Re: more maths

From: Martin Owen (mowen@rem.bangor.ac.uk)
Date: Mon Oct 29 2001 - 02:08:05 PST


xmca@weber.ucsd.edu writes:
>
>Jerry-- I do not think the discussion of maths has gone away for good.
Always a little guilty.I do not have the time at this juncture to get into
the crisis debate but the mats issue does map onto what I am currently
paid to do.

That perception of number in a cultural historic context is well
understood in my local context. In my own promary education Welsh language
counting was done in a post-Roman form: examples are:
13 translated as 1 and twelve; fifteen had its own word, seventeen is two
and fifteen, eigthteen was two-nines and so on. The complexity is clear.
Some of it is shared with English (special words like eleven and twelve
etc).

Modern Welsh counting was introduced in the sixties. It is regular base
ten counting.

11 is one ten one
34 is three tens four
76 is seven tens six.

This is shared with Korean, Chinese, and Japanese.
 
Wales is quite a useful lab for cross linguistic studies.We are able to
find well matched groups with many cultural and economic commonalities
using a different language living side by side. A recent study by Lloyd
and Bowker compared children in Welsh language schools with children in
similar neighbouring English language schools. They note:

"Many of the advantages of Welsh counting can be attributed to the
opportunity for drawing meaning directly from the language. However, this
means that number words have to be constructed and understood in terms of
the component tens and ones. If lower ability children fail to make this
connection between number words and the number value, then it could be a
source of confusion when dealing with novel tasks such as representing a
specified number with coins, particularly for children whose first
language is not Welsh. (Conversely, for higher ability children, the
insight gained through the meaningfulness of the number words in Welsh is
advantageous, and may provide an extremely solid base on which to found
more complicated concepts in the future). The effects of ability on
linguistic/bilingual advantages would be an interesting point for further
study. In this work however, Welsh bilinguals were, on average,
equivalent or better than monolingual children on all the tasks, with only
some less able Welsh bilinguals struggling to represent amounts using
coins.

In contrast to this, monolingual English children in this study
experienced difficulty with -teen numbers at age 6, with residual problems
still expressed at age 8 by one less able child. The 40 Welsh-speaking
children however did not make a single error of this type. Once again the
irregular structure and phonetic similarity between -teen and -ty numbers
are the primary explanations for this observation. Five of the 24 stimuli
(number pairs) in the Number comparisons task contained a -teen number,
but the misreads of children in group WE do not seem to feature
disproportionately in these pairs, and thus the observed differences in
misreading between groups is not merely an effect of phonetic confusion. "

There are clearly other implcations in having a number naming convention
that maps directly onto the calculating system which may effect learning
in more complex arithmetic.

Martin Owen
Labordy Dysgu- Learning Lab
Prifysgol Cymru Bangor- University of Wales, Bangor

"How do you explain school to a higher intelligence?"



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