Abstract:

The topic of Similarity in Euclidean geometry presents a significant challenge within the South African Grade 12 mathematics curriculum. Consistent evidence shows that learners struggle with this concept, as reflected in the country's performance in the National Senior Certificate ( NSC) examinations. The Grade 12 NSC diagnostic reports from 2017 to 2023 highlight persistent difficulties among learners in understanding concepts related to Similarity in Euclidean geometry. Teachers play a crucial role in addressing these challenges, as their expertise and teaching strategies directly impact student success.

This study adopted a qualitative research design to explore these challenges in depth. Eight mathematics teachers from six conveniently selected secondary schools in the Gauteng North district were purposively chosen. These teachers were responsible for teaching Grade 12 mathematics, where learners face significant pressure to succeed in the NSC examinations. Data were collected by analyzing the teachers' responses to learners’ written work on Similarity, specifically focusing on the teachers’ ability to identify and correct common misconceptions.

The findings revealed a significant gap in the teachers' Pedagogical Content Knowledge (PCK) regarding Similarity in Euclidean geometry. Specifically, many teachers struggled to identify and address common misconceptions and errors in learners' work. This gap in teachers' knowledge mirrored the challenges faced by learners, as highlighted in the diagnostic reports, creating a cycle of misunderstanding that contributed to poor student performance. The study underscores the need for targeted professional development programs that focus on improving teachers' content knowledge and pedagogical strategies, enabling them to better diagnose and correct learner misconceptions in Euclidean geometry.

Keywords:

Euclidean geometry, similarity, pedagogical content knowledge (PCK), errors, misconceptions.