knowledge of numbers

[laurenfuentes]

Sorry its a bit late, computer difficulties.
See you tomorrow!

I thought that both the Hauser and Spelke article, as well as the supplemental study by Karen Wynn, were very interesting and tied in well with our recent readings on the origin of knowledge— especially the last article by Fei Xu. Hauser and Spelke identify two separate systems that make up our knowledge of number. The first, the large approximate number system is based on the idea of ratios, meaning that one is able to differentiate two groups of objects not by comparing the exact number of objects between groups but rather by comparing visible ratios of the groups’ objects. The authors argue that this is an abstract process that develops with age as the ratio threshold decreases steadily in infancy.
Secondly, the small precise number system describes our innate ability to unconsciously process very small numbers. In other words we can see one, two or three objects and process their presence without having to count. This system was especially interesting to me since it seems that the understanding of such small numbers requires little to no processing. It is as if we take in three maybe four objects as like a set rather than counting them. The authors mention that in the child’s counting process, one is learned first with other numbers representing more than one, and eventually two is learned with all numbers above that representing more than two. It seems that even though we have a mental representation for say twenty-four, there is still a threshold for understanding which lies at three or four. Perhaps what we understand as twenty-four is really what we understand as three plus twenty-one which we have learned with counting will add up to twenty-four. The authors site studies addressing the numerical abilities of animals, namely primates, and make the distinction between our ability to represent larger numbers and their inability to do so. I believe that though apes and other animals they mentioned have a less complex and some may argue capable brain, that to some degree they too ought to understand larger numbers. Humans learn how to count from an early age and use it constantly in our day to day life. We are also motivated to create representations of these larger numbers whereas apes do not beyond the treats they get in training, nor do they use these skills beyond when asked to. I believe that the difference in our numerical representation abilities lies in the demand for it which varies between species.
The authors seem to allude to the Fei Xu article as they discuss the reasons for why animals may not construct the two number systems. Their idea is that true understanding of numbers may be dependent not only on the two core systems, but also on natural language. As Fei Xu would argue, mental representation of objects seems to come online only when the child begins to use words as verbal representations. Before this point, the child is incapable of mental representation. The authors site studies where adults doing mental arithmetic have been found to activate areas in the brain known to be devoted to language and that numerical knowledge is best accessed in the language it was learned in. It seems that representational thinking comes online at a certain point and that both language and numerical understanding are tied into this cognitive growth. What we might also think about are other aspects of emerging infant cognition that may come online at this time due to representational thinking. Beginning of theory of mind? Pretend play? And how might the child be affected if this representational thinking we interrupted or stunted?