Assessment is essential for teaching and learning mathematical concepts. Teachers’ and learners’ understanding of how assessment is to be conducted in mathematics classrooms will guide what is to be taught and learnt and how teaching and learning will be conducted. The researchers’ assertion is that circle geometry lessons require thinking-based instructions. This necessitates that an associated assessment approach that elicits learners’ thinking must be formulated. Circle geometry requires rigorous logical, creative, critical, and reflective thinking, thus an assessment approach that will nurture learners’ thinking is essential. This exploration was a qualitative case study, conducted at a high school in South Africa involving two groups of grade 11 mathematics learners; both the control group and the experimental group had 34 participants. Data were gathered through classroom observations, a standardised test, and activities/investigation tasks. APOS theory (actions, processes, objects, schemas) was adopted as the theoretical framework and also as data analysis tool and circle geometry lessons were carried out in a collaborative classroom setting. Circle geometry lessons were conducted in line with the four APOS mental conception levels to evoke participants’ thinking, namely action lesson, process lesson, object lesson, and schema lesson. This study ascertained that the interactive didactic assessment was appropriate, as it enhanced participants’ metacognitive development and participants’ conceptual understanding and mathematical reasoning skills were developed. The researchers, therefore, recommend that this formulated assessment approach be implemented for the teaching and learning of mathematics, especially circle geometry, in schools in South Africa.
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