After reading the first article, “Numerical abstraction by human infants” by Starkey, Spelke and Gelman, my impression was that infants are very intelligent in terms of mathematics. The fact that every culture has some evidence of mathematical abilities suggests strongly that the knowledge may by innate. Starkey brings up a couple of possibilities to explain infants’ knowledge of numbers; including cultural diffusion, reflective abstraction (“child will abstract properties from the action schemes, interiorize and organize them, and form an operational scheme. The child’s subsequent coordination of operational schemes would produce a structure capable of supporting deductive numerical reasoning”) and that mathematical competence may exist in human infants. Reflective abstraction is based on the internal reflection of knowledge available. If relationships are constructed between objects, could it be possible that the experiments in the article, “The representations underlying infants’ choice of more: Object Files vs. Analog Magnitudes” by Feigenson, Carey and Hauser, that combined sound and visual activity showed results of reflective abstraction instead of knowledge of numbers? Another question to ask is why infants are better at detecting differences in the number of object displays when they hear drum beats that correspond with the number of objects in the display. Is it because infants relate a pattern of sound to a pattern of visual activity? Do they innately know that the sounds equal the number of objects, or do they recognize the pattern of both (sound and visual activity) and compare the two?
Starkey hypothesizes that “the emergence of the earliest numerical abilities does not depend upon the development of language or complex actions, or upon cultural experience with number.” To test this hypothesis, Starkey performed five experiments where the “solution depends on the recognition of one-to-one correspondence between the members of different collections of items.” In each experiment, the infants were shown displays with either 2 or 3 objects. After reading Feigenson’s article, I wondered how different the results of the first article may be if they had used more than 2-3 object displays. Feigenson performed an experiment where the infant had a choice of fewer crackers or more, starting with 1 vs. 2, 2 vs. 3, and 3 vs. 4. In the first two instances, most chose the option with more crackers. When comparing 3 vs. 4 crackers, infants had a hard time determining the difference. This difference in research methods leads me to believe that if Starkey had used more than 2-3 object displays, the infants might not have detected the differences.
Another difference in these sets of experiments is that Feigenson suggests that “for sets within the object file range, infants at least sometimes compare object file representations on the basis of the physical variables bound to those representations, rather than via one to one correspondence.” This contradicts Starkey’s study that depends on one-to-one correspondence between collections of items. If infants rely on object file representations and compare volume and surface area rather than one to one correspondence like Feigenson suggests, one question to ask is how Starkey decided in the first experiment that the determining property between the collections could not have been the brightness, contour density, or surface area. He says because the properties of the objects varied, these things didn’t matter. However, in Feigenson’s experiment, the crackers varied in size and surface area was a determining property. After reading both of these articles and thinking about the findings, it seems that infants’ knowledge of numbers and less/more is a deeply complex system that must be studied in more detail and with different kinds of experimental methods.
1 comment:
I would have to agree with your last statement about infant’s knowledge of numerical concepts. I do think that numbers and less/ more is a complex subject that needs to be looked at more. Most humans have an understanding of numbers and less/ more. Without this common understanding our world would be ran in a different way. In the United States, we are able to trade four quarters for one dollar and this is because we have this common understanding in our culture that this equal. Native Americans were able to trade furs and food with someone from another tribe even though they did not share the same language but they had an innate understanding of value and numbers. Native Americans didn’t have school to teach them how to count or to add and subtract, this was an innate capability. I think that our basic knowledge of quantity is innate but we learn through experience more complex ways of thinking about numbers and adding/ subtracting.
The main reason that I think quantity is innate is because of Gelman and Gallistel’s counting principles. I have a four old cousin who is capable of all five of these principles and I have seen him use these skills on numerous occasions. The first principle one-to-one is the concept that each object represents one. Infants and young children do this type of representation all the time. One important aspect of a child’s life is making sure things are fair for example that each person receives one cookie. If one child had two cookies and the rest of the class had one cookie, all the children would recognize this and not be happy. The second concept that children understand is the stable order of counting. Children do this through routine they understand that one thing comes before and after another, an example of this is the alphabet. Children would be baffled if you said A-B-C-Z because there is a long list of words that come before Z. The third principle is order invariance of counting items, which is that each item represents one and can be counted in any order and the initial amount will remain the same. The fourth principle is cardinality, is the idea that the last number is the amount you have. When children are counting the last number that they say is the loudest because they understand that this is the amount they have. The fifth and final principle is abstraction, as long as the things you are counting is discrete then it is okay. These five principles show that infants have an innate basic understand of quantity.
I do think that more complex ideas of math and quantity such as multiplication and division are learned from experience but basic understandings are innate. Our basic understanding of quantity is something that we need in order to survive. Animals also posses this capability, monkeys, dogs, birds, and many other animals use this skill to obtain food and detect danger. Our knowledge of numerical concepts is something that is very important in our world and I think that we posses some type of prior understanding of it.
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