, S. (2020). Factors affecting students’ achievement in mathematics in secondary schools in developing countries: A rapid systematic review. Statistical Journal of the IAOS, 36(1_suppl), 73–76. https://doi.org/10.3233/SJI-200713

Bashir, S., Lockheed, M., Ninan, E., & Tan, J. P. (2018). Facing forward: Schooling for learning in Africa. Washington, DC: World Bank. https://doi.org/10.1596/978-1-4648-1260-6

Benckwitz, L., Dumont, H., Trautwein, U., Kohl, K., Suárez, N., Núñez, J. C., & Guill, K. (2024). Perceived quality of parental homework assistance and students’ academic functioning in secondary school: Does grade level play a role? Learning and Individual Differences, 110, 102422. https://doi.org/10.1016/j.lindif.2024.102422

Berkowitz, R., Moore, H., Astor, R. A., & Benbenishty, R. (2017). A research synthesis of the associations between school climate and student outcomes. Review of Educational Research, 87(2), 179–232. https://doi.org/10.3102/0034654316672069

Boadi, E. A. (2023). Inequality and returns to education in Ghana [Doctoral thesis]. University of Cape Coast, Ghana. http://hdl.handle.net/123456789/11193

Bofah, E. A., & Hannula, M. S. (2017). Home resources as a measure of socio-economic status in Ghana. Large-scale Assessments in Education, 5, Article 7. https://largescaleassessmentsineducation.springeropen.com/articles/10.1186/s40536-017-0039-5

Butakor, P. K., & Nyarko, K. (2018). The home environment as a predictor of mathematics achievement in Ghana. International Journal of Research Studies in Education, 7(1), 1–13. https://doi.org/10.5861/ijrse.2017.1653

Carew, M. T., Rotenberg, S., Chen, S., & Kuper, H. (2024). Counting who makes the grade: Updated estimates of the share of over-age for grade learners in sub-Saharan Africa using MICS6 data. International Journal of Educational Development, 107, 103035. https://doi.org/10.1016/j.ijedudev.2024.103035

Carifio, J., & Perla, R. J. (2008). Resolving the 50 year debate around using and misusing Likert scales. Medical Education, 42(12), 1150–1152. https://doi.org/10.1111/j.1365-2923.2008.03172.x

Castro, M., Expósito-Casas, E., López-Martín, E., Lizasoain, L., Navarro-Asencio, E., & Gaviria, J. L. (2020). Parental involvement on student academic achievement: A meta-analysis. Educational Research Review, 31, 100335. https://doi.org/10.1016/j.edurev.2020.100335

Coleman, J. S. (1988). Social capital in the creation of human capital. American Journal of Sociology, 94(S1), S95–S120. https://doi.org/10.1086/228943

Cortina, J. M. (1993). What is coefficient alpha? An examination of theory and applications. Journal of Applied Psychology, 78(1), 98–104. https://doi.org/10.1037/0021-9010.78.1.98

Costanzo, A., & Desimoni, M. (2017). Beyond the mean estimate: A quantile regression analysis of inequalities in educational outcomes using INVALSI survey data. Large-scale Assessments in Education, 5, 1–25. https://doi.org/10.1186/s40536-017-0048-4

Davis-Kean, P. E. (2005). The influence of parent education and family income on child achievement. Journal of Family Psychology, 19(2), 294–304. https://doi.org/10.1037/0893-3200.19.2.294

Djekourmane, D., Zhang, Y., Li, M., & Cai, Z. (2025). Family cultural capital predicts student cognitive performance: The mediating role of student academic engagement and academic self-efficacy in a comparative cross-national context. PLOS ONE, 20(10), e0329770. https://doi.org/10.1371/journal.pone.0329770

Eccles, J. S., & Wigfield, A. (2002). Motivational beliefs, values, and goals. Annual Review of Psychology, 53, 109–132. https://doi.org/10.1146/annurev.psych.53.100901.135153

Eccles, J. S., & Wigfield, A. (2020). From expectancy–value theory to situated expectancy–value theory. Contemporary Educational Psychology, 61, 101859. https://doi.org/10.1016/j.cedpsych.2020.101859

Else-Quest, N. M., Hyde, J. S., & Linn, M. C. (2010). Cross-national patterns of gender differences in mathematics: A meta-analysis. Psychological Bulletin, 136(1), 103–127

Enders, C. K. (2010). Applied missing data analysis. Guilford Press.

Erdem, C., & Kaya, M. (2020). A meta-analysis of the effect of parental involvement on students’ academic achievement. Journal of Learning for Development, 7(3), 367–383. https://doi.org/10.56059/jl4d.v7i3.417

Fan, X., & Chen, M. (2001). Parental involvement and students’ academic achievement. Educational Psychology Review, 13(1), 1–22. https://doi.org/10.1023/A:1009048817385

Field, A. (2018). Discovering statistics using IBM SPSS Statistics (5th ed.). Sage.

Flannery, D., Gilleece, L., & Clavel, J. (2023). School socioeconomic context and student achievement in Ireland. Large-scale Assessments in Education, 11, 1–26. https://doi.org/10.1186/s40536-023-00171-x

Fredricks, J. A., Blumenfeld, P. C., & Paris, A. H. (2004). School engagement. Review of Educational Research, 74(1), 59–109. https://doi.org/10.3102/00346543074001059

Guo, J., Parker, P. D., Marsh, H. W., & Morin, A. J. S. (2018). Achievement, motivation, and educational choice: A longitudinal study of expectancy–value theory. Developmental Psychology, 54(1), 73–89. https://doi.org/10.1037/dev0000393

Haile, G., & Nguyen, A. (2008). Determinants of academic attainment. Education Economics, 16, 29–57. https://doi.org/10.1080/09645290701523218

Hajovsky, D., Villeneuve, E. F., Schneider, W. J., & Caemmerer, J. M. (2020). An alternative approach to cognitive and achievement relations research: An introduction to quantile regression. Journal of Pediatric Neuropsychology, 6, 83–95. https://doi.org/10.1007/s40817-020-00086-3

Hanushek, E. A., & Woessmann, L. (2015). The knowledge capital of nations: Education and the economics of growth. MIT Press.

Hanushek, E. A., & Woessmann, L. (2011). The economics of international differences in educational achievement. In E. A. Hanushek et al. (Eds.), Handbook of the Economics of Education (Vol. 3, pp. 89-200). https://doi.org/10.1016/B978-0-444-53429-3.00002-8

Harris, A. L., & Robinson, K. (2016). A new framework for understanding parental involvement: Setting the stage for academic success. RSF: The Russell Sage Foundation Journal of the Social Sciences, 2(5), 186–201. https://doi.org/10.7758/RSF.2016.2.5.09

Hidayatullah, A., & Csíkos, C. (2023). The role of students’ beliefs, parents’ educational level, and the mediating role of attitude and motivation in students’ mathematics achievement. The Asia-Pacific Education Researcher, 33, 1–10. https://doi.org/10.1007/s40299-023-00724-2

Hill, N. E., & Tyson, D. F. (2009). Parental involvement in middle school: A meta-analysis of the strategies that promote achievement. Developmental Psychology, 45(3), 740–763. https://doi.org/10.1037/a0015362

Koenker, R., & Bassett, G. (1978). Regression quantiles. Econometrica, 46(1), 33–50. https://doi.org/10.2307/1913643

Koenker, R., & Hallock, K. F. (2001). Quantile regression. Journal of Economic Perspectives, 15(4), 143–156. https://doi.org/10.1257/jep.15.4.143

Koenker, R. (2005). Quantile Regression. Cambridge University Press.

Kohl, G. O., Lengua, L. J., & McMahon, R. J. (2000). Parent involvement in school: Conceptualizing multiple dimensions and their relations with family and demographic risk factors. Journal of School Psychology, 38(6), 501–523. https://doi.org/10.1016/S0022-4405(00)00050-9

Lariviere, D., Powell, S., Fall, A., Roberts, G., & Arsenault, T. (2025). Language predictors of word-problem performance among third-grade students with mathematics difficulty. Journal of Learning Disabilities, 58(6). https://doi.org/10.1177/00222194241311979

Larson, K. E., Nguyen, A. J., Orozco Solis, M. G., Humphreys, A., Bradshaw, C. P., & Lindstrom Johnson, S. (2020). A systematic literature review of school climate in low and middle income countries. International Journal of Educational Research, 102, 101606. https://doi.org/10.1016/j.ijer.2020.101606

Li, A., & Hamlin, D. (2019). Is daily parental help with homework helpful? Reanalyzing national data using a propensity score based approach. Sociology of Education, 92(4), 367–385. https://doi.org/10.1177/0038040719867598

Marsh, H. W., Pekrun, R., Parker, P. D., Murayama, K., Guo, J., Dicke, T., & Arens, A. K. (2019). The murky distinction between self-concept and self-efficacy: Beware of lurking jingle-jangle fallacies. Journal of Educational Psychology, 111(2), 331–353. https://doi.org/10.1037/edu0000281

McNeal, R. B., Jr. (2012). Checking in or checking out? Investigating the parent involvement reactive hypothesis. The Journal of Educational Research, 105(2), 79–89. https://doi.org/10.1080/00220671.2010.519410

Mensah, B., & Koomson, E. (2020). Linking teacher-student relationship to academic achievement of senior high school students. Social Education Research, 1(2), 102-108.

Molina-Muñoz, D., Contreras-García, J., & Molina-Portillo, E. (2025). Understanding educational inequality in Spain. Social Sciences, 14(8), Article 463. https://doi.org/10.3390/socsci14080463

Niu, J., Xu, H., & Yu, J. (2025). Identifying multilevel factors on student mathematics performance for Singapore, Korea, Finland, and Denmark in PISA 2022: Considering individualistic versus collectivistic cultures. Humanities and Social Sciences Communications, 12, Article 151. https://doi.org/10.1057/s41599-025-04466-y

Norman, G. (2010). Likert scales, levels of measurement and the “laws” of statistics. Advances in Health Sciences Education, 15(5), 625–632. https://doi.org/10.1007/s10459-010-9222-y

OECD. (2023). PISA 2022 results (Volume I): The state of learning and equity in education. OECD Publishing. https://doi.org/10.1787/53f23881-en

Patall, E. A., Cooper, H., & Robinson, J. C. (2008). Parent involvement in homework: A research synthesis. Review of Educational Research, 78(4), 1039–1101.

Peixoto, F., Mata, L., Monteiro, V., Santos, N., Sanches, C., & Pekrun, R. (2024). Am I to blame because my child is not motivated to do math? The role of parents’ beliefs in children’s motivation and mathematics achievement. European Journal of Psychology of Education, 39,1561-1586. https://doi.org/10.1007/s10212-023-00774-6

Perry, L. B., Saatcioglu, A., & Mickelson, R. A. (2022). Does school SES matter less for high-performing students than for their lower-performing peers? A quantile regression analysis of PISA 2018 Australia. Large-scale Assessments in Education, 10, Article 17. https://doi.org/10.1186/s40536-022-00137-5

Pomerantz, E. M., Moorman, E. A., & Litwack, S. D. (2007). The how, whom, and why of parents' involvement. Review of Educational Research, 77(3), 373–410. https://doi.org/10.3102/003465430305567

Quaye, J., & Pomeroy, D. (2022). Social class inequalities in attitudes towards mathematics and achievement in mathematics cross generations: A quantitative Bourdieusian analysis. Educational Studies in Mathematics, 109(1), 155–175. https://doi.org/10.1007/s10649-021-10078-5

Rhemtulla, M., Brosseau-Liard, P. É., & Savalei, V. (2012). When can categorical variables be treated as continuous? A comparison of robust continuous and categorical SEM estimation methods under suboptimal conditions. Psychological Methods, 17(3), 354–373. https://doi.org/10.1037/a0029315

Schafer, J. L., & Graham, J. W. (2002). Missing data: Our view of the state of the art. Psychological Methods, 7(2), 147–177. https://doi.org/10.1037/1082-989X.7.2.147

Sijtsma, K. (2009). On the use, the misuse, and the very limited usefulness of Cronbach’s alpha. Psychometrika, 74(1), 107–120.

Susperreguy, M. I., Davis-Kean, P. E., Duckworth, K., & Chen, M. (2018). Self-concept predicts academic achievement across levels of the achievement distribution: Domain specificity for mathematics and reading. Child Development, 89(6), 2196–2214. https://doi.org/10.1111/cdev.12924

Tabachnick, B. G., & Fidell, L. S. (2019). Using Multivariate Statistics (7th ed.). Pearson.

Thapa, A., Cohen, J., Guffey, S., & Higgins-D’Alessandro, A. (2013). A review of school climate research. Review of Educational Research, 83(3), 357–385. https://doi.org/10.3102/0034654313483907

Wang, M. T., & Degol, J. L. (2016). School climate: A review of the construct, measurement, and impact on student outcomes. Educational Psychology Review, 28(2), 315–352.

Wang, M.–T., Degol, J. L., & Seipp, A. (2020). School climate and adolescent academic functioning. Child Development, 91(6), 1718–1733.

Wang, X. S., Perry, L. B., Malpique, A., & Ide, T. (2023). Factors predicting mathematics achievement in PISA: A systematic review. Large-scale Assessments in Education, 11, Article 24. https://doi.org/10.1186/s40536-023-00174-8

West African Examinations Council [WAEC]. (2025, December 3). Release of provisional results for WASSCE SC 2025 [Press release]. https://waecgh.org/2025/12/03/release-of-provisional-results-for-wassce-sc-2025/

World Bank, UNESCO, UNICEF, United States Agency for International Development, Foreign, Commonwealth & Development Office, & Bill & Melinda Gates Foundation. (2022). The state of global learning poverty: 2022 update. World Bank. https://documents1.worldbank.org/curated/en/099551612232212904/pdf/IDU0ad554dbc0c1a60431d0bf0805957739d6ae0.pdf

Wu, X. Z., & Tian, M. Z. (2008). A longitudinal study of the effects of family background factors on mathematics achievements using quantile regression. Acta Mathematicae Applicatae Sinica, English Series, 24(1), 85–98. https://doi.org/10.1007/s10255-006-6066-6

Xu, J., Guo, S., Feng, Y., Ma, Y., Zhang, Y., Núñez, J. C., & Fan, H. (2024). Parental homework involvement and students’ achievement: A three-level meta-analysis. Psicothema, 36(1), 1–14. https://doi.org/10.7334/psicothema2023.92

Yang, Y., Zhang, L., Sun, X., & Wang, M.-T. (2024). Reciprocal relationships between parental involvement and adolescents’ academic performance. Journal of Youth and Adolescence, 53, 1–16. https://d-nb.info/1353576256/34

Zhu, Z., Zuckerman, A. P., Shero, J. A., Willcutt, E. G., Thompson, L. A., & Petrill, S. A. (2024). How relations between early reading skills and third-grade mathematics outcomes vary across distribution: A quantile regression approach. Developmental Psychology, 60(12), 2385–2395. https://doi.org/10.1037/dev0001772

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2026-05-30

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Armah, P. H. . (2026). Distributional Inequality in Mathematics Achievement: Quantile Regression Evidence from Low-Performing Secondary Schools in Ghana. International Journal of Learning, Teaching and Educational Research, 25(5), 252–282. Retrieved from https://www.ijlter.net/index.php/ijlter/article/view/2853

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