Re: Math is not a memoriter course.

Herman Rubin wrote:

In article <1187966095.414568.184130@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
<aatu.koskensilta@xxxxxxxxx> wrote:


Someone wrote:


Do they really believe that it could possibly do more harm to the
student than would be done over a lifetime by not knowing the single
digit multiplication facts?



Why do they have to know the single digit multiplication
facts? I often do base 16 computations, and I have made
no attempt to memorize its multiplication table.

In fact, one the touted methods of teaching, Chisenbop,
only assumes that multiplication by 1, 2, 5, and 10 are memorized, and uses the distributive law for the rest.
Since multiplying by 5 is essentially dividing by 2, not too much has to be learned. But the only thing
gained by learning tables is speed; why do we not have
children memorize the tables to 100 or 1000?



My experience is that students who cannot multiply without the aid of a calculator have all the more trouble with later subjects such as algebra and statistics. How can one learn to factor polynomials if one cannot multiply? Very slowly, I guess.

Only slightly off topic, it still annoys me if, when I ask a student what half of 0.05 is (e.g., in the process of determining a rejection region for hypothesis testing), s/he to pull out a calculator to give me an answer



I have no idea where you get the idea that children aren't taught the
multiplication table. I also find I have not been horribly harmed by
not knowing the multiplication table.



See the above. Napier's "bones" were devices for people
who could add but not multiply. But computers and calculators
are even faster.



There are real problems with mathematics education today -- some quite
widespread, some specific to certain countries --, and it would be
more sensible to concentrate on those, instead of ranting on imaginary
ills.



Students do not understand any of te concepts involved
with the integers, and cannot formulate problems. This
is FAR more important than knowing how to solve standard
problems; anything which is learned about solving problems
below the graduate level can NOW be done by machine.


This is not a matter of either/or. Students need to learn some basic machinery by heart. And they should understand concepts as well. Usually, a lack of the former really hinders the latter.

--
Stephen J. Herschkorn sjherschko@xxxxxxxxxxxx
Math Tutor on the Internet and in Central New Jersey and Manhattan

.

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