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Re: As goes reading education, so goes math education
Posted:
Jun 8, 2010 5:08 PM
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Pam had some interesting things to share in these two posts
http://mathforum.org/kb/message.jspa?messageID=7091463&tstart=0
http://mathforum.org/kb/message.jspa?messageID=7091582&tstart=0
regarding how different parts of the brain are used differently by those with different levels of skill.
I wonder whether these sort of studies of brain regions has been done with respect to "reading" mathematics - meaning comprehending written mathematics, especially written mathematics like equations.
I wonder whether knowledge of observed differences in parts of the brain activated for those students who are proficient at comprehending written mathematical symbolism and those who are not proficient could be useful to create effective teaching and learning strategies.
In other words, couldn't ways of teaching students to proficiently comprehend written mathematical symbolism be found that, like in the teaching of how to proficiently read, the brains of those who don't proficiently comprehend written mathematical symbolism be made over time to look like the brains of those who do, with perhaps the hoped for correlation that they more proficiently comprehend written mathematical symbolism?
I ask this because it seems to be that mathematical literacy must include to a large degree the ability to comprehend written mathematical symbolism well enough to "see" ahead of time what implied forms that symbolism can be transformed into. This would include being able to "see" ahead of time a sequence of implied expressions, including different potential sequences. This would be much like those proficient enough in chess being able to "see" ahead of time what the chess board looks like several moves ahead, in a sequence of moves, including different potential sequences.
I note that the type of thing I just described is the type of thing that is included at being proficient in mathematics beyond arithmetic, starting with algebra. This replacing of expressions with implied expressions again and again, creating sequences of implied expressions until the final solution is reached is a skill that is fundamental to what algebra skill in general is.
Perhaps a major reason why so many have problems in mathematics starting with algebra is because they have not had sufficient practice beforehand with this skill of replacing expressions with implied expressions again and again, creating sequences of implied expressions until the final solution is reached?
That is, perhaps they have not been sufficiently taught beforehand such that they develop this mathematical literacy of being able "read" written mathematical symbolism so as to "see" these implied expressions ahead of time, including in these sequences?
(This "seeing" is of course a "mind's eye" thing that is pretty much in the "peripheral vision" of the mind's eye, meaning that this seeing is pretty abstract and even somewhat subconscious. But it seems to me that those who are good at this and those who are not would show different areas of the brain lighting up, and that this difference could somehow be exploited by mathematics education theorists.)
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