Re: Teaching math (was urgency of belief)

On Sun, 22 Jan 2006 17:34:10 -0600 Mervin Bitikofer <mrb22667@kansas.net>
writes:
>
> First of all --- is anybody still out there? Or did I
> accidentally
> get unsubscribed from the ASA list? Two days with nothing! I'm
> going
> into withdrawal.
>
> I encountered a book title at the library that has piqued my
> interest
> even though I won't have time to read it for a while. "Myth of
> Ability: Nurturing Mathematical Talent in Every Child" by John
> Mighton
> (2003).
>
> The title alone provoked a whole train of thoughts for me. As a
> teacher I've developed opinions of my own regarding the balance of
>
> "nature vs. nurture" (or the balance, rather, that those two things
>
> have.) What strikes me, though, is the difference between what I
> feel
> compelled to maintain as a "working" belief and what I actually
> think
> about the subject if I were cornered and forced to theorize on
> reality. I will never (at any parent-teacher conferences or any
> other
> situation wearing my "teacher's hat") -- never ever let the
> admission
> slip: "well -- Johnnie just isn't very good at math." It is
> expected
> that this will never come from my lips even if Johnnie has been
> failing
> -- even if his parents and everybody else are saying that he just
> can't
> do it (which could be part of the problem, but not always), even if
> that
> thought has formed into a conviction in my own mind. My profession
>
> demands that I believe in the latent ability of each and every one
> of my
> students to master all the material I am prepared to teach. The
> moment
> I concede to them or anybody that their performance or lack thereof
> has
> been genetically hardwired into them is to lend undue power of
> suggestion to that very argument (even if it is true to some extent,
> as
> I believe it is) and to undermine my own professional calling.
> Nothing
> is less helpful than a parent who suggests in front of their own
> child:
> "Well -- I was never any good at spelling so I'm not surprised my
> child
> isn't either." As good-intentioned as this 'comfort' is supposed to
> be,
> it gives the student permission to let up on the effort since, after
>
> all, they "just are the way they are". Any of us with children
> are
> probably guilty of similar comments at one time or another. But
> professional pedagogues must be vigilant against this for obvious
> reasons.
>
Don't know what happened to you, but I've gotten a reasonable number of
posts from ASAers every day. It's not the same as when there are hot
button issues, when many are active. But there have always been some.

I am convinced that you have been suckered by the claim that all children
can learn arithmetic, apparently at grade level. There are different
levels of ability in accomplishing various tasks. Now that we have the
ability to track brain activity, we have found that some brains are wired
differently. This may be overcome to some extent, especially if there is
early intervention when the brain is more plastic. But I am quite certain
that we will discover that there is a numerical counterpart to dyslexia.
I recall a period when the accepted wisdom was that differences between
boys and girls was purely the result of nurture. That claim has been
disproved, although there is a range in both groups.

There are factors which can injure innate abilities. I think of a couple
cases. A college student's intended career required that he take
calculus. He flunked. He retook the course. Another F. Then he took
symbolic logic, and was at the top in the class. Told that the abstract
thinking in logic paralleled that in math, he took calculus the third
time and got an A. I learned that when he was in grade school his
teachers had made it clear that math was difficult, too difficult for him
to understand. Not till he got over that block could he use his innate
ability. The second case was a boy who, at four, was consulting /TV
Guide/. At five, he went to kindergarten, where what he was reading was
more interesting to his classmates than what the teacher was doing. At
six he could no longer read.

A required course where I went to school was sight reading music. Prof.
Gerber took the task seriously, but he always had some students with a
problem singing on key. In an experiment, he had some of these
individuals sing a note, any note. Then he hit the corresponding key on
the piano. He said they always then slid off. There are evidently some
individuals who cannot sing on key.

There is another problem that is not addressed in elementary schools
today, aggravated by mainlining almost all children. What a teacher can
do one on one cannot be accomplished with a class of 30, especially when
much time has to be devoted to the "special needs" child or children.

What I have noted, based on having two outstanding teachers in the
immediate family, is essentially negative. On the positive side, we
expect too little from students. Raising expectations has consistently
raised accomplishment.

I would encourage you to do your best, but don't fall for malarkey.
Schools can do better, but a requirement in most is a radical change in
orientation and expectation.
Dave
Received on Sun Jan 22 23:50:36 2006