Rina Durandt (University of the Witwatersrand, Johannesburg, Südafrika): Can Good Modelling Teaching Compensate for Weak Prior Mathematical Knowledge? Evidence from South African University Students
Abstract:
Students enter university mathematics with highly diverse mathematical backgrounds, and diagnostic assessments are commonly used to identify knowledge gaps and students at risk of failure. However, an important question remains: To what extent does prior mathematical knowledge actually determine students' opportunities to develop mathematical modelling competency in university classrooms?
This presentation brings together findings from two complementary studies conducted within the Comparative Studies into Teaching Approaches for Mathematical Modelling (CoSTAMM) project involving first-year engineering and science students in South Africa. The first study examines students' prior mathematical knowledge through a large-scale diagnostic assessment and qualitative error analysis. The findings reveal substantial conceptual and procedural weaknesses across several mathematical domains, particularly functions, analytical geometry and modelling, highlighting the complexity and heterogeneity of students' mathematical preparedness for tertiary study. The second study investigates how these differences in prior knowledge influence students' learning during a five-lesson mathematical modelling intervention implemented using two teaching approaches: a teacher-directive and a method-integrative design. While students entered the intervention with markedly different levels of prior knowledge, quantitative and qualitative analyses show that modelling competency developed across all achievement levels. Prior mathematical knowledge was only weakly associated with modelling gains, whereas the characteristics of the learning environment—especially cognitively demanding modelling tasks, strategic teacher support, opportunities for independent work, and metacognitive scaffolding—played a far more influential role. Students with weaker initial knowledge frequently demonstrated substantial growth in modelling competency.
Taken together, the studies suggest that diagnostic assessment should serve not only to identify students' mathematical preparedness but also to inform the design of responsive modelling instruction. The presentation argues that high-quality, modelling-oriented teaching can create meaningful learning opportunities for students with diverse mathematical backgrounds and therefore has important implications for supporting the transition into university mathematics.