Yesterday's NPR Weekend Edition Saturday featured an interview with Stanford University professor Keith Devlin on the importance of Algebra, and while I listened to it, it suddenly occured to me why more mathematicians don't oppose Reform Math.
Here's what I posted on the NPR website:
Keith Devlin suggests that, given calculators, students should focus less on accurate arithmetic calculations, and more on algebraic reasoning. But, as Devlin's fellow mathematicians (e.g., Howe, Klein, & Milgram) have argued, mastering the basic algorithms of arithmetic is essential preparation for algebra. And while the most mathematically inclined students--including Devlin himself--may be able to master these algorithms without much hands-on, numerical practice, the vast majority do need lots of practice, and striving for correct answers is an essential part of that practice.
When our most prominent, accomplished mathematicians, who themselves may well have gotten by without developing accurate arithmetic skills, discount the importance of teaching such skills to the general population, they do a terrible disservice to elementary school math education (and may themselves be horrified by the results, years later, when today's grade school students enter their classrooms).Today's arithmetic, unfortunately, has been seriously watered down by the new "Reform Math". More mathematicians need to examine this curriculum and speak out against it; ironically, because they can get by without much arithmetic practice, and because so many of them found arithmetic boring, too few mathematicians have considered the potentially dire consequences that the latest trends in grade school math present to the rest of the population (and to the country as a whole).
Consider what one other NPR poster has taken away from the Devlin interview. As she writes in her post:
I want to thank Dr. Devlin for a great quote that I plan to post at the front of my classroom. "Mathematicians often make mistakes in elementary arithmetic because we have our minds on higher things." That will come in very handy!Yikes!
"Mathematicians make mistakes in elementary arithmetic" -- now there's an inspirational motto for the school day.
ReplyDeleteSo much preferable to out-of-date homilies like "Practice, practice, practice!"
ReplyDeleteOr even
ReplyDeletePerfect practice makes perfect.
Deliberate practice makes perfect.
Distributed practice makes perfect.
und so weiter....
Yes!
ReplyDeleteI know one accomplished mathematician who frequently uses herself as an example of why boring practice is unnecessary for most students.
Otoh, I know of another brilliant mathematician who seems to acknowledge that he is an outlier, and his children are using Kumon.
Devlin is sort of the Liberace of the math world. He has true gifts but he relies on pizazz more than the gifts. He wrote a column a few months ago about multiplication, that it "ain't no repeated addition", which people are still arguing about. Fortunately there are mathematicians who argue against the faddish reforms. These would include but are not limited to: Jim Milgram, Wayne Bishop, Ralph Raimi, David Klein, Steve Wilson, Stanley Ocken, Dick Askey, Hung-Hsi Wu, Tom Parker, Scott Baldridge, Greg Bachelis, and Wilfried Schmid.
ReplyDeleteMathematicians do not get paid to fight for good K-12 programs, however. So we are doing battle with organizations such as NCTM, and the various ed schools which carry the message of NCTM. These people do get paid to do what they do. And they do their job very well.
If you've never taught, I can see how you would think it OK to skip fundamentals. This would be especially true for someone who has acquired a high level of expertise in some content area. If you're really good at something, the fundamentals are automatic. They may even be automatic to a degree where you've lost contact with what you are doing underneath the covers.
ReplyDeleteIt's also true that being a mathematician, even a very accomplished one, doesn't mean a thing when it comes to teaching math. You could even make a strong argument that a strong mathematician would be a bad person to teach math, too far from the fundamentals to explain them.
What astounds me is when an educator makes these same claims. If you work in a classroom, with actual kids, there is no way you will support skipping fundamentals. I'm amazed, every day, by what simple things can make a child stumble. Then I go home, reflect, and realize that 'simple' is entirely relative and proportional to one's experience.
Math hasn't changed in the last hundred years or so, at least the stuff you need to get out of high school. Why do we need to change the way it's taught?
Even if you own a Ferrari, you still need to learn how to walk.
Devlin is sort of the Liberace of the math world.
ReplyDeletewow ---- trying to come up with an image to match that!
Then I go home, reflect, and realize that 'simple' is entirely relative and proportional to one's experience.
ReplyDeleteYES! YES! YES!
I've been taking tennis lessons since last summer, knowing NOTHING about tennis -- and nothing much about any other sport, either.
IT IS SO HARD.
I often think that parents and teachers (AND DEFINITELY ADMINISTRATORS & ED SCHOOL PROFESSORS) should all take lessons in something they have ZERO background knowledge in & try to reach "proficiency" in a year's time or so.
You have exactly the experience Paul is describing, except from the student's side.
It is staggering how the tiniest thing can be beyond reach or even perception.
It took me the longest time to figure out that when you serve your feet are always facing the same direction, no matter which side of the court you're aiming for.
Who knew?
My tennis teacher, who I think is terrific (he went to ed school, btw!) is constantly taking me back to basics.
ReplyDeleteIf I come in for a lesson having lost whatever it was I thought I had, he moves me back down the ladder of difficulty.
I was a mess when I got back from Aruba.
It's also true that being a mathematician, even a very accomplished one, doesn't mean a thing when it comes to teaching math. You could even make a strong argument that a strong mathematician would be a bad person to teach math, too far from the fundamentals to explain them.
ReplyDeleteUnfortunately, the Devlins of the world give mathematicians a bad name. There are mathematicians (some of whom I named above) who would disagree with Devlin. They would be the first to agree that they would not be good at teaching math in K-12, but they are in a fairly good position to know what content is important to learn and master. Both Wilfried Schmid and Hung-Hsi Wu were on the National Math Advisory Panel and the list of what should be mastered in K-7 is a fairly good one. PaulB feels a strong argumentcan be made that mathematicians are the wrong people to teach math. This is a cry I have heard uttered by a variety of ed school professors, some of whom have told mathematicians like Jim Milgram and Steve Wilson that they don't know what they're talking about. This is a slippery slope (sorry for using the phrase; I hate it). I don't want to throw out the mathematicians just yet. Maybe Devlin, Uri Treisman, and Jerry Becker and others like them; but not the ones who understand what content must be learned.
Rereading this, I'm reminded of a 'simple' thing I encountered this week. I wrote a test question, "What is the unit price for donuts priced at 5 for $2.00." One student was totally hung up on the word 'at' in my question. He had never seen this construct before.
ReplyDeleteI was at a loss to explain it and the more I think about the construct, the less I understand it myself. Under pressure, I just changed it to "Donuts cost 5 for a dollar. What is the unit price?" With that, no problems ensued.
I went home and asked my spousal unit, a highly skilled word wizard, to explain the construct to me. She laughed and accused me of being a fossil. She claims, "Nobody ever says that anymore!", siding with the child's confusion.
Sighhhhh.
So, ok, maybe I'm a fossil but it gave me a chance to tell the student all about the @ symbol so on balance a win, eh?
You never know what's going to get in the way and I'm not smart enough to know what to throw out, so fundamentals get the highest of priorities in my room.
yay lefty!
ReplyDeleteand yay catherine, too:
"I often think that parents and teachers (AND DEFINITELY ADMINISTRATORS & ED SCHOOL PROFESSORS) should all take lessons in something they have ZERO background knowledge in & try to reach "proficiency" in a year's time or so."
comes pretty close to dead-center on
one of my big dogmas-of-the-moment.
while i'm at it, barry's list of allied mathematicians
shows an easy command of the relevant literature.
this is the kind of thing that keeps me
coming around to KTM. keep 'em coming!
as to mistakes, i make a heck of a lot of 'em
ReplyDeleteright there in lectures and make a point
early on each quarter to call attention to this fact...
"that hasn't changed in all these years.
what *has* changed is that i'm a *lot* better
at *finding* my mistakes!"
typically this is followed by
"thanks for the correction.
keep 'em coming!".
in mistakes begin insights...
It's because they don't have kids in school.
ReplyDeleteI know that the best maths teacher I had at school was one who said he'd struggled with maths himself.
ReplyDeleteI only got him in 7th form (the last year of school) for mathematics with calculus (that was my third year of learning calculus), and yet even then he was focused on the basics.
/*devlin is sort of the liberace of the math world*/
ReplyDelete& nothing says "spring" like repeated-addition.
how i love and hate this world-wide-web. \heartsign