Re: Why do so many people hate or have trouble with math? Your input is needed!

In article <1160089395.123919.112970@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
LearningNerd <LearningNerd@xxxxxxxxx> wrote:
Thanks for your thoughtful response!

Don't top-post.

http://www.xs4all.nl/~hanb/documents/quotingguide.html

And edit the message you are quoting when you reply so you only
include relevant portions. Just adding your response on top of the old
message combines most of the bad habits of usenet.

I guess I used the wrong word when
I said "fun"; I don't mean that learning math should be like playing a
game. Replace "fun" with "interesting".

Basic math skills are as important as basic literary skills. Everyone
needs to know how to read and write, basic reading comprehension, and
the basic ability to express simple ideas in written form. We drill
students on reading and writing.

By the same token, there are some basic mathematical skills that
everyone, in today's world, needs. A basic "numeracy" to borrow from
Paulus; you need to drill students in the basic multiplcation tables
as much as you drill them in writing "mama". And in today's they need
to understand the basics of descriptive statistics, at least. Those
skills, we don't need to make them "interesting" any more than we make
learning how to read "interesting". They need to know them, they need
to be second nature to them.

Later on, again, I have to wonder: why does math need to be
"interesting", "fun", "enjoyable"? The basic skills we are supposed to
be learning/being taught in grade school and high school are supposed
to be skills we ->need<-. Not stuff we might enjoy. The basic math
does not need to be interesting. What it needs to be is
->useful<-. Basic statistics and probability to understand the world
we live in (perhaps based on something like the wonderful "How to Lie
With Statistics"); basic arithmetic and algebra skills; basic logic;
how many people do not understand the problem with affirming the
consequent?

Now, granted. We teach students Shakespeare out of a sense that they
need some basic culture, and we do make efforts to make it
interesting; that is as far as mathematical instruction ought to be
taken. The mathematical instruction is the parallel of the basic
language skills instruction. But for some reason it is not looked at
that way.

I agree that one of the main problems is that so many math teachers
aren't interested in math. Most of them don't even try to make it sound
interesting; they just jump right into what needs to be memorized.

Some stuff ->needs<- to be memorized. I'm sorry, but just as you need
to memorize the alphabet, you also need to memorize the basic
multiplication tables. And some things ->do<- require drill. Drill is
not bad per se, and it is not good per se. You do not need to do
drill all the time, but neither should it be avoided like the plague;
sometimes it is necessary. (I know many here disagree; Prof Rubin
definitely disagrees with my view ont his, for example, and he
certainly has more experience to bear than mine).

Halmos, I believe, said that good mathematical teaching stands on a
tripod of understanding, memorization, and drill. You need all
three. Some things you need to memorize, some things you need to drill
on, and some things you need to understand. Take the derivative: it is
important to know ->what<- it is (understanding, and knowing how to
use it to solve certain kinds of problems given what it is); but it is
also important to know certain formulas by heart (product rule, chain
rule), and to drill on them until they become second nature. Short
change any of the three, and you end up with a still that doesn't
stand straight.

Some topics require an emphasizing of one of the legs over the others,
but almost invariable all three are needed. And, for the past 50 years
or so, there's always been one leg that gets ignored. New Math
emphasizing understanding and dropped drill; the reaction to New Math
dropped understanding; New New Math despises memorization, and
essentially ->forbids<- drill, calling it "drill and kill". And so we
have a generation of teachers who were deformed by educational
experiments and cannot teach the subject properly.

[...]

--
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes" by Bill Watterson)
======================================================================

Arturo Magidin
magidin-at-member-ams-org

.

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