math education

[cellio]

Being of a certain age, I learned arithmetic the conventional way and neatly dodged New Math. I knew things had changed since then -- at least in the ability of high-school graduates to do arithmetic unassisted -- but I didn't realize just how strange things had gotten. amergina posted a link to this (longish) news story broadcast: math education: an inconvenient truth. Sigh.

To summarize, some (apparently-big-name) published curricula are now skipping conventional methods to teach new ways of doing arithmetic. Some are different ways of breaking down the problems; others are primarily notational differences. All of them seem, on average, slower and more error-prone.

Now granted, I sometimes do arithmetic by the "reason through it" process the reporter dislikes (what did they call that, clusters?), but it's kind of specialized. For example, a 15% tip reduces to a 10% tip and half again; that's fast and easy. If I'm multiplying by a number ending in 9 or 1, it's often easier to reduce to another problem and then deal with the leftovers. If I need the square root of 4862 (I just pulled that number out of thin air), I can't tell you exactly what it is but I know it's a bit less than 70. Sometimes I think in patterns like that. I think this is a fine thing to teach people after they have mastered conventional write-it-down-and-work-it-out methods. Not before, and certainly not instead of. (And I think it's better if you can give them an educational environment in which they figure out these "tricks" for themselves, like I did.)

I assume these new teaching methods (which include "use calculators") are largely responsible for many people being unable to get order of magnitude right. Those of the previous generation undoubtedly said that about the move away from slide-rules, but I never used a slide-rule (except as a novelty) and I can approximate... I once had a calculator-armed teenage clerk at a produce stand insist that my bag of vegetables came to over $200. Even if he had no instincts about what vegetables cost, he should have been able to tell that the price codes he'd read off the list didn't add up to that and maybe he'd mistyped something.

(When shopping I tend to keep rough a mental tally, so when I get to the check-out I know approximately what the total should be. I gather that this is unusual. It's just the way I learned to shop, probably from a time when you had to make sure you didn't exceed cash on hand. Now I use plastic for everything, but the habit remained.)

Well, I guess I can take comfort in one thing: if what they say about mental exercise is correct, I should be pretty close to immune to Alzheimer's. :-)

Comments

[starmessenger.livejournal.com]

I think the woman in this video is ignoring the richness of the new-math curriculum in favor of a narrow interpretation of what it means to be proficient in math.

I've been impressed by (and even jealous of) my daughter's new math education. New math got her ready and eager to take advanced geometry in ninth grade.

My kid and her fourth-and-fifth-grade classmates learned all the techniques lamented in the video. They also learned the standard algorithms, plus visualization techniques (plots, charts, graphs, arrays, maps) that I didn't get to in the old-math regime until ninth-grade algebra. The algorithm-lady sneers at the textbook chapter on visualizations, but visual support for what she was doing with numbers was crucial to my kid's understanding and enjoyment of math.

Example: when Gwen was in fifth grade, she showed me how she'd learned about squared and cubed numbers by drawing me a picture of a "number square" and a "number cube", and showing me how the visualization and annotation were related. Dang, we didn't even get to the *number line* until I was in middle school! Under new math, kids are doing the number line, and learning visually about negative numbers, in third and fourth grade.

Her elementary-school curriculum made math so interesting to my daughter that she routinely shared what she was learning with me. Sometimes she needed help with mechanics, but just as often what she was learning sparked relationships in her mind, and she wanted to talk about them. New math gave me a way to talk to ten-year olds about hypercubes -- fun for them, fun for me, and they've been chomping at the bit for physics ever since.

Compare: in fifth grade, my classmates and I were having our minds numbed with rote memorization and practice of the standard algorithms for multiplication and division. We spent *years* doing nothing but multiplying and dividing columns of numbers. The algorithms are efficient, but what do you have when you're done? Bored, math-loathing fifth-graders who can efficiently multiply and divide long numbers.

Death to old math, I say, and good riddance.

[starmessenger.livejournal.com]

I should add that I'm not talking about a fancy private school here. My daughter went to a public K-8 elementary school that met every definition of "inner-city urban." The school was in the middle of the ghetto, and most of the students were from the neighborhood. This isn't a case of home-nurture by geeky CMU parents, either. *Half* the students in my daughter's eighth-grade year were taking Algebra 1. Not pre-algebra or some watered-down "fake" algebra -- this was the equivalent of high-school Algebra 1. All of those students have gone on to take geometry in ninth grade.

Can you fake being ready for high-school geometry? Is this some new-math trick or lowering of national standards? I'd have to check the statistics, but I think that American students have been doing better and better at math and science over the last twenty years.

[cellio]

I am beginning to get the feeling that my (suburban, non-wealthy, public-school) math education was advanced for its time. I thought it was typical. We certainly encountered the number line by fourth grade at the latest (I think third), used at least some visualization techniques, and were well past rote division by fifth grade. Algebra I was in 8th grade.

Yes, I also had a knack for math, and I was usually the first person in the class to figure out the untaught "rule" (pattern). I don't think that was most of it. (Interestingly, in most ways my school system seemed pretty bad; it particularly failed high-school students. Maybe they put all their focus on the early years and got that right?)