Integrating mathematical modelling and critical theory to address water consumption challenges

Abstract

Water consumption is a critical global issue influenced by a complex interaction of environmental, economic and social factors. In education, tackling these challenges necessitates teaching methods that go beyond mere technical problem-solving to encompass critical engagement with real-world situations. This study examines the integration of mathematical modelling and critical theory by instructors in South Africa to improve mathematics instruction, fostering critical thinking and engaging students with real-world social issues including water usage and distribution. Although mathematical modelling provides significant quantitative insights, it often overlooks the social dynamics, power relations, and lived experiences that shape water utilisation. Critical theory offers a complementary qualitative framework that enables learners and teachers to examine social factors and address environmental challenges with greater scrutiny. By integrating these two methodologies, this study aims to develop a holistic framework for mathematics education that captures both structural patterns identified through modelling and context-specific insights revealed through critical reflection. The analyses demonstrate how critical theory informs pedagogical strategies for teaching water-related environmental issues and how teachers can use mathematical modelling to support students’ understanding of water consumption challenges. In addition, the study identifies the tools, professional support, and training that teachers need to successfully integrate these approaches. Through qualitative analysis, the study shows how integrating critical theory and mathematical modelling can enhance students' engagement with real-world issues and foster the development of community-focused, socially responsive mathematics education methods.