Angel Mukuka, Védaste Mutarutinya, Sudi Balimuttajjo


Literature is well-stocked with studies confirming that an instructional approach, self-efficacy, and mathematical reasoning skills are critical for enhancing students’ conceptual understanding and achievement in mathematics. However, there has been little emphasis on establishing whether being able to reason mathematically depends only on the instructional approach or students’ self-efficacy beliefs about mathematics also play a hidden role. A quasi-experimental study involving 301 grade 11 students from six public secondary schools in one district was carried out to investigate the mediating effect of self-efficacy on the relationship between instruction and students’ mathematical reasoning. Participants of the study were selected using the cluster random sampling method. Data were collected before and after the intervention via a mathematical reasoning test and a mathematics self-efficacy beliefs questionnaire. A Parallel Multiple Mediator Model in SPSS using the PROCESS custom dialogue version 3.4 was employed for data analysis. Findings suggest that mathematics self-efficacy and task-specific self-efficacy beliefs collectively and significantly mediate the effect of the instructional approach on students’ mathematical reasoning. The Student Teams-Achievement Division (STAD) was found to be an effective approach for enhancing students’ mathematical reasoning alongside self-efficacy beliefs. These findings provide evidence on the need to select an instructional approach that does not only focus on developing students’ cognitive abilities such as mathematical reasoning but also fosters students’ affective attributes such as maths self-efficacy beliefs.


instructional approach; mathematical reasoning; self-efficacy beliefs; STAD

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Adams, W. K., & Wieman, C. E. (2010). Development and validation of instruments to measure learning of expert-like thinking. International Journal of Science Education, 33(9), 1289–1312. /09500693.2010.512369

Ardiyani, S. M., Gunarhadi, & Riyadi. (2018). Realistic mathematics education in cooperative learning viewed from learning activity. Journal on Mathematics Education, 9(2), 301–310.

Baines, E., Blatchford, P., & Webster, R. (2015). The challenges of implementing group work in primary school classrooms and including pupils with special educational needs. Education 3–13, 43(1), 15–29.

Bandura, A. (1986). The explanatory and predictive scope of self-efficacy theory. Journal of Social and Clinical Psychology, 4(3), 359-373.

Baumann, J. F. (1988). Direct instruction reconsidered. Journal of Reading Behavior, 37, 712-718.

Bonne, L., & Lawes, E. (2016). Assessing students’ maths self-efficacy and achievement. Assessment News, Set 2, 60–63.

Buchs, C., Filippou, D., Pulfrey, C., & Volpé, Y. (2017). Challenges for cooperative learning implementation: Reports from elementary school teachers. Journal of Education for Teaching, 43(3), 296-306.

Butera, F., & Buchs, C. (2019). Social interdependence and the promotion of cooperative learning. In K. Sassenberg, & M. Vliek (Eds.). Social Psychology in Action (pp. 111-127). Cham: Springer.

Cheema, J. R., & Skultety, L. S. (2016). Self-efficacy and literacy: A paired difference approach to estimation of over-/under-confidence in mathematics- and science-related tasks. Educational Psychology, 37(6), 652–665.

Child, D. (2006). The Essentials of Factor Analysis (3rd ed.). New York: Continuum.

Creswell, J. (2014). Research Design: Quantitative, Qualitative, and Mixed Methods Approach (4th ed.). New York: SAGE Publications

Curriculum Development Centre. (2013). O’ level Secondary School Mathematics Syllabus Grade 10-12. Ministry of General Education.

Czocher, J. A., Melhuish, K., & Kandasamy, S. S. (2019). Building mathematics self-efficacy of STEM undergraduates through mathematical modelling. International Journal of Mathematical Education in Science and Technology, 51(6), 807–834.

Examinations Council of Zambia. (2012). Chief Examiner’s Report.

Examinations Council of Zambia. (2016). Examinations Performance Report for 2015 in Natural Sciences.

Examinations Council of Zambia. (2018). 2017 Examinations Review Booklet: School Certificate Ordinary Level Chief Examiner’s Reports.

Field, A. (2013). Discovering Statistics Using SPSS (4th ed.). New York: SAGE.

Fraenkel, J. R., Wallen, N. E., & Hyun, H. H. (2006). How to Design and Evaluate Research in Education. Mc Graw Hill.

Gardner, P. L. (1995). Measuring attitudes to science: Unidimensionality and internal consistency revisited. Research in Science Education, 25(3), 283–289.

Ghaith, G. M. (2018). Teacher perceptions of the challenges of implementing concrete and conceptual cooperative learning. Issues in Educational Research, 28(2), 385–404.

Gillies, R. M. (2016). Cooperative learning: Review of research and practice. Australian Journal of Teacher Education, 41(3), Article 3.

Gillies, R. M., & Boyle, M. (2010). Teachers’ reflections on cooperative learning : Issues of implementation. Teaching and Teacher Education, 26(4), 933–940.

Grigg, S., Perera, H. N., McIlveen, P., & Svetleff, Z. (2018). Relations among Math Self Efficacy, Interest, Intentions, and Achievement: A Social Cognitive Perspective. Contemporary Educational Psychology, 53(2), 77–86.

Guadagnoli, E., & Velicer, W. F. (1988). Relation of a sample size to the stability of component patterns. Psychological Bulletin, 103(2), 265–275.

Hayes, A. F. (2018). Introduction to Mediation, Moderation, and Conditional Process Analysis: A Regression-Based Approach (2nd ed.). New York: A Division of Guilford Publications, Inc.

Hendriana, H., Johanto, T., & Sumarmo, U. (2018). The role of problem-based learning to improve students’ mathematical problem-solving ability and self-confidence. Journal on Mathematics Education, 9(2), 291–300.

Hong, D. S., & Choi, K. M. (2014). A comparison of Korean and American secondary school textbooks: The case of quadratic equations. Educational Studies in Mathematics, 85(2), 241–263.

Hossain, A., & Ahmad, R. (2013). Effects of cooperative learning on students ’ achievement and attitudes in secondary mathematics. In F. Odaba?? (Ed.), 3rd World Conference on Learning, Teaching and Educational Leadership (WCLTA-2012) (Vol. 93, pp. 473–477).

Jäder, J., Sidenvall, J., & Sumpter, L. (2016). Students’ Mathematical Reasoning and Beliefs in Non-routine Task Solving. International Journal of Science and Mathematics Education, 15(4), 759–776.

Jeannotte, D., & Kieran, C. (2017). A conceptual model of mathematical reasoning for school mathematics. Educational Studies in Mathematics, 96, 1–16.

Johnson, D. W., & Johnson, R. T. (1999). Making cooperative learning work. Theory into Practice, 38(2), 67–73.

Kohen, Z., Amram, M., Dagan, M., & Miranda, T. (2019). Self-efficacy and problem-solving skills in mathematics: the effect of instruction-based dynamic versus static visualization. Interactive Learning Environments, 1–20.

Kramarski, B., & Mevarech, Z. R. (2003). Enhancing mathematical reasoning in the classroom: The effects of cooperative learning and metacognitive training. American Educational Research Journal, 40(1), 281–310.

Li, M. P., & Lam, B. H. (2013). Cooperative learning: The active classroom. Hong Kong: The Hong Kong Institute of Education.,-m.-p.-_-lam,-b.-h.-2013-cooperative-learning.pdf

Liu, R.-D., Zhen, R., Ding, Y., Liu, Y., Wang, J., Jiang, R., & Xu, L. (2017). Teacher support and math engagement: roles of academic self-efficacy and positive emotions. Educational Psychology, 38(1), 3–16.

Mata-Pereira, J., & da Ponte, J. P. (2017). Enhancing students’ mathematical reasoning in the classroom: teacher actions facilitating generalization and justification. Educational Studies in Mathematics, 96, 169–186.

May, D. K. (2009). Mathematics self-efficacy and anxiety questionnaire. Doctoral dissertation. Georgia: University of Georgia.

Mukuka, A., Balimuttajjo, S., & Mutarutinya, V. (2020a). Applying the SOLO taxonomy in assessing and fostering students’ mathematical problem-solving abilities. In I.S.P. Vale, L. Westaway, & Z. Nhase (Ed.), Proceedings of the 28th Annual Conference of the Southern African Association for Research in Mathematics, Science and Technology Education (pp. 104–112). SAARMSTE

Mukuka, A., Balimuttajjo, S., & Mutarutinya, V. (2020b). Exploring students’ algebraic reasoning on quadratic equations: Implications for school-based assessment. In K. K. Mashood, T. Sengupta, C. Ursekar, H. Raval, & S. Dutta (Eds.), Proceedings of the epiSTEME8 International Conference to Review Research in Science, Technology, and Mathematics Education (pp. 130–138). Mumbai, India:

Mukuka, A., Mutarutinya, V., & Balimuttajjo, S. (2019). Exploring the barriers to effective cooperative learning implementation in school mathematics classrooms. Problems of Education in the 21st Century, 77(6), 745–757.

Mukuka, A., Mutarutinya, V., & Balimuttajjo, S. (2020). Data on students’ mathematical reasoning test scores: A quasi-experiment. Data in Brief, 30, Article 105546.

Nurlaily, V. A., Soegiyanto, H., & Usodo, B. (2019). Elementary school teacher’s obstacles in the implementation of problem-based learning model in mathematics learning. Journal on Mathematics Education, 10(2), 229–238.

Ozgen, K., & Bindak, R. (2011). Determination of self-efficacy beliefs of high school students towards math literacy. Educational Sciences: Theory & Practice, 11(2), 1085–1089.

Öztürk, M., Akkan, Y., & Kaplan, A. (2019). Reading comprehension, mathematics self-efficacy perception, and mathematics attitude as correlates of students’ non-routine mathematics problem-solving skills in Turkey. International Journal of Mathematical Education in Science and Technology, 1–17.

Pajares, F., & Kranzler, J. (1995). Self-efficacy beliefs and general mental ability in mathematical problem-solving. Contemporary Educational Psychology, 20(4), 426–443.

Palincsar, A. S. (1998). Social constructivist perspectives on teaching and learning. Annual Review of Psychology, 49(1), 345-375.

Ross, K. A. (1998). Doing and proving: The place of algorithms and proof in school mathematics. The American Mathematical Monthly, 3(105), 252–255.

Saleh, M., Prahmana, R. C. I., Muhammad, I., & Murni. (2018). Improving the reasoning ability of elementary school students through the Indonesian realistic mathematics education. Journal on Mathematics Education, 9(1), 41–54.

Santia, I., Purwanto, Sutawidjadja, A., Sudirman, & Subanji. (2019). Exploring mathematical representations in solving ill-structured problems: The case of quadratic functions. Journal on Mathematics Education, 10(3), 365–378.

Slavin, R. (1987). Cooperative Learning: Student Teams (2nd ed.). Washington: National Education Association.

Slavin, R. E. (2015). Cooperative Learning in Schools. In International Encyclopedia of Social & Behavioral Sciences (2nd. ed., Vol. 4, pp. 881–886). Elsevier.

Taber, K. S. (2018). The use of Cronbach’s Alpha when developing and reporting research instruments in science education. Research in Science Education, 48(6), 1273–1296.

Tejeda, S., & Gallardo, K. (2017). Performance assessment on high school advanced algebra. International Electronic Journal of Mathematics Education, 12(3), 777–798.

Waller, B. (2006). Math interest and choice intentions of nontraditional African – American college students. Journal of Vocational Behavior, 68(3), 538–547.

Zaslavsky, O. (1997). Conceptual obstacles in the learning of quadratic functions. Focus on Learning Problems in Mathematics, 19(1), 20–44.



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Journal on Mathematics Education
Doctoral Program on Mathematics Education
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