**2-6 July 2012**

Location: CPD6

10:30-13:00 | Rafael Núñez (Invited Talk) The study of mathematical practice and cognition as an empirical endeavor: The case of the cognitive science of the number line |

11:30-11:40 | Comfort break (no refreshments served) |

11:40-12:20 | Matthew Inglis and Lara Alcock Watching Experts and Novices Read Proofs |

12:20-13:00 | Andrew Aberdein The Parallel Structure of Mathematical Reasoning |

14:30-15:10 | Alan Smaill Mathematical Notation and Analogy |

15:10-15:50 | Alison Pease and Ursula Martin Seventy Four Minutes of Mathematics: An analysis of the third Mini-Polymath project |

15:50-16:00 | Comfort break (no refreshments served) |

16:00-17:00 | Liesbeth De Mol (Invited Talk) Taking the machine seriously. A study of 'mechanized mathematics' |

8:40-9:20 | Sandra Visokolskis Discovery in Mathematics as an Experiential Practice of Privation |

9:20-10:00 | Manfred Kerber, Christoph Lange and Colin Rowat Formal Representation and Proof for Cooperative Games |

10:00-10:30 | Coffee/Tea Break |

10:30-11:10 | Brendan Larvor What Philosophy of Mathematical Practice Can Teach Argumentation Theory about Diagrams and Pictures |

11:10-11:20 | Gabriella Daróczy Dialogue with a Mathematical Assistant Cognitive Aspects of Designing Rule Based Dialogue Guidance (poster) |

14:00-15:00 | José FerreirósConvergence, not Reduction: On cognitive science and studies of mathematical practice (Invited Talk) |

15:00-16:00 | Panel discussion |

Further details of invited talk:

Rafael Núñez: The study of mathematical practice and cognition as an empirical endeavor: The case of the cognitive science of the number line

Abstract: The investigation of mathematical practice and cognition
can be informed by multiple sources such as history, philosophy, and
descriptive studies. In this talk I'll argue that the field also needs
multidisciplinary empirical (experimental) hypothesis-testing
methods. In order to illustrate my point I'll focus on a few empirical
questions involving the nature of the number line - fundamental to
modern mathematics - and its relation to cognition, cultural
practices, and biological constraints. What are the cognitive origins
of the number line? Are the intuitions underlying the number line
"hard-wired"? Is the number line a cultural construct? Contemporary
research in the psychology and neuroscience of number cognition has
largely assumed that the representation of number is inherently
spatial and that the number-to-space mapping is a universal intuition
rooted directly in brain evolution. I'll review material from the
history of mathematics as well as empirical results from two of our
recent experimental studies to defend a radically different picture:
the representation of number is not inherently spatial and the
intuition of mapping numbers to space is not universal. In one study
we show that there are non-spatial representations of numbers that
co-exist with spatial ones, as indexed by instrumental manual actions,
such as squeezing and bell-hitting, and non-instrumental actions, such
as vocalizing. Moreover, the results suggest that the number-to-line
mapping - a **spatial** mapping - is not a product of the human
biological endowment but that it has been culturally privileged and
enhanced via specific practices. The other study, which we carried out
in the remote mountains of Papua New Guinea, shows experimentally that
individuals from a culture that has a precise counting system (and
lexicon) for numbers greater than twenty - but no measurement
practices - lack the intuition of a number-to-line mapping, suggesting
that this intuition is not universally spontaneous, and therefore,
unlikely to be rooted directly in brain evolution. The number-to-line
mapping appears to be learned through - and continually reinforced by
- specific cultural practices, such as measurement tools, writing
systems, and elementary mathematics education. It is over the course
of exposure to these cultural practices that well-known brain areas
such as the parietal lobes are recruited to support number
representation and processing. Implications for the study of
mathematical practice and cognition will be discussed.

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