Presented by Dave Hewitt (Loughborough) & Michael Barany (Edinburgh)

  • 2pm-2:50pm Talk 1: Dave Hewitt

Title: Generalisation strategies in finding the nth term rule for simple quadratic sequences.

Abstract: In this talk I will identify ways in which a sample of 18 graduates with mathematics related first degrees found the nth term for quadratic sequences from the first values of a sequence of data, presented on a computer screen in various formats: tabular, scattered data pairs and sequential. Participants’ approaches to identifying the nth term were recorded with eye-tracking technology. Our aims were to identify their strategies and to explore whether and how format influences these strategies.

  • 3:00pm-3:45pm Discussion of Will Self "Against Theory"

Discussion on:

  • 4:00pm-5:00pm Michael Barany (Edinburgh) 

Title: ‘Fart Upon Euclid’: Misprision, calculation, pedagogy, and the organs of early modern algorithmic reason.

Abstract: Algorithms found significant new audiences in early modern mathematical pedagogy through vernacular arithmetics like Robert Recorde’s 1543 Ground of Artes, which stood for a century and a half as a leading primer in the numerical arts. Recorde presented rule-based algorithmic methods as powerful but error-prone, requiring practice and expertise to apply effectively. In contrast to later mechanistic views of algorithms, sixteenth-century algorithmic thinking reflected expert judgement, not just in the manipulation of numbers but in the contextual appreciation of mathematical knowledge. Such knowledge came as much from the gut as from the head, and the period’s pungent wordplay reinforces an image of algorithms as rude and unruly. Focusing on Recorde’s explanation of long division, the first of its kind in English, I will show how the history of mathematics education can challenge common accounts of reason and modernity and suggest new perspectives on vital concerns for mathematics education today.

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Fenner Tanswell
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