Sunday, April 16, 2006

Teaching Math

The following quotes come from a Seattle Times article, which I surfed to from somewhere:

Research shows kids learn math best when they begin with a thorough grounding in mathematics fundamentals and progress in an orderly sequence, with the help of similar instructional approaches, from class to class and grade to grade.

But in Washington, many kids face bamboozling instruction that can be a mile wide and an inch deep. They endure competing approaches and instructional materials. And many textbooks aren't even in sync with the material kids will be expected to know on the WASL.

Wait a minute! You mean that math should be taught in a sequential manner? That instruction should be for "mastery" and not just "introduction"? Say it isn't so!

This is why I support California's state standards. What's recommended above is exactly how our standards are constructed.

And by high school, kids have spent years marinating in a culture that disses math. Few people in this country boast about being illiterate. But it's long been a laugh line to declare "I'm not a math person." Not so in countries such as Japan and Singapore, where students are expected to conquer math — and keep trying until they do.

And in America, where are the math bees, the volunteer math tutorial corps, the math-is-fundamental public-service campaigns? As a society, we root for reading. But we expect success in math to just happen ... or not.

Ilana Horn, associate professor of mathematics education at the University of Washington, says that makes a big difference. "We have a belief in innate ability. It perpetuates this idea that you either have it or you don't, instead of that you aren't trying hard enough.

"It allows teachers to not question student failure in the same way, and it allows parents to excuse the kids' poor performance, and kids to excuse their own poor performance."

John Allen Paulos, in his groundbreaking book Innumeracy, said pretty much the same thing.

One thing about the above quote, though--should a newspaper really be using street language in an article? Dissing? Come on; a reporter should have a better vocabulary than that.

The state is ramping up its attention to math. A review of curriculum is under way to help districts make choices aligned with state standards. A small cadre of math specialists is helping teachers with instruction and curriculum. And 10th-graders who fail the math segment of the WASL this week will be eligible for extra help, at state expense, before retaking the test.

That's good.

Math matters. Mastering math means learning problem solving, abstract thinking and the ability to make connections between ideas. Math trains the mind. It also pays the bills.

It's a simple formula: The higher the math a kid can master, the higher the wage he or she is likely to earn later on. More than 80 percent of workers in professional jobs, including managers, engineers, doctors and lawyers, got at least as far as algebra II, and more than half of them completed at least some trigonometry, according to a 2003 study by the Educational Testing Service, which creates and scores standardized tests.

I'm beginning to think we should stop this utilitarian line of reasoning. Knowing math has value beyond how much money a person makes. And how many of those managers use the Algebra II or trig in their jobs? I'm sure they use an easy facility with numbers, but let's stop pretending that everyone needs trig to get rich. They need it to be able to think--to have those critical thinking skills about which we talk so much.

To close the achievement gap between whites and ethnic minorities, teachers also have to bring mathematical concepts to students from other cultures in a way that engages them. That can require not only mastery of the material, but a creative approach.

Utter crap. How is it that Asian immigrants to America do so well in our math classes? Every time I read about this subject I get the same answer--hard work. Studying. Not expecting the learning to be easy.

The secret, [Michigan State University math expert] Schmidt said, is coherence. Instruction should progress in a sequence of topics over the grades that is consistent with the inherent structure and logic of mathematics. Kids have to master the basics, such as ratios, decimals, percents and fractions before they are ready to tackle algebra and geometry.

Otherwise, kids get confused and don't see the connections between topics. Clutter — teaching kids topics before they are ready for them — and holes in the logical sequence are traps kids may never dig their way out of.

Here we're again fighting against the mile-wide-inch-deep philosophy that permeated American math instruction for so long. I still hear it at my own school: "Kids need to see this topic in Algebra II so it won't be new to them in trig." My take: they should master the Algebra II standards in the Algebra II class and master the trig standards in trig class. Wacky concept, isn't it?

"We are moving from math taught in a cut-and-dried, calculation-based fashion to more explanation. Teachers weren't trained that way, and it's hard for them to teach it that way in the classroom. It's a huge expectation, it's moving in the right direction, it's just that the students and teachers are caught in the middle."

I'm ok with in-depth explanations. That's what I do--at least I hope that's what I do. My fear here is that people will make the presentation methodology, and not the content, the focus of the class. I've heard this kind of talk before, and it sounds very fuzzy.

But let's assume they're sincere. If so, then Washington State is moving in the right direction as far as math (maths?) education goes.


Lillian said...

We have STAR testing coming up in a week, and I've been doing a review with my students, which are all Below Basic or Far Below Basic in Math and/or Language Arts.
These kids do not know how to do basic math, and yet they are expected to know pre-ALGEBRA, etc. So I'm taking time to refresh and reteach...not concerned with 'what happened' or why they missed these fundamentals. Math Teachers need to take at least 10-15 minutes at the beginning of the period with a review of the basics, by giving quizzes daily so kids can 'catch up'. I can see the 'lights' going on as kids begin to actually 'get it'. I also get kids up to the board so I can see with my own eyes exactly how they're doing certain computations. Call me 'old school' but there are just some teaching strategies that still work! You can't play in the NBA if you don't know how to dribble!

Robert said...

Good find and good commentary, Darren. Consider this a manual trackback:

The gist of my article: Our belief in "innate ability" is too weak of a term. Try "mathematical predestination".

Darren said...

We did board work in math *every day* at West Point. I need to incorporate more of it into my classroom. I wish I had the assets available to have small whiteboards, pens, and erasers for each student--then they could *all* work at "the board" and hold their answers up all at once for me to see.

A little technique I learned from AVID training.

cassandra said...

Thanks for the link. I am running for my state's legislature on the No to Fuzzy Math platform, and this is good ammo. The big problem with all this, of course, is that 90% of parents and pols think to themselves, well I wasn't good in math either...argggh!

Onyx said...

Darren I can solve your small white board problem, sort of. There is a white paneling that works like a white board. It won't last forever, but I"ve been using mine for three years now, and their not in bad shape. At about $20 for a 4 x 8 panel then cut them up into the sizes you want, have the kids bring old clean socks for erasers.