|‘Can you do Addition?’ the White Queen asked.
‘What’s one and one and one and one and one
and one and one and one and one and one?’
‘I don’t know,’ said Alice. ‘I lost count.’
|Lewis Carroll, Through the Looking-Glass, Chapter IX.|
[Copyright neth.de, 1999–2014]:
Hans Neth and Steve Payne (2011): Interactive coin addition: How hands can help us think. Paper presented at CogSci2011.
Hansjörg Neth, Stephen J. Payne
|The truths about numbers are in us; but still we learn them.|
|G.W. Leibniz (1765), Nouveaux essais sur l’entendement humain, p. 85|
[Copyright neth.de, 2010]:
Helen De Cruz, Hans Neth, Dirk Schlimm (2010). The cognitive basis of arithmetic.
Overview: Arithmetic is the theory of the natural numbers and one of the oldest areas of mathematics. Since almost all other mathematical theories make use of numbers in some way or other, arithmetic is also one of the most fundamental theories of mathematics. But numbers are not just abstract entities that are subject to mathematical ruminations — they are represented, used, embodied, and manipulated in order to achieve many different goals, e.g., to count or denote the size of a collection of objects, to trade goods, to balance bank accounts, or to play the lottery. Consequently, numbers are both abstract and intimately connected to language and to our interactions with the world. In the present paper we provide an overview of research that has addressed the question of how animals and humans learn, represent, and process numbers.