Integrating the anthropological theory of didactics in multivariate calculus education: Challenges, pedagogical shifts, and innovative activities

The anthropological theory of didactics (ATD) provides a lens to view mathematics education by placing mathematical practices within socio-cultural and historical contexts. The significance of institutions, in what regards with educational establishments, societal structures, cultural norms, and historical contexts, influences the perception and practice of mathematics in both students and teachers. This perspective is relevant for understanding the complexities of teaching multivariate calculus. Traditional approaches to this subject have been lecture-based, but with the evolution of educational paradigms, active pedagogies have emerged as vital. These include among others inquiry-based learning, collaborative learning, the flipped classroom approach, technology-enhanced active learning, and project-based learning. The challenges students face in multivariate calculus range from conceptual complexities to visualization challenges and over-reliance on memorization. In this work, we propose a holistic approach for defining class activities in multivariate calculus with emphasis in integrating visualization techniques, real-world applications, collaborative activities, and feedback mechanisms. Accordingly, four class activities, grounded in the principles of ATD and tailored to address challenges in multivariate calculus, are proposed. These activities aim to foster significant understanding, relevance, and engagement in students.