The article I read this week titled “Psychology and Mathematics
Education” discusses the difference between cognitive psychology and the
psychology of mathematics education.
The author says that Piaget’s idea of psychology does not match up with
the psychology of math education because it was not interested in the effects of instruction on the
development of mathematical reasoning and because he believed that intellectual
development is essentially a logical one.
He states, “The "psychology of mathematics education" is not
produced by applying psychology to mathematics education. Rather, it is
achieved by identifying genuine psychological problems in mathematical
activities” and proceeding from there.
This
idea is very true about different curriculums and/or concepts in general. For example, there have been some
articles we have read in our education programs about a teacher in a math
classroom performing a certain task that sounds great, but applying it to our
specific classroom might not turn out in the same way it did for the teacher in
the article. Just like what might
work for one student might not work for another student in terms of learning
style or organization or amount of practice problems to be completed or…the
list could go on forever. In fact
the author makes note that psychology may be very helpful in math education,
but only as a general theoretical framework. This concept applies to Beth’s articles we read last week
about color-blindness, the voice of the textbook, and revoicing students’ words
or ideas. I think all of her
articles were very insightful, but at the same time a bit one-sided. I think that any concept in life may be
related to another concept or provide a “general” description, but will never
be the exact same thing. Just how
all textbooks do not have the same, unfriendly kind of language, not all of
psychology can be applied to each subject area and work perfectly.
I have to say, judging from how you explained the paper, that I'm a bit confused by the statement that the psychology of mathematics education is achieved by identifying "genuine psychological problems in mathematical activities." Aren't "genuine psychological problems in math education" still psychological problems? So then, can't we still consider Piaget's psychology of learning to math education? I've often struggled with the question of what makes mathematical thinking so different from other types of thinking. It's fine to say that Piaget's idea of psychology doesn't match up since it doesn't account for "instruction" and other aspects, but does this imply that one cannot learn mathematics without instruction? How are we defining "instruction" here?
ReplyDeleteI'm again frustrated by people's mentality of totality. There seems to be this habit for researchers to be totally enthralled with one idea or another; it's that way or the highway. The author here seems to be implying that we should just throw away Piaget because of this one flaw. Why do we have to throw it away completely? Isn't it useful in some light?
AH! I just saw the point you made about the author saying that it is useful as a general theoretical framework. Ok, I feel a little less passionate about what I said above. At least I'm not in total disagreement.
This makes me think of some of the readings we did in Ann's class last term - in particular I remember one about children's (mis) representations of fractions - The idea that young people can conceptually understand mathematical concepts, without necessarily understanding the language that we (mathematicians? adults?) usually associate with them. I wonder if people who make broad statements about 'psychology of math education' take this into account.
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