Leading theories of mathematics learning

Abstract

This review article provides an overview of the main theories underpinning mathematics learning. It explores both psychological perspectives (Piaget's constructivism, Vygotsky's sociocultural theory, and Bruner's rediscovery approach) and cognitive perspectives (Dubinsky's APOS theory, Pirie-Kieren's theory of understanding, and Papert's constructionism). Additionally, it examines social constructivist theories in the didactics of mathematics, highlighting Brousseau's Theory of Didactic Situations, Chevallard's Anthropological Theory of Didactics, Artigue's Didactic Engineering Theory, Cantoral's Socioepistemology, Godino's Ontosemiotic Approach, Radford's Theory of Objectification, and Glasersfeld's Radical Constructivism. This comparative analysis reveals a rich diversity of approaches, each providing valuable tools for understanding the processes of teaching and learning mathematics. Psychological theories emphasize the student's active construction of knowledge, while cognitive theories focus on the mental processes involved in solving mathematical problems. Social constructivist theories, on the other hand, emphasize the importance of social and cultural contexts in the construction of mathematical knowledge. Together, these major theories offer a solid conceptual framework for designing more effective teaching strategies and for understanding the challenges students face when learning mathematics, as well as for guiding research in the scientific community. None of these theories is superior to the others; rather, each plays a crucial role in the field of mathematics didactics. Finally, there are many other theories that readers can explore according to their needs and academic background.