Re: The Latest -F¡Math Crisis¢

[Brian <http://www.cs..edu/~b>]

On 9/23/23 11:05 AM, Robert wrote:
> https://www.counterpunch.org/2023/09/19/the-latest-math-crisis/
> 
> Noelle sent this to me.  You may be interested in it, if you don't already
> know about it.

Oh, that's really annoying!  I mean, yes, there's a lot of bad teaching, 
not only in math.  But many of the details in the article are wrong.

For example, I /wish/ the textbooks were aimed at the math whizzes! 
When I was a kid, around 65 years ago, there were /some/ secondary math 
textbooks for math whizzes.  But the ones in elementary school (where 
the damage is done) have always been for slower math students, although 
not, I guess, for the very slowest.

But that's another big problem: The article talks as if there's no 
middle ground between math geniuses and math idiots.

And the article's idea of math geniuses is kids who can do arithmetic 
/quickly./  But the real math geniuses are the ones who understand how 
and why the arithmetic works, and who may or may not be the fastest at 
drill problems.  But yes, I agree with the author that schools put way 
too much emphasis on speed -- and, for that matter, although the author 
doesn't say this, too much emphasis on arithmetic altogether. 
Especially these days, when absolutely everyone has a calculator at hand 
at all times (because there's one in your phone), maybe we could teach a 
little less arithmetic.  And there's been progress about that; we teach 
elementary school kids about prime and composite numbers, for example. 
In the fifth grade where I volunteered they even teach the unique prime 
factorization theorem, a/k/a the Fundamental Theorem of Arithmetic. 
They don't prove it formally of course, but they explore it empirically. 
  Every table group start with 24.  This table, group it as 12x2.  Next 
table, group it as 6x4.  And so on.  Then every table keep factoring as 
far as you can.  What do you know, every table ended up with the same 
prime factors!  Now let's try 150, etc.  The kids who just can't do 
arithmetic at all don't enjoy that activity, but both the medium kids 
and the geniuses do enjoy it -- supposing they feel safe in the class to 
begin with.

But I mean, really, are there still teachers who call kids names, out 
loud?  I thought those ones all died off.  There are still teachers who 
/think/ of kids in bad names, but you have to really hate kids to tell 
them in so many words that they're stupid.  Instead we have a whole 
bureaucratic structure wherein kids get Individual Education Plans after 
an assessment of whatever learning disabilities they might have.

I confess that I find it very hard to teach a kid who just can't do 
anything.  I'm inclined, with such kids, to forget about math for a 
while and just try to find out what the kid's life is like.  But I can 
teach the medium kids.  It entails looking at the kid's particular wrong 
answers and using them to read the kid's mind, working out the model 
that's in the kid's head.  And then it's easy to get past it.  (Which 
doesn't mean the same thing won't happen about some other 
misunderstanding next week.)

Personally I love teaching the math geniuses, just as the article 
claims, but that's not true of all teachers.  Some, for example, are 
afraid of smart kids.  Others find it easier to just go through the 
curriculum as it stands, without indulging kids' detours into questions 
they find interesting.

One of the problems, especially in elementary school, where one teacher 
teaches all subjects, is that the teacher may not understand the math 
themself.  Such a teacher isn't going to do a great job with kids who 
can't understand the worksheet by themselves.

But many of the problems are the fault of the school as an institution, 
not of the individual teacher.  In particular the one about "we have to 
move on or we won't finish the curriculum" is all about standardized 
testing, which these days penalize the school and the teacher as well as 
the kid.

The New Math (of the 1950s-60s), which everyone makes fun of, was a huge 
curriculum effort specifically aimed at non-math-genius kids.  People 
think it was aimed at the geniuses, because it taught things like the 
commutative and associative laws, but no, the geniuses figure those out 
by themselves.  It's the medium kids who need to be taught those rules 
explicitly.  Maybe if I could redo all that, I'd pick less intimidating 
/names/ that kids could spell and pronounce: the Swapping Law and the 
Grouping Law, or something.  But it's too late, since the big names are 
still in modern curricula.

Curriculum can be undone if teachers follow it too slavishly.  For 
example, these days they teach kids three or four different algorithms 
for multiplying multi-digit numbers, for the benefit of medium kids, 
each of whom may take to a different algorithm.  But if a kid has 
learned one well, it's silly to make the kid also learn all the rest, 
and to ask test questions that insist on using a particular method. 
(Show your work.)

Anyway, tl;dr: There are many pitfalls in kids' learning arithmetic, 
some of which are the teacher's fault but most of which aren't.