[Xmca-l] Re: units of mathematics education

[Andy Blunden]

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