This reminds me of a professor I had on numerical methods.
The guy was an absolute genius. He helped write some amount (a lot?) of the FORTRAN compiler for at least one of its variants. And... we used state of the art numerical methods. We had a textbook on numerical methods, sure, but this was always just a starting place for what we used. (To this day, I've got some numerical algorithms I coded in FORTRAN that can crush those from common libraries.) If you missed a lecture, there was no making it up by reading the book. You were SCREWED if you didn't get a really good copy of the notes.
Another thing: When lecturing, he barely glanced at his notes even in the middle of complicated derivations of error bounds and things like that.
But here's the real point of this discussion: He had a way of testing that produced similar results to what this article is talking about.
We wouldn't be tested on a general survey of the methods we covered in the class. No. We would be tested on just one or maybe two of the methods we had learned over the entire semester, and the exam questions would be a DEEP, DEEP dive into that method. (I had this guy for 3 semesters, always the same.) When asked what the exam would be on, he'd basically just say: "The numerical methods we've covered thus far". So you had no idea which method you'd need to learn to the maximum degree of depth. This forced you to simply study the shit out of them all. I mean, you had to know some really subtle things about the method if you wanted to get a reasonable grade on the exam.
I actually grew to appreciate this as a testing method. It was the first class I'd ever had where I actually really needed to study. And study I did. Every other class would involve at most a cursory review of a couple of example problems I thought I might run into. This class though was always a minimum of like 3 full days of complete and thorough review, in teams with the other students.
Loved your post, but as an aside, this stood out to me:
>It was the first class I'd ever had where I actually really needed to study
I wish we had a way of challenging every smart kid with proper material. When I got to university and suddenly had to try, it was quite a shock to my system. I could, in theory, have used the first 18 years of my life much more productively.
The real tragedy there is that how to handle being challenged is a super important skill. And many of our best and brightest don't get to practice it all until it's too late. You can't learn a skill without practice. That's just not how it works.
It makes no sense to me at all that children from all different backgrounds and abilities go through an identical curriculum at an identical rate. Like, have the people that set that up never met humans and human children before?
My sister has the luxury of home-schooling her kids. And so they all have workbooks they can go through at their own individualized pace. As a result, one of them, my 6 year old nephew is now at about a 7th or 8th grade level in mathematics. He just loves doing math. Can you imagine how long that kid would have had to wait to actually be challenged in math if he went through the public school system? ...And they're actively trying to get rid of advanced study paths for such kids.
We lost something in the path from homeschooling to one-room schoolhouse to the massive school factories we have today - which was pacing the students. Now we try to group everyone by age.
It's much easier when there's only a small group of kids - but who's to say the massive schools shouldn't be close to large groups of one-room schoolhouses instead of the age-segregated blocks we have now?
Done correctly this helps all kids, except those who just happen to be perfectly aligned with their age.
We need something like the Young Lady’s Illustrated Primer. I’m sure you can hire a couple of thousand professors and experts and map out a huge interactive curriculum tree.
This can’t replace school - you still need socialization, disciple, adult supervision, sport, etc. But academically this would beat my high school experience six-love.
I think part of the discussion will be realizing you do NOT need teachers who are expert in the subject to teach; you need teachers who are good at teaching - especially at the elementary/high school levels.
And part of that may be having the same teacher or group of teachers throughout the student's career, and with authority and flexibility to modify the curriculum as needed.
But we'd also have to admit that some students are going to do better than others, and the outcomes may not be all equal and at the same time.
Aside from varying paces at which children learn, temperament makes a big difference too. I remember in elementary school, there was a subject I didn't like. Finally in 5th grade, I decided to try a different approach for one grading period. I did not participate in that subject. As in, when the teacher said to get out the materials, I instead got out a novel and read it. I turned in no work and did no homework.
When my report card came out, I was astonished to find I had a D (the lowest passing grade). My lesson for that quarter: it is impossible to fail at school (this lesson proved to generalize all the way through high school). At this point, I stopped putting any effort at school into something I didn't find personally gratifying. Most of my fellow cohort of "smart kids" were mystified by this; they would go through an existential crisis in the very rare event that they got a B+. Pretty much any of the straight-A students could have had almost-straight-As with 10% of the effort they put in to ensure they would never get a B+.
When I finally reached college, it became possible to fail, but still not particularly easy. I would skip evening exams to save myself the trouble of having to reschedule my weekly D&D session. I only studied when failing an exam would put me in danger of being kicked out of school (this happened maybe two or three times). I graduated with a C average.
I'm not sure what the moral of this story is other than to say that some kids will study no matter the difficulty of the material while other kids will not.
I'm not entirely convinced it's a very good proxy (at least for the hard sciences). Certainly in my physics classes, raw-intellect trumped conscientiousness; using tidiness as a proxy for conscientiousness and "holds an advanced degree from a distinguished university" as a proxy for GPA, a walk-through of the professors offices in that same department would also dispute that.
I think GPA is closer to a proxy for (A + g) * (B + conscientiousness) with values A and B varying from school to school and department to department (as well as the threshold for "perfect" varying). I had 3 roommates with higher conscientiousness than me flunk out, so YMMV.
[edit]
While we are talking personality traits, I think a high GPA is probably also a proxy for neuroticism; certainly many of the straight-A students exhibited these traits (as does the child of mine who gets the best grades). FWIW I score low in both conscientiousness and neuroticism on a Big Five test.
[edit] changed from "not convinced this is true" to "not convinced it's a very good proxy"
My gut feeling is that I was successful in spite of these things, not because of these things. With counterfactuals there's no way to be sure though.
> One could argue it was a failing on your parents to set proper boundaries/discipline. I’m a lot of environments, you’d certainly not be helped by it.
My parents did everything short of beating me to try and get me to do my homework. After school they sat me at the dining room table with nothing but my textbooks, pencil, and paper. I had to have my list of HW assignments signed off on by my teacher; if it wasn't signed I wasn't allowed to go out and play after school. All of that resulted in me sometimes doing my homework.
By the time I was in high school they loosened up on the structure just because they believed that I only had 4 years left to figure out how to do this on my own, but I still was banned from attending various social events because of my lack of effort in school. By the end of 10th grade, I had grown distant from my main group of friends just because I essentially never hung out with them outside of school so there was a lot of missing shared-experiences.
As a parent now, I have no idea what they could have done differently. My own personal nightmare is one of my kids acting like I did (despite my parents saying I was the "easy kid")...
I was the same way, and share the nightmare with kids. Personally i’ve spent a lifetime learning how to say No to things I don’t want to do (very hard) and finding the things that work for me.
It’s far from perfect, and it has sometimes come at the cost of heavy mistakes before I figured out why something wasn’t working.
It does give me the ability to explain and help my kids try and find what works for them, and I have been materially successful enough to afford them options sometimes.
Which is huge. I’ve been very lucky. I’ve also faced many hard truths that others have refused to, and worked my ass off too, to get there.
I still do need to work my ass off every day.
One consolation perhaps - I have several friends who were similar that I grew up with whose parents didn’t stop short at beatings.
They succeeded very well in a specific environment afterwards (military), but at the cost of non-trivial mental health issues that are hard to properly describe. A inability to say No to an authority figure being one of them, perhaps, even when it leads to catastrophe. And a severe difficulty in trusting themselves to be independent thinkers.
They’ve objectively done well for themselves by societies standards, as have I. But each of us has our own regrets.
Mainly that it was easier to get into college 25 years ago, but also I scored in the top 1% on the SATs. I also was a bit scared of not getting into college, so I managed to get my GPA up to a 2.9 by the end of junior year (which included a metaphorical rolling-over and showing my belly to my English teacher, who was giving me bad grades out of spite).
Most colleges don't care, especially if your standardized test scores are high enough. The main problem is with obtaining scholarships, they will care about grades a lot. I left before completing even a single semester because I hated it, but my 2.0 GPA didn't stop me from getting admitted anywhere.
Competitive colleges are a small minority in US. Less than 300 colleges reject more students than they accept. CUNY isn’t the only college with no entrance standards (open enrollment) and community colleges are also open enrollment and have transfer agreements for fours year colleges. Lots of countries have similar institutions.
The difficulty of course, and the reason that doesn’t happen often, is it requires deep knowledge of a subject by the teacher and a keen and interested mind.
Hard material with someone who doesn’t understand it or isn’t interested in it just burns students out, or doesn’t go anywhere.
There aren’t a lot of people capable and interested in doing it for every subject, and even fewer interested in doing it for the amounts typically paid in school.
Luckily with the internet we can have great teachers achieve scale for the first time ever. This isn’t a solved problem yet but at least a tantalizing possibility.
> I wish we had a way of challenging every smart kid with proper material.
We do. It’s called acceleration. It’s not used because no one cares. The school system is not set up for learning. If it was students who were proficient at grade level could learn the material of the next grade up or two levels up.
I'm familiar with this testing strategy. It has one major upside: It allows an exam to test the material in great depth without being enormously long.
But it also has one major downside: Students may not learn all of the material equally well. If the random point in the material space that the exam focuses on happens to be a point that the student didn't learn as well, the exam result will appear as if the student learned all of the material poorly.
In other words, the exam has higher random variance.
This happened to me in my computer graphics class. The first exam had a multi-part problem where the first part involved quaternions. I was familiar with quaternions from my time as a physics major, but did not remember the professor introducing them. I reviewed my notes afterwards and found that he did in fact mention them in passing in a lecture two weeks previous to the exam, but did not call particular attention to them nor did he assign any homework involving them.
Going the opposite way, here's a story of an electrical engineering class I had in college. The class subject was a slightly off-the-main-path course, taught by a visiting professor from overseas. It involved deep analysis of electrical circuits with some heavy math. At the final exam, the first thing I noticed was how thin the exam packet was. It was a harrowing experience when I opened the exam -- it consisted of exactly one question. As it turned out, it required using nearly everything we learned during the course to solve that one question, which I thought was a fascinating if scary way to test students, as forgetting one of the methods taught could block progress.
The guy was an absolute genius. He helped write some amount (a lot?) of the FORTRAN compiler for at least one of its variants. And... we used state of the art numerical methods. We had a textbook on numerical methods, sure, but this was always just a starting place for what we used. (To this day, I've got some numerical algorithms I coded in FORTRAN that can crush those from common libraries.) If you missed a lecture, there was no making it up by reading the book. You were SCREWED if you didn't get a really good copy of the notes.
Another thing: When lecturing, he barely glanced at his notes even in the middle of complicated derivations of error bounds and things like that.
But here's the real point of this discussion: He had a way of testing that produced similar results to what this article is talking about.
We wouldn't be tested on a general survey of the methods we covered in the class. No. We would be tested on just one or maybe two of the methods we had learned over the entire semester, and the exam questions would be a DEEP, DEEP dive into that method. (I had this guy for 3 semesters, always the same.) When asked what the exam would be on, he'd basically just say: "The numerical methods we've covered thus far". So you had no idea which method you'd need to learn to the maximum degree of depth. This forced you to simply study the shit out of them all. I mean, you had to know some really subtle things about the method if you wanted to get a reasonable grade on the exam.
I actually grew to appreciate this as a testing method. It was the first class I'd ever had where I actually really needed to study. And study I did. Every other class would involve at most a cursory review of a couple of example problems I thought I might run into. This class though was always a minimum of like 3 full days of complete and thorough review, in teams with the other students.