A convergent mixed-methods approach to enhancing learners’ mathematical problem-solving skills in disadvantaged contexts

Brantina Chirinda

doi:10.58524/jasme.v6i3.1104

Authors

Brantina Chirinda University of Witwatersrand, South Africa

DOI:

https://doi.org/10.58524/jasme.v6i3.1104

Keywords:

Disadvantaged Contexts, Mathematical Problem-Solving Skills, Metacognition, Mixed Methods Approach, Problem-Centered Teaching And Learning

Abstract

Background: Mathematical problem-solving is a fundamental competency emphasized in the South African Curriculum and Assessment Policy Statements (CAPS). However, learners in disadvantaged contexts continue to struggle with applying mathematical knowledge to unfamiliar problems, partly due to teaching practices characterized by low cognitive demand.

Aims: This study investigated the effects of a multi-component problem-centered teaching and learning (PCTL) intervention on Grade 8 learners’ mathematical problem-solving performance and attitudes in a disadvantaged South African secondary school and explored the instructional mechanisms underlying observed changes.

Method: A convergent mixed-methods design involved 98 Grade 8 learners. Quantitative data were collected through pre- and post-intervention problem-solving tests and an attitude questionnaire, while qualitative data were obtained from classroom observations, reflective learner journals, and semi-structured interviews with learners and teachers. Both strands were integrated to explain the intervention outcomes.

Results: The experimental group demonstrated significant improvement in mathematical problem-solving performance from pre-test to post-test, t(48) = 9.72, p < .001, d = 1.39. Gain scores were also significantly higher than those of the comparison group, t(96) = 8.54, p < .001. Learners showed moderately improved attitudes toward mathematical challenges. Qualitative findings revealed a shift toward learner-centered discourse characterized by increased teacher wait time, productive struggle, active participation, and metacognitive reflection.

Conclusion: The multi-component PCTL intervention was associated with meaningful improvements in mathematical problem-solving performance and learner attitudes. The findings highlight metacognitive reflection and student-led discourse as important mechanisms for strengthening conceptual problem solving and provide implications for mathematics teacher professional development in resource-constrained settings.

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