Concrete-pictorial-abstract approach for learners'conceptual understanding of common fraction

Abstract

This study explored how using the Concrete-Pictorial-Abstract (CPA) approach improves learners’ conceptual understanding of fractions in the Capricorn North District of South Africa. The research was framed within the conceptual understanding theory rooted in cognitive constructivism. Conceptual understanding is understanding of mathematical ideas as an integrated and functional system with three components: comprehension, operations, and relations. A pretest-posttest research design in a one-phase concurrent embedded mixed-method research approach, within a pragmatism paradigm was used. Data were gathered qualitatively through written classwork tasks and task-based interviews and quantitatively through pretests and post-tests. Deductive thematic analysis with pre-existing themes; operations, comprehension and connections, was used to analyse qualitative data. The quantitative data were analysed using descriptive statistics - mean, median and mode and inferential statistics - independent and paired sample tests. Seventy (75) purposefully sampled Grade 7 learners participated in the study. The findings indicate that the CPA approach improved the learners’ conceptual understanding of fractions though the effect size of the intervention was minimal and negligible. Furthermore, the study found that the incorporation of concrete objects and visual aids was efficient. Additionally, the qualitative results revealed how learners’ conceptual understanding of fractions was enhanced during the intervention. This study contributes to innovative teaching methods of fractions, potentially enhancing mathematics performance and inspiring teachers to explore new teaching approaches