Exploring the application of procedural knowledge and conceptual knowledge in geometry: a case of schools in Bushbuckridge in the Mpumalanga province, South Africa

Abstract

The study focuses on the application of procedural and conceptual knowledge in the teaching and learning of geometry. It explores grade 6 and grade 9 learners' proficiency in both types of knowledge through a geometry test. The research also investigates the impact of teaching procedural and conceptual knowledge in learning geometry through semi-structured interviews. Moreover, it explores how grade 6 educators impart both procedural and conceptual knowledge to their learners through educators' observation during geometry lessons. Participants in the study include educators and learners. The theoretical framework for this research is rooted in Van Hiele and Concrete Pictorial Abstract (CPA) theories. The research design for this study utilises a mixed-method approach, incorporating both qualitative and quantitative research. Various data collection methods are employed, including the observation of educators (n=5) during geometry lessons, semi-structured face-to-face interviews with learners (n=10) and educators (n=5), and the administration of a test to learners (n=429). The research involves 5 primary schools with grade 6 classes and 2 high schools with grade 9 classes. The performance of grade 6 and grade 9 learners is evaluated using the grade 6 assessment to measure their procedural and conceptual knowledge. The study compares the knowledge performances of grade 9 learners with those of grade 6 learners and examines the growth of this knowledge over time. Some notable findings suggest that educators predominantly employ traditional methods in teaching. The results reveal that learners in both grade 6 and grade 9 performed poorly in the assessment of procedural knowledge and conceptual knowledge in geometry. Additionally, the findings indicate that learners generally exhibit a positive attitude towards geometry, displaying a stronger inclination towards learning through conceptual knowledge, which involves using concrete objects, visuals, and technology instead of procedural knowledge or traditional teaching approaches. These findings suggest that the underperformance is attributed to learners being taught with traditional methods and rote memorisation in geometry. The recommendations are that educators adopt teaching methods that actively involve learners, such as utilising tangible objects, technological tools, and real-life examples to facilitate the connection of concepts with their personal experiences