anti abstraction

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Axeman
Posts: 146
Joined: Wed Jul 20, 2005 4:20 pm
Location: New Zealand

anti abstraction

Post by Axeman » Thu Jan 22, 2009 6:05 am

In New Zealand their is a new push towards teaching mathematics that recognizes that mathematical understanding develops in children by their grasp of concepts that become increasingly more abstract. From the very beginning concept of 'counting all' through 'counting on' and then onto 'part whole' and later multiplicative understandings of number. Counting all being where the child counts every item in a group of objects (often physically). Counting on, where told there are 5 of something being masked by a card the child is able to count a whole group as one and then add the remaining things. Part whole, where the child can break numbers into components that add up to round numbers in sums like 8 + 5 i.e 8 +2 = 10, 10+3 = 13 and so on.
Considering this..
The bottom line is that each pitch category needs to be populated with concepts. The principal difficulty in finding effective concepts is that adults' understanding of sound is not embodied and integral (a bell is F-sharp) but causal and dissociated (a bell produces F-sharp).

...it would seem that in trying to teach adults a child-like ability like AP it may be successful if the process employed to teach children, for example, the above mathematics concepts, i.e. a continual increase in abstraction, were reversed.
We obviously as adults have the ability of this kind of perception and labelling because we can name colours in this way. It is just that in the case of AP our minds have been trained to abstraction and not toward the embodiment or integrality cited above.
We have to force the adult to go, to continue the analogy, from the 'multiplicative' stage back through the other stages to 'counting all'. The trick will be finding out what the stages of development in abstraction are as concerns pitch. Then it maybe easy enough to go back through them.

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