The Role of History and Philosophy in University Mathematics Education

In Michael R. Matthews (ed.), International Handbook of Research in History, Philosophy and Science Teaching. Springer. pp. 837-871 (2014)

Abstract
University level mathematics is organised differently in different universities. In this paper we consider mathematics programmes leading to a graduate degree in mathematics. We briefly introduce a multiple perspective approach to the history of mathematics from its practices, reflections about uses of history and the research direction in philosophy of mathematics denoted ‘Philosophy of Mathematical Practice’. We link history and philosophy of mathematical practices to recent ideas in mathematics education in order to identify different roles history and philosophy can play in the learning of mathematics at university level. We present, analyse and discuss different examples of inclusions of history and philosophy in university programmes in mathematics. These presentations are divided into courses in history and philosophy, respectively, since this is the main way they are organised at the universities. We shall see, however, that the history courses address philosophical questions and that the philosophy courses employ historical material. The chapter ends with comments on how mathematics educations at university level can benefit from history and philosophy of mathematics.
Keywords History of Mathematics  Philosophy of Mathematics  Mathematics Education
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