Author (Your Name)

Louis Fallon, Colby College

Date of Award


Document Type

Senior Scholars Paper (Open Access)


Colby College. Psychology Dept.




Psychological Mechanisms in learning Mathematical Concepts: Jean Piaget, the Swiss psychologist, did theoretical and experimental work based on the idea that there is an invariant heirarchy of responses by which everyone acquires mathematical concepts. Basically we tried to use the geometric symmetry concept as a vehicle for studying this process of concept acquisition using subjects ranging in age from three to 25. They were asked to reproduce a series of stimulus "pictures," simple geometric patterns, which could be used without major alteration for each age group. Symmetric responses were divided into four types which were set up into a heirarchy of transformations involved in making the response. This method proved to be a good indicator of the subjects' capabilities. Typical tests made with children involved the notions of equivalence and conservation of matter. The child might be asked which of the two numbers, was greater, for example; or whether under a change of shape a volume remains constant when it might appear to change. We found that subjects' use of the symmetry notion was largely unconscious and some regressed in response to a more complex task without realizing it. Instead of using length and width to get the area of a rectangle, for example, a child might line up and count the smaller squares within, a mode that had proved successful earlier--perceiving no regression and assuming he was doing it the "right" way. Every inferential replication we did proved Piaget to be correct and the concept of heirarchy was perhaps the major idea that came through most clearly. There is an invariant sequence of events -- stages of operations or levels of sophistication -- through which anyone must progress in order to learn Mathematics.


Learning, Psychology of, Mathematical ability, Mathematics -- Study and teaching

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