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whoa—
is there a critical period for learning algebra?
is there a different critical period for girls & boys?
This is highly preliminary work, but it's interesting, because Carolyn and I have talked about a possible critical period for learning math. I wonder about this because there's something of a critical period for learning accent-free spoken language, and because kids who are put radically off-track in math as children usually never get back on track. The standard explanation for this is that it's simply too hard to make up for lost time once you have the demands of teen or adult life to deal with as well. But I'm not so sure. I have an insanely demanding life, and I'm not finding it hard to go back and re-learn math; as a matter of fact, I'm finding it fairly easy (knock on wood). It always seems to me that the reason I find it fairly easy is that I already learned this material once. I didn't learn it profoundly or conceptually....but I learned it in some way that worked. Another thing. There are plenty of times, dealing with the little math-brains in my Singapore Math class, when I think: uh-oh. These kids are way smarter than I am, when it comes to math. I know more; I can (still) do more. But when they get a problem, they get it fast. The fact that Christopher easily solved the string orchestra problem is a perfect example. Ed and I both thought that was a 'not enough information' problem. Christopher is SERIOUSLY not a math whiz (if yesterday's test is any guide, and I fear that it is) and he solved a SET THEORY problem with ease.
calculus in middle age This is something that gives me pause....can a person learn calculus for the first time in middle-age? I guess I'll find out. It's not like there's a lot of people I can ask. I've never heard of anyone who's done it, or, more to the point, wanted to do it. I hope a sudden urge to study calculus isn't symptomatic of some rare syndrome only Oliver Sacks has ever heard of. Carolyn said the other day, 'Well, you'll never get Alzheimer's.' That's probably true, unless suddenly wanting to study calculus is a sign I already have it.
btw, given what (little) I know of the brain (and given the fact that I've only skimmed this article), it's possible these findings tell us only that adolescents learn faster than adults....
source:
Algebra and the adolescent brain, Beatriz Luna, TRENDS in Cognitive Sciences Vol.8 No.10 October 2004, pages 437-439
-- CatherineJohnson - 15 Nov 2005 Back to: Main Page.
whoa—
New fMRI evidence suggests that adolescents could be at an advantage for learning algebra compared with adults. Qin and colleagues present findings indicating that after several days of practice adolescents rely on prefrontal regions to support the retrieval of algebraic rules to solve equations, as do adults. Unlike adults, however, after practice adolescents decrease their reliance on parietal regions, which assist in the transformation of the equations, suggesting an enhanced ability for learning algebra. These findings are discussed with regard to adolescent brain maturation.
is there a critical period for learning algebra?
In the framework of the proposed ACT-R model, the fMRI results indicate that adolescents decrease their reliance on the imaginal/parietal module after they have practised (‘learned’) algebraic equations, whereas adults are still dependent on this module even after practice. These results are very intriguing because they seem to suggest that, as adults, we might be limited in our ability to ‘learn’ the mental operations underlying this level of problemsolving. Could it be that our teenagers are actually ‘smarter’ than we are? [ed: the answer is no] It is premature at this point to say that adolescence is the ‘critical period’ for learning higher-order problem-solving, especially because actual performance for the two age groupswas equivalent, indicating no advantage to using one circuitry over another.
is there a different critical period for girls & boys?
Gender differences would also be of interest given the discrepancy in math scores between males and females. fMRI could potentially indicate brain differences that might limit females in their ability to learn such problem solving at the same age as males. [ed: I assume that if there is a difference, girls would need to take algebra at a younger age than boys]
This is highly preliminary work, but it's interesting, because Carolyn and I have talked about a possible critical period for learning math. I wonder about this because there's something of a critical period for learning accent-free spoken language, and because kids who are put radically off-track in math as children usually never get back on track. The standard explanation for this is that it's simply too hard to make up for lost time once you have the demands of teen or adult life to deal with as well. But I'm not so sure. I have an insanely demanding life, and I'm not finding it hard to go back and re-learn math; as a matter of fact, I'm finding it fairly easy (knock on wood). It always seems to me that the reason I find it fairly easy is that I already learned this material once. I didn't learn it profoundly or conceptually....but I learned it in some way that worked. Another thing. There are plenty of times, dealing with the little math-brains in my Singapore Math class, when I think: uh-oh. These kids are way smarter than I am, when it comes to math. I know more; I can (still) do more. But when they get a problem, they get it fast. The fact that Christopher easily solved the string orchestra problem is a perfect example. Ed and I both thought that was a 'not enough information' problem. Christopher is SERIOUSLY not a math whiz (if yesterday's test is any guide, and I fear that it is) and he solved a SET THEORY problem with ease.
calculus in middle age This is something that gives me pause....can a person learn calculus for the first time in middle-age? I guess I'll find out. It's not like there's a lot of people I can ask. I've never heard of anyone who's done it, or, more to the point, wanted to do it. I hope a sudden urge to study calculus isn't symptomatic of some rare syndrome only Oliver Sacks has ever heard of. Carolyn said the other day, 'Well, you'll never get Alzheimer's.' That's probably true, unless suddenly wanting to study calculus is a sign I already have it.
btw, given what (little) I know of the brain (and given the fact that I've only skimmed this article), it's possible these findings tell us only that adolescents learn faster than adults....
source:
Algebra and the adolescent brain, Beatriz Luna, TRENDS in Cognitive Sciences Vol.8 No.10 October 2004, pages 437-439
-- CatherineJohnson - 15 Nov 2005 Back to: Main Page.