Friday, August 15, 2008

Dyscalculia: If I were king...

Many of my students have little facility with numbers.


I'm not talking about algebra or geometry--I'm talking arithmetic.


While it's easy to lay blame on the kids, cell phones, television, their parents, the streets, vaccines, or perhaps a national conspiracy to raise better consumers, I think that schools can make some changes that might help.


First, make sure the curriculum works. This is the big one, and well-intentioned folks in charge of large budgets are wrestling with it in districts around the country.

(I first saw this video at Elona Hartjes' bloggsite, Teachers at Risk--it should be seen by every parent with a child in elementary school. I also recommend a look at Linda's thoughts in Technology in Teaching.)







In the meantime, here are a few things we might consider:

*Ban calculators until a child hits physics class

No excuses, no excuses, no excuses--calculators kill number sense.

If you happen to wander into some trignometry, I'll make allowances for a slide rule. Heck, I used to be able to calculate physics problems faster than the calculators we had back in the 1970's, which actually had a noticeable lag when doing some functions.

I have children today who do not grasp that 100 divided by 20 is not the same as 20 divided by 100, and who will argue the point because when they use their calculator their way they get their number.

*Return analog clocks to the classrooms

I'm old enough to rant about digital music--I only caved in to the CD thing because Aerosmith's Pump was not released on vinyl, and, well, I liked their elevator music.

Still, digital music loses something in the process, beyond the romanticized snack, crackle, pop of vinyl records.


Digital clocks give less information than analog faces. That I even have to
explain this saddens me, but here it goes:

1) Kids need clocks--blame the Benedictine monks if you will, but time matters. A digital clock is a number that flips now and again.

Time was divided into minutes and seconds long before the monks developed the timepieces that plague us today.

Hours and minutes and seconds plunges us into radians. Blame the Babylonians, too , but for whatever reason (perhaps 360 was close enough to the number of days in a year), circles are divided into 360 degrees. Western civilization is encumbered by circles divided into degrees--and despite (or maybe because of) a handy-dandy button on your calculator that flips radians into degrees, folks venturing into physics and engineering need a smattering of understanding of how degrees work.

An analog clock takes you halfway there

2) "It's quarter past one" doesn't work in digital land; 1:15 flashing in LED red cannot convey any sense of quarters or "half pasts" or any fractions at all.

An analog clock makes fractions visual. Daily.

*Teach baseball

Baseball is our national game. It's being eliminated from the Olympics, true, and the NFL now dominates our national psyche, but baseball remains an integral part of who we are.

Baseball is all about numbers. Batting averages, slugging percentage, earned run averages.

I bet half the kids in my neighborhood grasped the concept of 0.2 vs. 0.3 (a "200" versus a "300" hitter) via baseball.



*Use an abacus

Alas, abaci have already been commoditized --you can own your own franchise!

The Japanese no longer spend a whole lot of time in class studying the abacus (though they do spend a little, likely more for historical interest), but abacus schools outside of class in Japan is all the rage. Studies have shown that kids who master abaci have a better comprehension of math.

An abacus makes the decimal system tangible.

(Along the same lines, I think kids should learn a number system besides our base 10; binary might be helpful, or maybe even hecidecimal if you're feeling flush--kids need the mend-bending antics of using a different base. It helps students grasp both how arbitrary a system as well as how powerful. Might even help them with programming.)


*Count to 100, or 1,000, or maybe even 10,000...at least once a year

OK, this sounds cruel, but bear with me. Sometime this year I will (again) challenge anyone to count to a billion (a second at a time), and several college bound sophomores will jump at the opportunity. In the three plus decades it takes them to finish, I will have likely have died.

Kids (and adults) have little sense of numbers.

Four or five times a year, have the class count aloud to a thousand, a second at a time. Figure it will take almost 17 minutes.

Once a year, try 10,000, and figure on using almost 3 hours. Now it may seem like a waste of time, but certainly no more deadening than a lot of the worksheets prescribed by our fancy textbooks.

Now a story.

My 7th grade teacher was Mr. Knukowski--he wore a bow tie and plaid jackets, and he had a crewcut in 1972.

If we got caught talking in class, he would make us write the word "quiet" a thousand times. Turns out he didn't care who actually wrote it out, just that it was done by hand.

A cottage industry developed in class, kids trading pencils, Twinkies, kisses, whatever, for sheets of paper holding a thousand "quiets. We learned a lot about economics, and the concept of thousand was forever ingrained in our minds, particularly among the gregarious.


*Play with American wrenches


In 1866, the metric system became legal in the States; in the 1970's, there was a huge push to make everything measurable metric. Today, you still need to know the difference between a 7/16 and 1/2 inch wrench.

Now it sounds trivial, but those of us who spent part of our adolescence under a hood got pretty good at knowing which wrench to call for if the 7/32 was a hair too big (or small).

If you have an old bag full of socket wrenches, which is the way most of us carried them, trying to dig through the bag without knowing which wrench was the next step up from a 7/32 cost a lot of time.

The metric system is way too easy--and while the American system is a testament to the stubbornness of our ways ("we don't need no stinkin' metric") and and to how strongly the inch is imprintedin our minds, it also provided immediate rewards for having some clue about fractions, at least the sixteenths and thirty-seconds sort.

5 comments:

Betty said...

I love your ideas. When I taught sixth grade math, I used baseball examples a lot. I also agree that digital clocks do little to help a child understand time. I remember my dad using a real clock and moving the hands to teach my sister and me how to tell time.

doyle said...

Thanks for your words.I'd love to hear other ways to develop numeracy.

I am too far removed from elementary school to know what's happening in classrooms there.

(That's a problem in itself--while we talk about possibly collaborating between subjects at the high school level, I'd love to see an in-service dedicated to promoting cross-pollination between all the grades, K through 12.)

Linda said...

I am a fanatic on the subject of eradicating innumeracy. I even wrote about it:

http://teacherlingo.com/blogs/dragonlady328pt/archive/2008/08/04/innumeracy.aspx

http://dragonlady328pt.blogspot.com/2005/08/innumeracy.html

A closely allied problem is the disinclination to read, although the basic skills are present.

http://rightasusual.blogspot.com/2005/02/not-illiterate-but-alliterate.html

Anonymous said...

When my daughter went to her specialty school after boot camp, they discovered that most of the sailors didn't know a fraction from a pizza. So, they had to take 3 weeks our of their training to teach fractions. These recruits were going to become jet electricians! My daughter knew her fractions so she was put on light duty in the dispensary during that time. What a pity that kids can graduate from high school and not know how to work with fractions. We teach them in 3rd grade!

doyle said...

No doubt we expose kids to fractions in elementary school, but clearly we are not teaching many of them. I think we're not teaching unless the student learns what we are trying to teach.

Pizzas are a great way to learn about eights, not a bad way to introduce fractions!