Grade 12 learners' difficulties in applying the concept of proportionality in triangles

Abstract

This research examines Grade 12 learners’ difficulties when dealing with geometric problems involving proportionality in triangles. The study also explores the kinds of difficulties learners’ experience when responding to similarity and proportional division theorem problems, and how their difficulties in similarity and proportional division affect their difficulties in complex geometric problems involving proportionality in triangles. Grade 12 learners’ difficulties in these concepts are investigated through the theoretical lens of Kilpatrick et al. (2001) four strands of mathematical proficiency: conceptual understanding, procedural fluency, adaptive reasoning and strategic competence. A mixed method design is utilized to present, analyze and interpret learners’ difficulties from their Preliminary 2023 and June 2024 Paper 2 examination scripts. Grade 12 learners (two different cohorts) from two participant schools at Gauteng East district were purposefully selected to be part of this study. A total of 139 learners’ scripts were selected for this study from both participant schools representing both the 2023 and 2024 cohorts. A total of 89 learners’ scripts for the 2023 cohort from both participant schools were selected for quantitative analysis. A total of 50 learners’ scripts for the 2024 cohort from both participant schools were also selected for both quantitative and qualitative analysis, but only those learners’ scripts which showed relevant information were qualitatively presented and analyzed. Learners’ difficulties in the concept of similarity due to their struggles with circle geometry concepts and similarity procedures negatively affected their chances of success in proportionality problems. Although learners’ performances in proportional division theorem were better, this did not translate to the correct application of the concepts in complex proportionality problems. The study found that Grade 12 learners experience difficulties associated with all four strands, but these difficulties are worse in situations where learners are confronted with complex proportionality geometric problems involving strategic competence. The study also explored how different teaching approaches including the use of ICT’s can be useful in addressing learners’ difficulties.