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Unfortunately your realization is empirically unsound, and the problems of “every teacher you know” have as much to do with lack of available expert teacher att

Unfortunately your realization is empirically unsound, and the problems of “every teacher you know” have as much to do with lack of available expert teacher attention per student and standard expected teaching styles and school structure with substantial friction/latency in feedback and huge amounts of wasted time as with inherent student ability. Start here http://web.mit.edu/5.95/readings/bloom-two-sigma.pdf http://web.mit.edu/5.95/readings/bloom-two-sigma.pdf but then there is a vast literature (thousands of studies and other research papers) exploring the general topic of math pedagogy. Some approaches and some teachers are radically more successful than others, given comparable students. If you hand me one of your 20th percentile students who is struggling but willing to learn, and give us the same amount of time which would otherwise be spent in a classroom for a year of one-on-one face-to-face time, with the student also spending a typical amount of time working independently, I can have them outperforming your 80th percentile students by the end of the year, without issue. The difficulty of course is that direct mentoring by an expert tutor is too expensive for society to be willing to pay for at scale. The main reasons that your teacher friends are stuck is because (a) many if not most of their students are unprepared before they arrive in any particular course, which is largely down to structural social factors and school scheduling inflexibility, and (b) the combination of lectures and independent work with inadequate feedback are for the average student a terribly inefficient and ineffective way to learn. Neither of those has all too much to do with biological predestination or whatever.

monic_binomial 9y ago
Heh. You can cite all the old wives' tales, superstitious folklore, and education research papers you want. None of that makes it more likely that a 95 IQ student will ever understand precalculus.
- jacobolus 9y ago
  I actually have direct experience getting a (I would guess) 95 IQ student to understand precalculus, tutoring for a few months back when I was a high school student ~15 years ago. She got an A, after having had a string of Cs in every prior high school math course, and not being properly fluent with 9th grade algebra at the beginning of the year. [I don’t say this to brag; I expect any competent tutor can achieve the same thing with a typical below-average student if the student is motivated and they get lots of 1-on-1 time.] However, I can well believe that a 95 IQ student who was dramatically unprepared at the beginning of the year and believes himself to be an irredeemable failure will have a lot of trouble in a standard lecture + homework drills format high school precalculus course taught by a teacher with no time to help him catch up on remedial material at his current level of understanding, give him any special attention, or make the class material engaging enough to give him reason to care. In that context, failure (or scraping by with an undeserved C) is the obvious outcome, but can’t fairly be blamed on the student’s effort during that year or some kind of mental deficiency. (Personally, I skipped half of precalculus and somewhat wish I had skipped the other half; I found it to be an uninspired grab-bag of disconnected topics, with much too rote a focus.)

monic_binomial 9y ago

Heh. You can cite all the old wives' tales, superstitious folklore, and education research papers you want. None of that makes it more likely that a 95 IQ student will ever understand precalculus.

jacobolus 9y ago
I actually have direct experience getting a (I would guess) 95 IQ student to understand precalculus, tutoring for a few months back when I was a high school student ~15 years ago. She got an A, after having had a string of Cs in every prior high school math course, and not being properly fluent with 9th grade algebra at the beginning of the year. [I don’t say this to brag; I expect any competent tutor can achieve the same thing with a typical below-average student if the student is motivated and they get lots of 1-on-1 time.] However, I can well believe that a 95 IQ student who was dramatically unprepared at the beginning of the year and believes himself to be an irredeemable failure will have a lot of trouble in a standard lecture + homework drills format high school precalculus course taught by a teacher with no time to help him catch up on remedial material at his current level of understanding, give him any special attention, or make the class material engaging enough to give him reason to care. In that context, failure (or scraping by with an undeserved C) is the obvious outcome, but can’t fairly be blamed on the student’s effort during that year or some kind of mental deficiency. (Personally, I skipped half of precalculus and somewhat wish I had skipped the other half; I found it to be an uninspired grab-bag of disconnected topics, with much too rote a focus.)