Impacts of Rubrics on Secondary Students’ Competencies in Quadratic Equations: A Quasi-Experimental Study in Mafinga District, Zambia

Extensive research supports the use of rubrics in assessing mathematics learning outcomes. However, their value in improving student performance is contradictory. This quasi-experimental study investigated the impacts of rubrics on students’ algebraic competencies in quadratic equations. Six grade eleven classes (n=149) were randomly sampled from three secondary schools in Mafinga district (Zambia). Three intact classes (n=78) were randomly assigned to experimental groups and used the rubrics to obtain feedback and support self-assessment in the second term of 2024. Three comparison groups (n=71) implemented the same formative assessment practices without rubrics. Students’ responses to quadratic equations were analyzed qualitatively based on the Structure of Observed Learning Outcomes (SOLO) taxonomy. The results showed that the students who used rubrics significantly improved their procedural skills in solving quadratic equations, including identifying formulas, analyzing problems, applying logical reasoning, and communicating solutions effectively. These findings demonstrate that by providing timely feedback and promoting students’ self-assessment, rubrics can significantly improve secondary students’ competencies in solving quadratic equations.

algebraic competences, quadratic equations, rubrics

1. Adeniji, S. M., Baker, P., & Schmude, M. (2022). Structure of the observed learning outcomes (SOLO) model: A mixed-method systematic review of research in mathematics education. Eurasia Journal of Mathematics, Science and Technology Education, 18(6), 1–17. https://doi.org/10.29333/ejmste/12087 [Google Scholar] [Crossref]

2. Anderson, L. W., & Krathwohl, D. R. (2001). A taxonomy for learning, teaching and assessing: A revision of Bloom’s taxonomy of educational objectives. Longman. [Google Scholar] [Crossref]

3. Andrade, H. G. (2019). A critical review of research on student self-assessment. Frontiers in Education, 4(August), 1–13. https://doi.org/10.3389/feduc.2019.00087 [Google Scholar] [Crossref]

4. Auxtero, L. C., & Callaman, R. A. (2021). Rubric as a learning tool in teaching application of derivatives in basic calculus. Journal of Research and Advances in Mathematics Education, 6(1), 46–58. https://doi.org/https://doi.org/10.23917/jramathedu.v6i1.11449 [Google Scholar] [Crossref]

5. Brookhart, S. M. (2024). Using rubrics in basic education: A review and recommendations. Studies in Educational Assessment, 35(Article r10803), 1–22. https://doi.org/https://doi.org/10.18222/eae.v35.10803 [Google Scholar] [Crossref]

6. Brookhart, S. M., & Chen, F. (2015). The quality and effectiveness of descriptive rubrics. Educational Review, 67(3), 343–368. https://doi.org/10.1080/00131911.2014.929565 [Google Scholar] [Crossref]

7. Busaka, C., Kitta, S. R., & Umugiraneza, O. (2022). Exploring assessment techniques that integrate soft skills in teaching mathematics in secondary schools in Zambia. International Journal of Learning, Teaching and Educational Research, 21(8), 144–162. https://doi.org/10.26803/ijlter.21.8.9 [Google Scholar] [Crossref]

8. Creswell, J. W. (2018). Mixed methods procedures. In In Research design: Qualitative, quantitative, and mixed methods approach (Vol. 5). [Google Scholar] [Crossref]

9. Examinations Council of Zambia. (2019). 2018 Chief examiner’s report for mathematics 4024/2. Examinations Council of Zambia. [Google Scholar] [Crossref]

10. Examinations Council of Zambia. (2022a). 2022 School certificate ( Grade 12 ) examination results highlights (Issue Grade 12). [Google Scholar] [Crossref]

11. Examinations Council of Zambia. (2022b). 2022 School certificate examination performance review report. [Google Scholar] [Crossref]

12. Examinations Council of Zambia. (2023). Primary school leaving examination performance review report (Issue 1). [Google Scholar] [Crossref]

13. Fachrudin, A. D., Putri, R. I. I., & Darmawijoyo. (2014). Building students’ understanding of quadratic equation concepts using naive geometry. IndoMS-JME, 5(2), 192–202. https://doi.org/10.22342/jme.5.2.1502.191-202 [Google Scholar] [Crossref]

14. Fitriyani, N., & Evendi, E. (2024). The effect of using rubrics in improving the quality of assessment of Mathematics learning. International Seminar on Student Research in Education, Science, and Technology, 1(April), 91–101. [Google Scholar] [Crossref]

15. Fraile, J., Gil-Izquierdo, M., & Medina-Moral, E. (2023). The impact of rubrics and scripts on self-regulation, self-efficacy and performance in collaborative problem-solving tasks. Assessment and Evaluation in Higher Education, 48(8), 1223–1239. https://doi.org/10.1080/02602938.2023.2236335 [Google Scholar] [Crossref]

16. Gallego-Arrufat, M. J., & Dandis, M. (2014). Rubrics in a secondary mathematics class. International Electronic Journal of Mathematics Education, 9(1–2), 75–84. https://doi.org/10.29333/iejme/282 [Google Scholar] [Crossref]

17. Golzar, J., & Noor, S. (2022). Defining convenience sampling in a scientific research. International Journal of Education and Language Studies, 1(November), 72–77. [Google Scholar] [Crossref]

18. Hattori, Y., Inoue, Y., Matsubara, K., Hakamata, R., & Hisadomi, Y. (2025). Enhancing critical thinking in mathematics education: A rubric for students’ social values. International Electronic Journal of Mathematics Education , 20(3). https://doi.org/10.29333/iejme/16186 [Google Scholar] [Crossref]

19. Hubber, P., Widjaja, W., & Aranda, G. (2022). Assessment of an interdisciplinary project in science and mathematics: Opportunities and challenges. Teaching Science: The Journal of the Australian Science Teachers Association, 68(1), 13–25. [Google Scholar] [Crossref]

20. Krebs, R., Rothstein, B., & Roelle, J. (2022). Rubrics enhance accuracy and reduce cognitive load in self-assessment. Metacognition and Learning, 17(2), 627–650. https://doi.org/10.1007/s11409-022-09302-1 [Google Scholar] [Crossref]

21. Lawshe, C. (1975). A quantitative approach to content validity. Personnel Psychology, 28(4), 563–575. https://doi.org/doi:10. 1111/j. 1744 -6570.1975.tb01393.x. [Google Scholar] [Crossref]

22. Lopez, J., Robles, I., & Martínez-Planell, R. (2015). Students’ understanding of quadratic equations. International Journal of Mathematical Education in Science and Technology, 47(4), 552–572. https://doi.org/10.1080/0020739X.2015.1119895 [Google Scholar] [Crossref]

23. Ministry of Education. (2013). “O” level mathematics syllabus: Grades 10 to 12 (Issue May). Curriculum Development Centre. [Google Scholar] [Crossref]

24. Ministry of Education. (2023). 2023 Zambia education curriculum framework. The Curriculum Development Centre. [Google Scholar] [Crossref]

25. Mohajan, H. (2017). Two criteria for good measurements in research: Validity and reliability. Annals of Spiru Haret University, 17(3), 58–82. https://mpra.ub.uni-muenchen.de/83458/ [Google Scholar] [Crossref]

26. Morton, J. K., Northcote, M., Kilgour, P., & Jackson, W. A. (2021). Sharing the construction of assessment rubrics with students: A Model for collaborative rubric construction. Journal of University Teaching & Learning Practice, 18(4), 1–15. https://ro.uow.edu.au/jutlp/vol18/iss4/9 [Google Scholar] [Crossref]

27. Mukuka, A., Balimuttajjo, S., & Mutarutinya, V. (2020a). Applying the SOLO taxonomy in assessing and fostering students mathematical problem-solving abilities. Proceedings of the 28th Annual Conference of the Southern African Association for Research in Mathematics, Science and Technology Education, January, 104–112. [Google Scholar] [Crossref]

28. Mukuka, A., Balimuttajjo, S., & Mutarutinya, V. (2020b). Exploring students’ algebraic reasoning on quadratic equations: Implications for school-based assessment. International Conference to Review Research in Science, Technology and Mathematics Education, 130–138. https://episteme8.hbcse.tifr.res.in/proceedings/ [Google Scholar] [Crossref]

29. Murangira, F., Uworwabayeho, A., & Twagilimana, I. (2025). Practical instruction and mathematics academic achievement in selected Ugandan secondary schools. International Journal of Evaluation and Research in Education, 14(6), 4966–4977. https://doi.org/10.11591/ijere.v14i6.30273 [Google Scholar] [Crossref]

30. Mwamba, E., Shumba, O., & Mulenga, H. (2025). Impacts of formative use of rubrics on secondary school students’ academic performance on Quadratic equation problems. Educational Assessment, 00(00), 1–17. https://doi.org/10.1080/10627197.2025.2562801 [Google Scholar] [Crossref]

31. Panadero, E., & Jönsson, A. (2013). The use of scoring rubrics for formative assessment purposes revisited: A review. Educational Research Review, 9(0), 129–144. https://doi.org/10.1016/j.edurev.2013.01.002 [Google Scholar] [Crossref]

32. Panadero, E., Jönsson, A., Pinedo, L., & Fernández-Castilla, B. (2023). Effects of rubrics on academic performance, self-regulated learning, and self-efficacy: A meta-analytic review. Educational Psychology Review, 35(4), 1–38. https://doi.org/10.1007/s10648-023-09823-4 [Google Scholar] [Crossref]

33. Powell, K. C., & Kalina, C. J. (2009). Cognitive and social constructivism: Developing tools for an effective classroom. Education, 130(2), 241–250. [Google Scholar] [Crossref]

34. Richiteanu-Nastase, E. R., & Mihaila, A. R. (2023). Effective use of rubrics in student evaluation: Best practice E-portfolios. In Chapter 6 (pp. 92–107). https://doi.org/10.4018/978-1-6684-6086-3.ch006 [Google Scholar] [Crossref]

35. Shirawia, N. H., Qasimi, A. B., Tashtoush, M. A., Rasheed, N. M., Khasawneh, M. A. S., & Az-Zo’bi, E. A. (2024). Performance assessment of the calculus students by using scoring rubrics in composition and inverse function. Applied Mathematics and Information Sciences, 18(5), 1037–1049. https://doi.org/10.18576/amis/180511 [Google Scholar] [Crossref]

36. Smit, R., Dober, H., Hess, K., Bachmann, P., & Birri, T. (2023). Supporting primary students’ mathematical reasoning practice: The effects of formative feedback and the mediating role of self-efficacy. Research in Mathematics Education, 25(3), 277–300. https://doi.org/10.1080/14794802.2022.2062780 [Google Scholar] [Crossref]

37. Tashtoush, M. A., Shirawia, N., & Rasheed, N. M. (2023). Scoring rubrics method in performance assessment and its effect on Mathematical achievement. Athens Journal of Education, 12(1), 1–20. [Google Scholar] [Crossref]

38. Tejeda, S., & Gallardo, K. (2017). Performance assessment on high school advanced algebra. International Electronic Journal of Mathematics Education, 12(3), 777–798. https://doi.org/10.29333/iejme/648 [Google Scholar] [Crossref]

39. Toalongo, X., Trelles, C., & Alsina, Á. (2022). Design, construction and validation of a rubric to evaluate Mathematical modelling in school education. Mathematics, 10(24), 0–19. https://doi.org/10.3390/math10244662 [Google Scholar] [Crossref]

40. Ukobizaba, F., Nizeyimana, G., & Mukuka, A. (2021). Assessment strategies for enhancing students’ mathematical problem-solving skills: A review of literature. Eurasia Journal of Mathematics, Science and Technology Education, 17(3), 1–10. https://doi.org/10.29333/ejmste/9728 [Google Scholar] [Crossref]

41. Valenzuela-Gonzalez, V., Hernandez-Quintana, A., & Camacho-Rios, A. (2021). Level of competence on the concept of basis of vector space using SOLO taxonomy. Journal Mathematical and Quantitative Methods, 5(8), 10–16. https://doi.org/10.35429/jmqm.2021.8.5.10.16 [Google Scholar] [Crossref]

42. Vygotsky, L. S. (1978). Mind in Society. Harvard University Press. https://doi.org/10.2307/j.ctvjf9vz4 [Google Scholar] [Crossref]

43. Weeda, R., Izu, C., Kallia, M., & Barendsen, E. (2020). Towards an assessment rubric for EiPE tasks in secondary education: Identifying quality indicators and descriptors. Proceedings 20th Koli Calling Conference on Computing Education Research Koli Calling 2020 November 19-22, 2020 Virtually Hosted from Koli, Finland, 1–10. https://doi.org/10.1145/3428029.3428031 [Google Scholar] [Crossref]

44. Willey, K., & Gardner, A. P. (2009). Investigating the capacity of self and peer assessment to engage students and increase their desire to learn . Proceedings of the 37th Annual Conference of the European Association of Engineering Education (SEFI): Attracting Student in Engineering-Engineering Is Fun., 1–11. https://doi.org/https://doi.org/10.1080/03043797.2010.490577 [Google Scholar] [Crossref]

45. Yazici, N. (2013). Comparative investigating of the effect of rubrics used based on SOLO taxonomy on the measurement of success. Unpublished Master Thesis, Kahramanmaras Sutcu Imam University, Institute of Social Sciences, Kahramanmaraş, Turkey. [Google Scholar] [Crossref]

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