[Xmca-l] Re: units of mathematics education

[Carol Macdonald]

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/
> >
> >
> > Ed Wall wrote:
> >> Andy
> >>
> >>     Asking that question was one of the dumber things I've done on this
> list. Apologies to all
> >>
> >>      Thanks for reminding me about pre-concepts. I've been thinking
> about something similar and wondering if this is part of what makes doing
> mathematics 'mathematical.' Historically, by the way, mathematics grew out
> of manipulating such material objects; however, there are indications that,
> at some point (and it may have happened more than once), there was sort of
> a leap.
> >>      Mathematics is considered a science; for instance, of patterns or,
> as Hegel puts it, quantity. I agree for a mathematician symbols of various
> sorts are effectively 'things'.
> >>
> >>       In the 80s some mathematicians (School Mathematics Study Group)
> in the US put together a formal curriculum - my aunt used it - which was a
> disaster (and a real pain for the kids involved). Indications are children
> learned little.
> >>
> >>       So to add a little to a discussion that possibly has continued
> far longer than it should. Mathematics may have a few characteristics that
> may distinguish it from other disciplines such as
> >>
> >>        1. A student has the ability, in principle, to be able to
> independently of teachers or peers verify a grade appropriate mathematics
> statement (not a definition although definitions admit, in a sense,  a sort
> of empirical verification).
> >>
> >>        2. Solutions to problems are, in general, not subject to social
> conventions (which probably is included in the above). Amusingly, I believe
> in the US a state legislature once tried to set the value of pi to 3.1417
> >>
> >> However, I'm not sure how such would fit together into a useful unit of
> analysis.
> >>
> >> Ed
> >>
> >>
> >
>
>
>


-- 
Carol A  Macdonald Ph D (Edin)
Developmental psycholinguist
Academic, Researcher,  and Editor
Honorary Research Fellow: Department of Linguistics, Unisa