From: bh@anarres.CS.Berkeley.EDU (Brian Harvey)
Newsgroups: k12.ed.math
Subject: Re: Memorizing Multiplication Tables
Date: 27 Sep 1992 21:55:54 GMT
Organization: University of California at Berkeley
NNTP-Posting-Host: anarres.cs.berkeley.edu

jac@ds8.scri.fsu.edu (Jim Carr) writes:
> bh@anarres.CS.Berkeley.EDU (Brian Harvey) writes:
>>                                                  School "math"
>>is just a never-ending sequence of arbitrary techniques to memorize.
>
>So is English, French, History, Anatomy, Computer Science, Biology, 
>Physics, Cooking, Carpentry, ... 

No.  English, in a good learning environment, is mostly reading wonderful
stories that make sense, along with some writing of things that one hopes
also make sense.  I agree that English grammar, especially as taught in
schools, is indeed full of arbitrary rules (most of which aren't even
true).  And, sure enough, most everyone hates grammar -- even though in
reality everyone *is* an expert at the grammar of his or her native
language, despite the worst efforts of schools.  It's interesting that
a lot of people, if you ask about English in school, think right away of
grammar, the "school-like" part, and don't think about all the wonderful
reading, since the reading has some obvious connection to reality and isn't
stupid and arbitrary, so it couldn't have happened in school.

French is, indeed, full of vocabulary to memorize.  The saving grace, I
think, is that everyone (even the teacher) admits that the vocabulary
is entirely arbitrary, and nobody acts as if you're stupid if you don't
see *reasons* why the French for X should be Y.  In math class they pretend
that the algorithms make sense and should be comprehensible.

History is an interesting case.  Traditional history teaching was indeed
full of dates of battles and orders of kings and presidents, and everybody
hated it, and modern historians and history teachers will tell you that
that was a terrible, trivializing way to teach.  These days, in a progressive
school, you're much more likely to see the teaching of history begin with
the history of this neighborhood right here, trying to get kids to understand
on a small scale the idea that events have consequences.

I grant you anatomy.

You have pushed one of my buttons by listing computer science, which is what
I used to teach in high school and currently teach in college.  What I gave
my high school kids was no curriculum at all, but rather a rich environment
(a Unix system with a source license) and lots of real work that needed to be
done.  (My kids wrote a text editor [Jove], a video game [Hack], and a Logo
interpreter that are still in widespread use around the world.)  There are
certainly a lot of details about computers, but you look up the details in
the manual when you need them.  I didn't give tests or grades.  The result
was that kids were in there seven days a week (they had keys to the room so
they could work unsupervised) and in four years I turned out a few dozen
excellent programmers who are now first-rate professionals.  By contrast,
of course, you go to a typical Skool and what you get is acronyms to
memorize, RAM and ROM and so on.  Bleagh!)

I don't know anything about biology -- I skipped it -- so I pass on that one.

Physics is quite the opposite of memorizing arbitrary and meaningless
details.  The whole point of physics is that a few basic ideas (e.g.,
Newton's laws of motion) explain a whole range of phenomena.  I suppose
you could find things to memorize in physics, but most physics teaching
instead relies on lab experiments and tries to make everything make sense
to the students.

In cooking, you often *follow* recipes, but you don't *memorize* them!
That's what cookbooks are for.  Even so, there are far too many rules
that are taught without explanation (e.g., don't cook X in an aluminum pot)
even though there are perfectly good explanations for them.  (Of course
the problem here is that the cooking teacher doesn't know the reasons!)
I always found that terribly frustrating, and I was delighted when I
discovered the book _On Food and Cooking_ by Harold McGee, in which all
these things are thoroughly explained.  If I were a cooking teacher,
that'd be the textbook!

I don't know much about carpentry, but my guess is that there are very
few algorithms that don't have immediately obvious reasons -- or at
least reasons that become obvious if you try it some other way.
Newsgroups: k12.ed.math