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Ed Wall
Posts:
843
Registered:
12/3/04


Musings about Question 4
Posted:
Mar 31, 2001 8:37 PM


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 fiveyear 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 K12 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.



