This paper revisits the nature of school mathematics by examining its philosophical foundations and the implications of these views for contemporary pedagogy. The paper examines how historical and modern conceptions of mathematics, ranging from absolutist philosophies such as Platonism, logicism, and formalism to progressive absolutist views (intuitionism, constructivism), as well as fallibilist perspectives, have shaped mathematics curricula and teaching practices. The analysis highlights the shift from viewing mathematics as a fixed body of infallible knowledge to understanding it as a fallible, evolving, and socially situated discipline. Drawing on both classical insights and recent peer-reviewed studies, we discuss how teachers’ beliefs about the nature of mathematics shape instructional models and curriculum implementation. Misalignments between reform-oriented curricula and traditional teacher beliefs are identified as a key challenge in educational change. The paper concludes with recommendations for teacher education and curriculum design, advocating for reflective practice and epistemological plurality to bridge the gap between philosophical ideals and classroom practice.
KeywordsPhilosophy of MathematicsAbsolutismFallibilismConstructivismMathematics Education
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