For example, if you look at a 30 year period in the second half of the 20th century, the standard primary and high school math programs probably didn’t change dramatically during this time, and they certainly didn’t become much harder.
I’m not so sure. Here’s a 2005 paper (‘Rising mean IQ: Cognitive demand of mathematics education for young children, population exposure to formal schooling, and the neurobiology of the prefrontal cortex’) suggesting that ‘cognitive demands of mathematical curricula’ in the US increased from about 1950.
Anecdotally, I remember occasionally surprising my parents by telling them about what I was learning in math—my schools’ math syllabuses apparently went faster than my parents’.
The question is if this effect (and/or effects like it in other school subjects) would be enough to mask the Flynn effect at younger ages; I guess it could be enough to partly mask it but not wholly mask it, in which case there are other explanations at work too. Maybe the Flynn effect is less in children than adults as well.
Unfortunately, I think we’ll have to wait for further major advances in brain science to make any conclusions beyond speculation there. Psychometrics suffers from too many complications to be of much further use in answering such questions (and the politicization of the field doesn’t help much either, of course).
Neuroscience could certainly help, but I would think one could make a good start just by repeatedly IQ-testing a huge number of kids through childhood, tracking them into middle age, plotting child IQ against adult achievement, and drawing a lowess regression line through it. If the line starts out relatively steep but flattens out with increasing IQ, you and me are right: IQ isn’t that informative about high flyers. I wouldn’t be that surprised if someone hadn’t already done something like this with the Project Talent data or some other big database.
Sputnik was a huge shock to the U.S., causing fear that the Soviet Union would eventually overwhelm or eclipse the U.S. One of the results of that fear was the enrollment of math professors in the design of a new model math curriculum called the New Math, which was widely deployed and in most places where it was deployed represented a sharp break with past math curricula. Elementary-school children were taught things like how to do addition in bases other than ten. The “laws of algebra” (e.g., the commutativity property) were introduced much earlier than they had been in the past. The New Math was a frequent topic of popular news articles and news segments in the late 1960s, probably because of the bewilderment of parents who attempted to help their children with math homework.
I was an elementary-school student in Massachusetts public schools in the 1960s, and this New Math was my favorite part of an otherwise uninspired factory-style elementary-school education, so I salute the Soviet space program of the 1950s for shocking certain elements of the educational establishment of my country out of its complacency.
Do we know if the early start actually led to more talent in math and science when children of this age became adults? Or did we just end up with a lot of lawyers who learned and then forgot Calculus?
All I can tell you is that I am very good at math and science and that I am significantly less likely to have turned out that way if in elementary school, I had been taught a lot of calculational arithmetic and elementary-algebra skills with no coherent and thoughtful attempt to teach the “concepts” or the “broader understanding”. My formal educational was pretty crappy, and I would have been much better off if someone’d just given me a small office or a desk and a chair in a quiet place and access to books at the end of elementary school, so I could have skipped the whole secondary-school experience like Eliezer did, but the elementary-school math was very well done, not because the teachers were particularly inspired but rather because the design and integrated nature of the whole curriculum or plan of tuition.
Also, let us not lose sight of my reason for writing, which is to present evidence that at least in the U.S., math education for the average child changed drastically during the 20th Century.
I’m not so sure. Here’s a 2005 paper (‘Rising mean IQ: Cognitive demand of mathematics education for young children, population exposure to formal schooling, and the neurobiology of the prefrontal cortex’) suggesting that ‘cognitive demands of mathematical curricula’ in the US increased from about 1950.
Anecdotally, I remember occasionally surprising my parents by telling them about what I was learning in math—my schools’ math syllabuses apparently went faster than my parents’.
The question is if this effect (and/or effects like it in other school subjects) would be enough to mask the Flynn effect at younger ages; I guess it could be enough to partly mask it but not wholly mask it, in which case there are other explanations at work too. Maybe the Flynn effect is less in children than adults as well.
Neuroscience could certainly help, but I would think one could make a good start just by repeatedly IQ-testing a huge number of kids through childhood, tracking them into middle age, plotting child IQ against adult achievement, and drawing a lowess regression line through it. If the line starts out relatively steep but flattens out with increasing IQ, you and me are right: IQ isn’t that informative about high flyers. I wouldn’t be that surprised if someone hadn’t already done something like this with the Project Talent data or some other big database.
Sputnik was a huge shock to the U.S., causing fear that the Soviet Union would eventually overwhelm or eclipse the U.S. One of the results of that fear was the enrollment of math professors in the design of a new model math curriculum called the New Math, which was widely deployed and in most places where it was deployed represented a sharp break with past math curricula. Elementary-school children were taught things like how to do addition in bases other than ten. The “laws of algebra” (e.g., the commutativity property) were introduced much earlier than they had been in the past. The New Math was a frequent topic of popular news articles and news segments in the late 1960s, probably because of the bewilderment of parents who attempted to help their children with math homework.
I was an elementary-school student in Massachusetts public schools in the 1960s, and this New Math was my favorite part of an otherwise uninspired factory-style elementary-school education, so I salute the Soviet space program of the 1950s for shocking certain elements of the educational establishment of my country out of its complacency.
Do we know if the early start actually led to more talent in math and science when children of this age became adults? Or did we just end up with a lot of lawyers who learned and then forgot Calculus?
All I can tell you is that I am very good at math and science and that I am significantly less likely to have turned out that way if in elementary school, I had been taught a lot of calculational arithmetic and elementary-algebra skills with no coherent and thoughtful attempt to teach the “concepts” or the “broader understanding”. My formal educational was pretty crappy, and I would have been much better off if someone’d just given me a small office or a desk and a chair in a quiet place and access to books at the end of elementary school, so I could have skipped the whole secondary-school experience like Eliezer did, but the elementary-school math was very well done, not because the teachers were particularly inspired but rather because the design and integrated nature of the whole curriculum or plan of tuition.
Also, let us not lose sight of my reason for writing, which is to present evidence that at least in the U.S., math education for the average child changed drastically during the 20th Century.