Mathematical cognition
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Another context where I explored the importance of diagramming is in the cognitive foundations of mathematics. I reconsidered the value and the limits of experimental evidence. It has been proved that humans are born with certain abilities and predispositions that allow for example to recognize certain invariant traits in the environment, what I call "perceptual invariances"; however, the emergence of new practices and the introduction in our culture of new cognitive artifacts are also part of the foundations of the mathematical concepts. In my view, different levels of competences should be distinguished, both in arithmetic and geometry.
Some papers:
Izard, V., Giardino V. et Viarouge, A. (in press), Acquiring numerical equality. In : Numerical Cognition : Debates and Disputes, edited by J. Park, R. Samuels and E. Snyder.
Giardino, V. (2023), ¿Somos “seres espaciales”? Razonamiento y espacialidad. In: J. Ferreiro ́s et M. de Paz (eds). La génesis de la geometría, edited by , Madrid: Plaza y Valdés Editores, pp. 51-68.
Cappelletti, M. – Giardino, V. (2007), The Cognitive Basis of Mathematical Knowledge. In : Mathematical Knowledge, edited by M. Leng and A. Paseau, Oxford : Oxford University Press, pp. 74 – 83.
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