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2010f.00058 Ackerberg-Hastings, Amy John Playfair in the natural philosophy classroom. Bjarnad\'ottir, Krist\'{\i}n (ed.) et al., `Dig where you stand'. Proceedings of the conference `On-going research in the history of mathematics education', Fj\"olbrautask\'olinn \'{\i} Gardab\ae, Gardab\ae r, Iceland, June 20--24, 2009. Reykjav\'{\i}k: University of Iceland, School of Education (ISBN 978-9979-793-99-1). 3-16 (2009). 2009 Reykjav\'{\i}k: University of Iceland, School of Education EN A30 B40 A60 history of mathematics education (18th century) student notes university teaching Summary: While textbooks are deservedly considered valuable and interesting primary sources by mathematicians as well as by historians of mathematics education, these materials generally provide little insight into how classes were conducted each day or into what students actually learned. To develop a more complete picture of educational practice, textbooks must be combined with information gleaned from administrative records, student notebooks, student reminiscences, obituaries, and the like. Unearthing that sort of documentation, though, often depends as much on serendipity as on systematic research. John Playfair (1748--1819) served as professor of mathematics and then of natural philosophy at the University of Edinburgh. In addition to Elements of geometry and Illustrations of the Huttonian theory of the Earth, the books for which he is best known, he organised his lectures into Outlines of Natural Philosophy (2 vol., Edinburgh, 1812--1814). There are also at least 5 extant sets of notes taken by students who attended his natural philosophy course. This paper will analyse the explanatory power of these particular notes and suggest broader conclusions about the historiography of mathematics education.