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Mental Imagery in Mathematics and Computer Science

Prof. Alain Finkel ( Ecole Normale Superieure de Cachan, France )
While the fundamental nature of thought remains a mystery, the processes underlying mental imagery have been extensively studied by philosophers (e.g., Berkeley 1734, Bergson 1900), by psychologists between 1850 and 1900 (e.g., Binet, Tichener), and again since 1970 by scientists from a wide variety of disciplines (e.g., Kosslyn, Shepard).

Mental imagery is the means by which we are able to create an internal world and manipulate, memorise, simulate, anticipate, etc., within it. This re-creation uses a range of mental processes: visuo-spatial, verbal, symbolic, phonological, experiential.

The role of mental representations in Mathematics and Computer Science (for teaching or problem-solving) is often downplayed or completely ignored by educators (and even sometimes psychologists!). Yet, teaching consists largely in transmitting, co-creating, and enabling the discovery and manipulation of mental objects. We argue for a more systematic study and use of mental representations, to assist in forming intuitions of mathematical concepts, and also to understand and build proofs. We illustrate these ideas with several examples.

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