Mathematics globally remains a gateway subject for entry into many higher education programmes of study, particularly STEM fields. In a society increasingly shaped by technology and artificial intelligence, mathematics is becoming indispensable (Shipolowski, Edele, Mahler & Stanat, 2021). Like many European countries grappling with improving immigrant student and other at-risk student performance in mathematics (e.g. Prediger, Dröse, Stahnke & Ademmer, 2023), South Africa similarly faces persistent poor performance in mathematics by the majority of its learners (Bowie, Venkat, Hannan & Namome, 2019). Enrolment in mathematics in the South African school leaving examination is declining even though the pass rate in mathematics increased (DBE, 2025). It seems likely that the increased pass rate is partially achieved by decanting learners who are potential mathematics failures from the mathematics pool to Mathematics Literacy, a distinct subject from Mathematics at Grades 10 – 12.

Declining participation rates coupled with a relatively low pass rate highlight the need to understand what happens in South African mathematics classrooms. What mathematics is taught to learners  and how is mathematics taught, particularly in the grades prior to the final school leaving examination?  South African research has tended to focus more attention on early grade mathematics in recent years with research on high school mathematics taking a back seat. This paper focuses attention on high school mathematics with a particular study of how mathematics is constituted, made available and mediated to learners in selected Grade 8 and Grade 10 South African classrooms. Particularly, this study aims at examining how pedagogic evaluation functions in mathematics lessons to reveal criteria that constitute what mathematics is taught and learnt. The research question guiding this study is stated as follows: how does pedagogic evaluation function in grade 8 and 10 mathematics classrooms and what mathematics is constituted in these classrooms? 

Bernstein (2000) posits that evaluation is a central and ever-present component of pedagogy. Using this proposition as a starting point, the paper looks at evaluative practices as the means through which what counts as legitimate and successful acquisition of the knowledge privileged in a pedagogic context is made available to learners. Pedagogic evaluation, therefore, is the mechanism employed by teachers to communicate to their learners what they ought to produce and how. Furthermore, the investigation of the functioning of pedagogic evaluation in mathematics lessons is informed by a computational theory of mind (see Gallistel & King, 2010) which posits that thought is computational.  In other words, the mathematics that unfolds in classrooms can be described as a series of computations that takes inputs and produces outputs through some process. The paper thus adopts a computational approach to analysis (Davis, 2013. Jaffer, 2018) which focuses on the operations, propositions and definitions used by teachers and learners when doing mathematics to ascertain the content that emerges in the classroom. Thus, instances of pedagogic evaluation such as teacher’s explanations of mathematics content as well as feedback on learner responses to teacher questions are examined in terms of the computations employed to reveal what mathematics is made available and how mathematics is communicated to learners.

The research sites included eight high schools in two South African provinces, representing polar ends of the socio-economic spectrum with regards to educational contexts in South Africa. The two provinces differ in terms of income levels and resourcing, with the Eastern Cape being largely rural much poorer than the more urban Western Cape province. Data collected focused on observations of two consecutive mathematics lessons taught by Grade 8 and 10 Mathematics teachers in each of the 8 research schools. In total 32 mathematics lessons, taught by 16 Grade 8 and Grade 10 teachers, were observed by a researcher together with trained fieldworker. In addition, detailed lesson descriptions of the lessons were produced by the researcher using video-recordings of the lessons. The video-recorded lessons allowed for in-depth computational analysis of the lessons not possible during observation. A closed-ended observation tool was used to code lessons in terms of pedagogic evaluation practices. In the coding, pedagogic evaluation was measured in terms of three interrelated dimensions: 1) articulating and explaining purpose and content of lesson; (2) checking learners’ understanding through questions and tasks given in the lesson; and (3) feedback from the teacher to learner responses in the lesson. The researcher and fieldworker completed the closed-ended observation tool immediately after the lessons in an attempt to achieve inter-rater reliability. Coding of pedagogic evaluation in lessons were ratified during in-depth analysis of the lessons using the video-recordings of the lessons. Each mathematics lesson was subjected to an in-depth computational analysis which focuses on the operations employed by teachers and their learners, identifying whether the operations employed are standard mathematical operations or “operations” located outside the field of mathematics such as “change sides, change signs” for solving an equation. Similarly, the definitions for mathematical concepts used by teachers were examined. The outcome of a computational analysis enabled a description of how pedagogic evaluation functions and consequently what is constituted as the mathematics in a pedagogic context. This paper discusses illustrative examples from the lessons observed to exemplify pedagogic evaluation in mathematics classrooms.

Most lessons are coded high with respect to content exposition, indicating that teachers’ explanations are clear and accurate. A smaller proportion of lessons scored medium in that teachers’ explanations are mostly clear and accurate but at a simple level. The reason for the absence of low and very low for teacher content exposition is surprising given that the literature highlights poor teacher knowledge as a major causal factor related to poor performance in mathematics (e.g. Mkhwanazi, Bansilal, & Brijlall, 2023). It appears that lessons score high for teacher exposition because in many lessons the focus is on drilling procedures for solving classes of problems particularly in algebra and measurement. A closer examination of the lessons reveals gaps in teacher knowledge and faulty mathematics knowledge. It appears that teacher knowledge gaps have little effect on short term goals aimed at learners’ successful completion of tasks in the lessons. Generally, lessons are characterised by the atomisation of content in that teachers dissect problems into smaller computations for learners and chart solution pathways rather than providing opportunities for them to solve mathematics problems independently through selecting and sequencing computations. Typically procedures are drilled in teacher exposition segments and again when marking tasks, essentially set for learners to practice the procedure rehearsed in lessons. Teacher questioning, consequently, is dominated by simple recall-type questions, questions focused on providing data from the problem statement or questions requiring simple calculations. Feedback to learners in most lessons took the form of repeating steps of a procedure. Only two teachers across the sample of 16 mathematics teachers focus on diagnosing learner errors, a central component of learning. The long term effect of the knowledge gaps, teacher misconceptions, the atomisation of content and narrow focus on procedure drilling may have effects on learners’ future learning later in school and beyond.

Bernstein, B. (2000) Pedagogy, symbolic control and identity. Theory, research, critique. Revised ed. . Rowman & Littlefield. Bowie, L., Venkat, H., Hannan, S., & Namome, C. (2019). TIMSS 2019 South African Item Diagnostic Report: Grade 9 Mathematics. Human sciences research council. Davis, Z. (2013). Constructing Descriptions and Analyses of Mathematics Constituted in Pedagogic Situations, with Particular Reference to an Instance of Addition over the Reals. (Plenary Address to the 7th Mathematics and Society Conference). In M. Berger, K. Brodie, V. Frith, & K. le Roux (Eds.), Proceedings of the Seventh Mathematics and Society Conference (pp. 31 – 59). Cape Town. Department of Basic Education (DBE). (2025). 2024 National Senior Certificate (NSC). School Performance Report. Pretoria: Department of Basic Education. Gallistel, C. R., & King, A. P. (2010). Memory and the Computational Brain: Why Cognitive Science Will Transform Neuroscience. Wiley-Blackwell. Jaffer, S. (2018). Pedagogic evaluatioon, computational performance and orientations to a study of the constitution of Grade 10 mathemaics in two secondary schools (Doctoral dissertation, University of Cape Town). Mkhwanazi, T., Bansilal, S., & Brijlall, D. (2023). High School Mathematics Teachers’ Knowledge of Trigonometry and Geometry. Journal of Educational Studies, 22(2), 75-97. Prediger, S., Dröse, J., Stahnke, R., & Ademmer, C. (2023). Teacher expertise for fostering at-risk students’ understanding of basic concepts: conceptual model and evidence for growth. Journal of Mathematics Teacher Education, 26(4), 481-508. Schipolowski, S., Edele, A., Mahler, N., & Stanat, P. (2021). Mathematics and science proficiency of young refugees in secondary schools in Germany. Journal for Educational Research Online, 13(1), 78-10.