Counting

I found it very intriguing that counting is innate knowledge, at least in small numbers. In the reading, it talked about infants’ understanding of small numbers. There are many studies that have been done on children’s understanding of counting and numbers, including Starkey’s experiment with numerical abstraction. The thing that I found particularly interesting about these experiments, and the knowledge gained from them, is that children’s ability to count seems to coincide with the preoperational stage of development. In the text, they discuss cardinality, and suggest that children grasp understanding of larger numbers as they age, which makes sense. The older they get, the more experience they have with numbers, and the more opportunities they have to assimilate knew information into their old schemas for counting.

The rules that children observe for counting are very interesting also, because it shows how much complexity there is to human thinking. I’m sure that most adults have never considered how they go about the counting concept, but we are able to determine, through observing children, how proficiency is gained in counting, and how much of it we are born with, and how much is gained through experience.

One thing that I did not understand from the text was how it could be useful that a child can use an incorrect counting system (1, 3, 6, etc.), though I did find it interesting that they would consistently use that system. I also wonder how they could come up with such an incorrect counting system that still incorporated numbers. What is it that keeps them from using letters or colors or shapes or other unspecified sounds to count? Is that something that is innate, or learned through hearing others count?

Another particularly interesting concept is that children can understand simple arithmetic as early as five months old. The thing that sparks my interest is that they have a basic understanding of the concept so early, but cannot explain their understanding much later in life, and often have trouble replicating it, for example on math tests in early school years.

It does seem like useful knowledge for a child to have, and perhaps there is an evolutionary explanation for why children are able to grasp only small numbers. Perhaps it has to do with being able to maintain a count of your family unit. I would assume that in the days of early humanity, family units were not very big, because excess numbers of children could not be provided for. This may cause infants to develop familiarity with just a few people early in their lives, and this leads to their basic understanding of the concept of numbers. I, of course, don’t really know how this came about, but I like to speculate about things like that. The comparison between the aboriginal children and the schooled children of Australia provided some interesting evolutionary understanding of spatial understanding, and perhaps could have been expanded to include basic number tasks as well. It has been mentioned that uneducated people in other countries are capable of doing math and taking measurements, but they often live in caste systems, or other types of systems where professions are handed down through families, and perhaps an informal education of mathematics occurs from generation to generation, in order to make each person’s job that much easier. Regardless, it is good to know that our concept of numbers isn’t completely socialized, but that experiences lead to further understanding and expansion of basic knowledge.

And on a completely different topic, I also was under the impression that both doors on a racecar are traveling at the same speed. I’m glad I was able to learn something about myself from the text as well. :-)