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Topic: Musings about Question 4
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Ed Wall

Posts: 837
Registered: 12/3/04
Musings about Question 4
Posted: Mar 31, 2001 8:37 PM
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Professor Zhang

Again my apologies as I must cut my musings short. It is clear, at
least, in my part of the US (smile) that children become aware of
negative numbers rather early. I remember one quote by a five-year
old as "these are the numbers under zero." So, it certainly seems
that some things with negative numbers can be done quite early. I
have seen an experienced US teacher introduce negative numbers in the
third grade, and know of US cases where such has been done in the 5th
grade. Thus it seems quite reasonable to begin certain operations
with negative numbers in the early elementary years. The difficulty
may be when one begins to multiply - most explanations are usually
unconvincing and become little more than memorization even for high
schoolers (it would seem ideal if addition and subtraction had been
done earlier and multiplication of such numbers became a natural
mathematical question for the students).
Let me point out that the Chinese K-12 curriculum does not include
calculus - although students might be able to learn such - for the
very good reason that you want to establish a strong basis before
venturing into a rather new topic. There may be similar reasons for
being hesitant about introducing negative numbers in the elementary
years. Just because the curriculum writers think that children can do
this in the 5th grade doesn't mean they should (I assume, that the
curriculum would be structured earlier to support such an
innovation). I wonder exactly what are the pyschologists' objections
you refer to - certainly the history of mathematics indicates there
may be some conceptual and notational difficulties (one can do a lot
of the work concretely but there is, it seems to me, required a new
level of abstraction). My preferred tendency has been to listen
reasonably carefully to psychologists - which doesn't mean they are
always correct - and err a little on the developmental side.

Ed Wall

>Question 4: When should we introduce the concept of negative numbers?
[Background] Shanghai has its own curriculum in which the negative
number system is introduced in the 5th. grade. Many psychologists
think it is too early; however, our curriculum makers insists it is
the correct choice.

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