Sources of Mathematical Thinking: Behavioral and Brain-Imaging Evidence by S. Dehaene, E. Spelke, P. Pinel, R. Stanescu, S. Tsiv
Submitted by Andrew on Sun, 03/01/2009 - 17:21.
Why bother reading any of my posts? I suspect many of you will look at the mathematical titles of the articles and decide that they are not for you, but for those of you who do feel so inclined, a reading of these articles will provide some unusual findings about the source of mathematical expertise. These findings also indicate support for particular theories about the nature of the mind – but if you want to find out you’ll have to read them yourself! It should be noted that the authors all share similar views in regard to the nature of mathematical expertise, and indeed most are part of the same research group. Nevertheless, whilst keeping this in mind, the results of their experiments are, I would suggest, reasonably compelling.
The posts can be read in any order but I suggest for background reading you start by looking at the attached article "Core systems of number, Trends in Cognitive Sciences, Vol.8, No.7, July 2004, by Lisa Feigenson, Stanislas Dehaene and Elizabeth Spelke”. Also of interest is the website of the Stanislas Dehaene led research group at the INSERM-CEA Cognitive Neuroimaging Unit in France which provides a wonderful resource of relevant articles.
Sources of Mathematical Thinking: Behavioural and Brain-Imaging Evidence by S. Dehaene, E. Spelke, P. Pinel, R. Stanescu, S. Tviv
“Words and language, whether written or spoken, do not seem to play any part in my thought processes. The psychological entities that serve as building blocks for my thought are certain signs or images, more or less clear, that I can reproduce and recombine at will” (Albert Einstein)
Many of the greatest mathematical minds in history have reported similar experiences to Einstein. For those of us not as mathematically proficient or who are entirely over-awed by mathematics, it seems somewhat incredible that these maths whizzes seem to “do maths” in numbers, shapes and images , entirely devoid of linguistic interference. In the short article here Stanislas Dehaene et al suggest that for the majority of us (I stress not everyone – I will come back to that briefly in the final blog and when I give the presentation of my dissertation) certain mathematical concepts (e.g. exact arithmetic) can only be accessed through the establishment of a linguistic scaffolding, a term employed by Andy Clark in his Supersizing the Mind. By contrast this linguistic scaffolding is unnecessary for certain other mathematical concepts (e.g. approximate arithmetic).
Their findings raise some very interesting questions. What might the consequences be for mathematical education if this postulate is proved correct? “Will it ever happen that mathematicians will know enough about the physiology of the brain, and neurophysiologists enough of mathematical discovery, for efficient cooperation to be possible?” (Jacques Hadamard, An Essay on the Psychology of Invention in the Mathematical Field (Princeton Univ. Press, Princeton, NJ, 1945) What does it tell us about the nature of the mind in general? Is mathematical innovation of a certain kind restricted to those whose brains are structured in certain ways? What does the nature of mathematical thinking imply for the nature of mathematical truth and knowledge? These are just some of the numerous quandaries that acceptance of these results leads us to.
The information contained in these Web pages is, to the best of our knowledge, true and accurate at the time of publication, and is solely for informational purposes. University College Dublin accepts no liability for any loss or damage howsoever arising as a result of use or reliance on this information.