Going through some old letters I wrote to my father, which he saved. An excerpt from December 4, 1978, when I had been a section leader for the first-year econ course at Harvard.
My exam really separated the men from the women. The four worst grades in the class were all from women, and a woman tied for the fifth worst. My class is a sample of students in which sex-based differences in upbringing are apparent. The women are not math and science oriented, whereas the men have some background in math and science.
The exam was not mathematical, but like all economics exams stressed applications to problems rather than knowledge of facts or formulas. I felt that the results, with a few exceptions, represented what people knew about the course.
One sad comment on my teaching is that the student who got the best grade is the one who comes to class least often.
Today, I would say that my teaching was a perfect example of the Null Hypothesis.
Being a teaching assistant at Harvard was eye-opening. It was scary how many weak students were in my section. I remember teaching a simple consumption function, C = a + bY and five of my students independently came up to me afterward because they did not understand what a and b were supposed to mean. They had been too uncomfortable with 8th-grade algebra to understand the concept of line with a slope and an intercept but too ego-protective to ask the question publicly in class.
By the way, if I had to bet, I would wager that Harvard students today are much better at 8th-grade algebra but are even more ego-sensitive. And I would wager that the male–female difference in ability to handle a course with simple applied math has narrowed or even reversed.
The next year, I was a teaching assistant at MIT. That was a completely different experience. There, when I was trying to explain the concept of “rational expectations,” (a concept typically not taught to first-year students in those days) one student piped up skeptically, “That’s like saying that the batter knows what the pitcher is going to throw before he throws it.” That was a darn good analogy.
Ken Rogoff told his first-year students at MIT that he would give an A to anyone who could help him prove a mathematical conjecture (this was for his Ph.D thesis). He ended up getting two different correct proofs.
MIT undergrads were scary that way.
I love these retrospective posts. Thank you.
BTW – is this far worse than your long-postponed “cancel-bait” post? Appreciate your courage.
The story goes that a student approached the express check-out lane in a Cambridge, MA, supermarket, which bore a large sign reading “10 items or less.” Depositing 20 items on the belt, he was greeted by an exasperated check-out clerk:
“Are you from MIT and can’t read, or from Harvard and can’t count?”
Solid.
What explains such a vast difference between MIT and Harvard undergrads?
I can’t speak to today. But back then, nobody went to MIT without really high math competence. Plenty of people went to Harvard without it.
My understanding is that MIT doesn’t have legacy admissions. Relatives of alumni are evaluated on the same basis as everyone else. Also, all freshman take the same general STEM courses (physics, calculus, chemistry, etc.) so even humanities majors — yes, they exist at MIT — must have STEM competency.
In recent years I’ve become disillusioned with high status institutions like Harvard. Apparently I should have been disillusioned with them before I was even born.
The MIT anecdote is impressive. Hopefully it’s largely still the same way.
My understanding is that MIT has been focusing on “diversity” since the late 90s and more holistic admissions under the guidance of Marilee Jones who was fired for claiming degrees on her cv she never earned. I have friends who did Caltech as an undergrad and MIT as a grad student. When they TA’d lower level math and science courses, they were shocked to find that the bottom of MIT’s undergrads were only capable of the most elementary calculus. You can see this descent in the requirements for first year math at MIT. They used to have 2 levels of first year calculus one for applied students like engineers and the other a more formal proof-based class like the only course available at Caltech. Today there is a third level math course that is so elementary (look up the text onilne if it’s still posted) that it would not be out of place at any low level state school. In contrast, Caltech still requires a minimum of one term of proof based calculus for all students regardless of major (though that too has been watered down from a full year a quarter century earlier). Both have been grade inflating in the last few decades. Since both schools have jettisoned the SATs for admissions now, in the next few years we should see the lower end at both of these once rigorous institutions sag more than ever before.
Of course, their average admit will still know more going in than at H.
I don’t know who’s dumber, the students or the TAs who still think calculus is worth learning in our by now fully CAD-driven tech sector. After a century of rapid technological change, it would be easy for online learning companies to come up with a curriculum orders of magnitude better than the pap taught at so-called “rigorous institutions” these days, who like the Chinese confuse difficulty for importance. Unfortunately, those putting up MOOCs and the like are largely chimps.
Cal Tech is reported to be full of people with frighteningly good native intelligence and math / science skills, and drive, and conscientiousness.
It is so competitive that many of the faculty brats can’t get admitted because of “regression to the mean.”
I read this somewhere–could dig up the citation in a week or two. It was a serious book of 10 or 15 years back, written for a popular audience, on who gets into competitive colleges. The book stated that Cal Tech was an outlier–no jocks, no development admits, no legacies, no affirmative action admits. Only preternaturally smart people tended to matriculate. As of 10 or 15 years ago, at least.
= – = – = – =
I don’t brag about my math skills. With that caveat, it seems clear to me that many people in the USA who are college graduates and allegedly educated don’t know much math or statistics. Maybe I’m only noticing it in “bull session” discussions where truth seeking is not a priority.
This could be a topic for blog post from Professor Kling. Sometime.
My point is that Caltech used to be like that because its grading and courses were so rigorous. It was useless to promote affirmative action or legacies because the average student of even the Ivy League would simply not have graduated. As late as the early 80s, one third of the entering class of Caltech would drop out before graduating. Most simply transferred to “easy” schools like Berkeley, Stanford, UCLA, Chicago, or Harvard (I know multiple examples of all of these). In contrast, the average student of most good state colleges could survive at HYP IF they chose a sufficiently easy major. They would be unhappy and intimidated but they would pass. But even today, a random clever but not super technically motivated student would get crushed by the minimal requirements (Physics, Chem, Bio, 2 years of math for ALL majors including history and lit). MIT’s minimum is lower than Caltech’s with more selection of sections with less rigorous material. Nonetheless, Caltech has gradually made it easier to graduate (partly because high dropout rates LOWERED Caltech ranking in US News, etc.) and because minorities struggled to pass and most smart premeds or business types could not have a reasonable chance of getting an A- average. Now, as C and M promote even more diversity (e.g. less qualified or unqualified Non Asian minorities) they will have to have even easier minimal requirements and grade inflation so that these people have some chance of finishing. In the old days there were people who became great writers and top academics who did not even have the ability to graduate from Tech. (For example Larry Niven and Harry Turtledove who both “proudly” state that they flunked out of Caltech.) It means the old system cannot survive the pressures of “equity.” Sic transit gloria mundi.
Yep, that difficulty plus the merit-based admissions charles mentions is why their enrollment hit 40% Asian a decade ago, which all the Ivies mentioned there studiously suppressed. However, one must not confuse difficulty for rigor: there’s obvious overlap but they’re not the same. I’d have to examine their curriculum to say for sure, but I suspect that they were similarly confused as most of academia on that point.
There’s a 2014 Business Insider article ‘Why Organic Chemistry is So Hard’ that likely gives some insight. A broad generalization would be that women tend toward the body of knowledge learning and men toward the problem solving side. I would suspect in 1978, the women were pushed by society further to the body of knowledge side.
“It’s rare for students to consider themselves excellent at memorizing things and excellent at solving problems.
“People who are great at memorizing things tend to try and stick to classes like anatomy and physiology where it is a feat of intelligence to be able recall massive amounts of detailed information.
“People who are great problem solvers tend to stay in physics where they can memorize first principles and then use their exceptional logic skills to fill in areas of the subject that others might try and memorize. They are probably capable of memorizing things, but they don’t feel like they should have to.
“Organic chemistry sits at the intersection of these two ways of thinking. It requires an exceptional amount of memorization and some pretty advanced problem solving. ”
https://www.businessinsider.com/why-organic-chemistry-is-so-hard-2014-1
“People who are great problem solvers tend to stay in physics where they can memorize first principles and then use their exceptional logic skills to fill in areas of the subject that others might try and memorize. They are probably capable of memorizing things, but they don’t feel like they should have to.”
I would certainly agree with this, and I have a physics Ph.D.
Yep, it is a dichotomy I observed in college decades ago and have remarked on occasionally over the years. I’m in tech because I prefer the logic side, despite having an excellent memory like the side of my family filled with doctors.
There are a few obvious exceptions:
1. Robert Oppenheimer taught himself foreign languages in his spare time. To me that sounds like memorization
2. John von Neumann knew all kinds of things. Maybe it was just that gymnasium back in Budapest. There is the anecdote that von Neumann didn’t seem to know any less about Byzantine history than a professor of the topic at Princeton, based on cocktail party conversation.
I think the Oppenheimer facility with language study is well documented.
von Neumann I’m not so certain about. Anecdote from West Hunter blog at link below:
https://westhunt.wordpress.com/2014/07/31/biology-and-human-capital/
Yes, there are always a few exceptions: that’s why they are the exceptions and not the rule.