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[Xmca-l] Re: units of mathematics education



Sure, Carol. You can teach children to manipulate children according to a set of rules. In my very limited experience, when kids learn how to manipulate symbols according to a social convention, they do not grasp the concept behind the rule, consequently when the rules get to a certain level of difficulty they just can't cope any longer and give up. Like learning to navigate a city by memorising the directions.

I imagine it is difficult to extract "divide" from "share" by decoding a text, and so on, but I guess if kids are taught to do this and practise it for hours each day they will learn to do it.

I take it that you are suggesting, Carol, that a "word problem" is in fact a way of presenting the child a real-life situation. This leaves the child the task of (1) understanding the words, (2) abstracting the maths problem, (3) successfully manipulating the symbols to a solution.

I think the issue is to grasp the problem here "genetically." A professional mathematician manipulates symbols. A preschool child counts real objects. To get from one to the other, is not, in my view, a jump from handling objects to handling symbols, it is a long drawn out process in which the rules of symbol manipulation still carry the marks of their origin in object manipulation, psychologically and logically. I think the "unit of analysis" problem is also the "germ-cell" problem. I think we have to conceive of learning mathematics genetically.

All this with the caveat that I know next to nothing about teaching maths. But I think this is the nub of the matter: are we teaching kids to manipulate symbols according to a social convention, or to solve real problems mathematically.

Andy
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*Andy Blunden*
http://home.pacific.net.au/~andy/


Carol Macdonald wrote:
Hi Andy

What about simply teaching symbol manipulation?  Just as 50 - 48 = 2,
children can readily do. We know, by the way that children find word
problems very difficult, and can't see the clues readily in language text.
Word problems are for them translating real-life situations into symbols
 They are if they are half well taught.  Otherwise teachers simply teach
word triggers like "shared" means divided.

Carol

On 27 October 2014 08:20, Ed Wall <ewall@umich.edu> wrote:

Andy

     Nice and important points. Thanks!

Ed


On Oct 26, 2014, at  11:31 PM, Andy Blunden wrote:

Well, I think that if you make a decision that mathematics is *not*
essentially a social convention, but something which is essentially
grasping something objective, then that affects what you choose as your
unit of analysis. Student-text-teacher is all about acquiring a social
convention.
Remember that when Marx chose an exchange of commodities as a unit of analysis of bourgeois society, he knew full-well that commodities are rarely exchanged - they are bought and sold. But Marx did not "include" money in the unit of analysis.
Andy
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*Andy Blunden*
http://home.pacific.net.au/~andy/