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This article focuses mainly on two key mathematical processes (representation, and reasoning and proof). Firstly, we observed how teachers learn these processes and subsequently identify what and how to assess learners on the same processes. Secondly, we reviewed one teacher’s attempt to facilitate the learning of the processes in his classroom. Two interrelated questions were pursued: ‘what are the teachers’ challenges in learning mathematical processes?’ and ‘in what ways are teachers’ approaches to learning mathematical processes influencing how they assess their learners on the same processes?’ A case study was undertaken involving 10 high school mathematics teachers who enrolled for an assessment module towards a Bachelor in Education Honours degree in mathematics education. We present an interpretive analysis of two sets of data. The first set consisted of the teachers’ written responses to a pattern searching activity. The second set consisted of a mathematical discourse on matchstick patterns in a Grade 9 class. The overall finding was that teachers rush through forms of representation and focus more on manipulation of numerical representations with a view to deriving symbolic representation. Subsequently, this unidirectional approach limits the scope of assessment of mathematical processes. Interventions with regard to the enhancement of these complex processes should involve teachers’ actual engagements in and reflections on similar learning.

The study explored the effect of the activity-based approach (ABA) on grade 11 learners' performance in solving two-dimensional (2D) trigonometric problems. A sequential explanatory design was used, starting with the quantitative, followed by the qualitative method. The experimental group (EG) and the control group (CG) were facilitated using ABA, while CG was taught using traditional teaching approach. A 2D trigonometry test was used as a pre-and posttest to measure learners' performance. EG's experiences of using ABA were captured through focus group interviews. The study findings reveal significant differences between EG and CG posttests [t(100)=.3. 95; p=.05] with Cohen d=.79. Also, ABA did not segregate between boys and girls. Despite ABA being time-consuming, learners in EG developed collaborative skills, trigonometry vocabulary, the ability to solve trigonometric problems, and learning autonomy, which improved their performance. The study recommends ABA to improve learners' performance.

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