Effective formative assessment practices in grade 11 analytical geometry: perspectives of mathematics educators

Abstract

The purpose of this study was to explore formative assessment practices used by Grade 11 mathematics educators in teaching Analytical Geometry in secondary schools in the Kgakotlou Circuit, Capricorn South District, Limpopo Province, South Africa. Analytical Geometry presents substantial conceptual challenges for Grade 11 learners, including interpreting gradient relationships, distinguishing between perpendicular and parallel lines, and accurately applying midpoint and distance formulas. Common learner errors include reversing values during gradient substitution, misinterpreting conditions for perpendicularity, and applying coordinate formulas procedurally without conceptual understanding. These persistent misconceptions highlight the importance of using Analytical Geometry as a context for examining how formative assessment can support conceptual development through the identification and remediation of learner errors. These challenges underscore the need to investigate formative assessment practices in mathematics classrooms to enhance learner understanding and engagement. The study addressed three research questions: (a) How do educators conceptualise formative assessment in the teaching of Analytical Geometry? (b) What formative assessment practices are implemented by Grade 11 mathematics educators in Analytical Geometry? and (c) What barriers do educators encounter when implementing effective formative assessment practices? The study was theoretically grounded in Lev Vygotsky’s sociocultural theory and the Learning-Oriented Assessment framework, which served as analytical lenses to understand formative assessment as a socially mediated process linking dialogue, scaffolding, feedback, and instructional responsiveness. A qualitative exploratory phenomenological design was employed. Data were collected through semi-structured interviews, classroom observations, and lesson plan analysis. Twelve Grade 11 mathematics educators were purposively selected from secondary schools within the circuit. Interviews provided insights into educators’ perceptions and experiences of formative assessment, classroom observations captured the enactment of formative assessment practices during lessons, and lesson plan analysis revealed how formative assessment was incorporated into instructional planning. Thematic analysis was used to identify recurring patterns and themes across the datasets. Trustworthiness was ensured through methodological triangulation, member checking, prolonged

engagement, and the maintenance of an audit trail, thereby enhancing credibility, dependability, and confirmability. The findings revealed that educators employed formative assessment practices such as questioning, classroom discussion, peer interaction, exercises, and oral feedback to monitor learner understanding, identify misconceptions, and adjust instruction. Learner participation and classroom dialogue were found to enhance reasoning, engagement, and conceptual understanding. However, the effectiveness of these practices was often constrained by contextual factors, including limited instructional time, large class sizes, and an examination-oriented curriculum, which restricted opportunities for individualised feedback and sustained interaction. This study contributes to mathematics education research by providing context-specific insights into the enactment of formative assessment in Grade 11 Analytical Geometry classrooms in rural South African schools. It further illustrates how structural constraints influence instructional responsiveness and learner participation. The study recommends increased support for educators in developing student-centred formative assessment strategies that promote active participation and deeper conceptual understanding in Analytical Geometry.