The South African school curriculum distinguishes between the school subjects Mathematics and Mathematical Literacy (ML). Mathematical Literacy is a discrete subject offered only to learners in the final three grades of high school (Grades 10-12). The SA National Curriculum describes Mathematics as a subject that supports the development of mathematical knowledge and competence with abstract mathematical structures through engagement with ‘symbols and notations for describing numerical, geometric and graphical relationships’ (Department of Basic Education [DBE], 2011a, p. 8). By contrast, Mathematical Literacy is described as a subject that prioritises the use of ‘more elementary mathematical contents in authentic real-world problem-solving experiences’ (Department of Basic Education [DBE], 2011b, p. 8). While both subjects involve working with mathematical contents, in Mathematical Literacy any mathematics used or learned is intended to be in service to and in support of problem-solving and decision-making in authentic real-world problem experiences (North, 2024). This paper is interested in how Mathematical Literacy teaching and learning unfolds in a selection of Grade 10 classrooms in South Africa. South Africa provides a unique context for this study since in most international conceptions of school curricula the development of mathematical literacy is seen as a component or by-product of the learning and application of mathematical knowledge in mathematics classrooms rather than as a separate knowledge domain (e.g. De Lange, 2003; Kilpatrick, 2001; Organisation for Economic Co-operation and Development [OECD], 2018).

This paper forms part of a broader study that investigated pedagogic structure, class heterogeneity, remediation and assessment in eight South African high schools. The broad framing concept of the study is pedagogic evaluation. According to Bernstein (2000, p. 50), “the key to pedagogic practice is continuous evaluation”. Thus, evaluation marks out criteria for the recognition and realisation of legitimate knowledge statements (Bernstein, 2000) and is central to the reproduction of knowledge in pedagogic contexts. Davis (2005) draws our attention to the fact that Bernstein uses the term evaluation rather than assessment. In other words, pedagogic evaluation is broader than tasks that assess learners’ knowledge and encompasses all forms of pedagogic communication such as teacher and learner talk or written productions, textbooks and other curriculum resources, tests and examinations.

Black and Wiliam (2009) argue that formative assessment does not have a precise and widely accepted meaning, however, from a range of descriptions it can be defined as “all those activities undertaken by teachers, and/or by their students, which provide information to be used as feedback to modify the teaching and learning activities in which they are engaged” (p. 1). Black and Wiliam (2009) conceptualise formative assessment as an aspect that is inherent in the whole of classroom practice, not a separate activity. It is similar to Bernstein’s notion of pedagogy as constant evaluation. The study focuses on the evaluative activity of the teacher and how the teacher makes criteria explicit through explanations and feedback on learner productions.

William and Thompson (2008) provide a framework to structure the analysis of formative assessment carried out in classrooms. The overarching idea of their framework is the use of evidence of student learning to adjust instruction to better meet the identified student learning needs.

Drawing on all of the above, we developed a theoretical framework and classroom observation tool for investigating pedagogic evaluation that focused on three key aspects of teachers’ practice, namely: Articulating purpose and explaining content; Checking learners’ understanding through questions and tasks; and Teachers’ feedback to learner productions.

We articulated our specific research questions as follows :

• How is content explained in lessons?
• What questioning strategies are used by the teacher?
• How do teachers provide feedback on learner responses?

The broad research project collected data in eight case study high schools in two South African provinces, the Western Cape and Eastern Cape. These two provinces represent distinct socio-economic, historical, and educational contexts in South Africa. The Eastern Cape is one of the poorest provinces in South Africa with high levels of unemployment, rural poverty, and limited infrastructure. By contrast, the Western Cape province is more urbanized, has better infrastructure, higher income levels and generally higher educational outcomes. The research employed an in-depth, multiple case study approach to discern how pedagogic evaluation functions across classrooms providing a qualitative perspective on issues of assessment, learning and remediation. To present a detailed understanding of pedagogic evaluation across classrooms, both closed- and open-ended forms of qualitative data were collected for each case. One researcher accompanied by a trained fieldworker observed classroom pedagogy across two consecutive lessons, collecting video and audio-recorded data and producing a detailed, written description of both lessons. After each lesson, the data collectors completed a closed-ended observation tool that was designed to measure scaled levels of pedagogic evaluation in the lesson observed. In this way, the completion of the tool was made in reference to detailed narrative accounts and subjected to a form of inter-rater reliability at the point of data collection. The video and audio-recorded data also allowed for later, in-depth analysis, and provided an alternative opportunity for coding where both data collectors could not be present in the same lesson. In total, seven Grade 10 Mathematical Literacy teachers were observed teaching two consecutive lessons, giving a total of 14 Mathematical Literacy lessons observed. This paper discusses illustrative examples from the Mathematical Literacy lessons observed to exemplify pedagogic evaluation through three interrelated pedagogic processes namely, articulating and explaining purpose and content of lesson, checking learners’ understanding through questions and tasks given in the lesson and feedback from teacher to learner responses in the lesson. The analysis focuses on the evaluative activity of the teacher and how the teacher makes criteria explicit through explanations and feedback on learner productions.

Overall Mathematical Literacy lessons observed were characterised by teacher exposition and explanations that were either very simplistic at best or at worst was unclear or inaccurate. Teacher exposition across the lessons suggested poor grasp of mathematical knowledge by the teacher. The poor grasp of mathematical knowledge of teachers could also be a contributing factor to the low level of questioning in most of the Mathematical Literacy lessons and the absence of elaborated feedback to learner responses. Teacher questions predominantly required simple recall responses and where the occasional question required some thinking and interpretation by learners, learners were generally unresponsive. Feedback to learners in most lessons took the form of teachers working through solutions that individual learners have written on the board. In this regard, feedback to individual learners constitutes feedback to the whole class. In more than one Mathematical Literacy lesson the teacher does not notice or correct errors in learner solutions written on the board, and so these errors are assumed to be correct by the whole class. Finally, in line with the curriculum expectation for Mathematical Literacy, teachers in most of the Mathematical Literacy lessons were at pains to bring ‘real-world contexts’ into the lesson. In many instances, the foregrounding of contexts felt superficial, and it was not always clear whether the contexts would necessarily enhance student learning of the contents or empower them to solve similar ‘real-world’ problems. Despite the foregrounding of contexts, especially in the introduction to topics, most of the exercises that students were given in lessons observed required completion of simple mathematical procedures and computations and very little application or interpretation of contexts. This seemed to undermine the curriculum intent for Mathematical Literacy to prioritise the use of elementary mathematical contents in authentic real-world problem-solving experiences.

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