What medieval people got right about learning (2019)(scotthyoung.com)
scotthyoung.com
What medieval people got right about learning (2019)
https://www.scotthyoung.com/blog/2019/06/07/apprenticeships/
118 comments
TFA misses a key difference between apprenticeship and classroom learning. Apprentice training tends to be one-on-one. When classroom instruction is done one-on-one, learning dramatically improves. This is called the "two sigma problem" in the educational literature. Ignoring this aspect gives the other factors discussed in TFA exaggerated significance.
Practice is extremely important, and I don't think its importance is exaggerated at all.
I would expect students in an environment with a typically high student-to-teacher ratio, but who actually practice what they're being taught, will significantly outperform students who are taught one-on-one by a personal tutor but rarely actually perform the thing that they're trying to learn.
Obviously, "¿Por Qué No Los Dos?" - doing both is even better. But tutoring isn't obviously superior to practice.
As a personal anecdote (not to replace the above general arguments), I've gotten several hundred hours of one-on-one tutoring in an advanced field of physics from a number of experts, and yet I learned significantly less than I have from significantly fewer hours studying a separate (but no less difficult) field of math when I actually worked the problems.
I would expect students in an environment with a typically high student-to-teacher ratio, but who actually practice what they're being taught, will significantly outperform students who are taught one-on-one by a personal tutor but rarely actually perform the thing that they're trying to learn.
Obviously, "¿Por Qué No Los Dos?" - doing both is even better. But tutoring isn't obviously superior to practice.
As a personal anecdote (not to replace the above general arguments), I've gotten several hundred hours of one-on-one tutoring in an advanced field of physics from a number of experts, and yet I learned significantly less than I have from significantly fewer hours studying a separate (but no less difficult) field of math when I actually worked the problems.
> But tutoring isn't obviously superior to practice.
Good tutoring will essentially be practice and worked problems with instant feedback -- not an individual "lecture".
While there is value to being in the forest entirely alone, I think for a motivated student good tutoring will outperform working problems on your own in speed of overall learning. Both are good though, and I agree working the problems out, and working a lot of problems, is the main thing.
Good tutoring will essentially be practice and worked problems with instant feedback -- not an individual "lecture".
While there is value to being in the forest entirely alone, I think for a motivated student good tutoring will outperform working problems on your own in speed of overall learning. Both are good though, and I agree working the problems out, and working a lot of problems, is the main thing.
> Good tutoring will essentially be practice and worked problems with instant feedback
Yes, but then we're conflating the two things we're trying to separate - one-on-one instruction, and worked practice.
I was using "tutoring" to mean specifically one-on-ones. I completely agree that a good tutor will have you practice what you're learning, and that's definitely much closer to optimal than the educational mess we're currently in.
Yes, but then we're conflating the two things we're trying to separate - one-on-one instruction, and worked practice.
I was using "tutoring" to mean specifically one-on-ones. I completely agree that a good tutor will have you practice what you're learning, and that's definitely much closer to optimal than the educational mess we're currently in.
They are related. They are both individual learning.
One thing I have observed in my own experience (my own, and my, mostly home educated, kids) is that both one to one teaching AND learning on one's own (the amount of it being practice varying with subject) are better than classroom/lecture learning. This is not a statistical sample or a study, but it is three people across multiple subjects, at a pretty full range of levels (from primary school level to postgrad).
Maybe much learning is an individual activity and learning in groups is just ineffective?
One thing I have observed in my own experience (my own, and my, mostly home educated, kids) is that both one to one teaching AND learning on one's own (the amount of it being practice varying with subject) are better than classroom/lecture learning. This is not a statistical sample or a study, but it is three people across multiple subjects, at a pretty full range of levels (from primary school level to postgrad).
Maybe much learning is an individual activity and learning in groups is just ineffective?
> Maybe much learning is an individual activity and learning in groups is just ineffective?
Learning in groups is wildly ineffective from the perspective of gaining functional mastery over some subject (whether writing well, solving algebra problems, etc).
However, it does have a lot of unrelated benefits, arguably more important: learning to collaborate with others, understanding how others think and learn, understanding your own skill level by direct comparison with others, competition as a motivator for learning, and more.
Learning in groups is wildly ineffective from the perspective of gaining functional mastery over some subject (whether writing well, solving algebra problems, etc).
However, it does have a lot of unrelated benefits, arguably more important: learning to collaborate with others, understanding how others think and learn, understanding your own skill level by direct comparison with others, competition as a motivator for learning, and more.
I am not convinced that those are realised in real life.
The joy of learning is a better and more sustainable motivator than competition.
Learning to collaborate with others is an important skill, but I am not sure it is particular often promoted within classroom learning. There are lots of things you can do (sports, hobbies, anything that aims at an end in a group) that are better at teaching collaboration.
Spending less time on learning frees up time for other, IMO better, ways of learning all those skill.s
The joy of learning is a better and more sustainable motivator than competition.
Learning to collaborate with others is an important skill, but I am not sure it is particular often promoted within classroom learning. There are lots of things you can do (sports, hobbies, anything that aims at an end in a group) that are better at teaching collaboration.
Spending less time on learning frees up time for other, IMO better, ways of learning all those skill.s
Learning in groups is not the same as learning in a classroom.
When I was a freshman, we created an impromptu "Calculus Brotherhood", met in 4-6 people and attacked problems together. It worked freakingly well.
When I was a freshman, we created an impromptu "Calculus Brotherhood", met in 4-6 people and attacked problems together. It worked freakingly well.
I would argue that learning in groups is potentially exponentially more effective. There is a lot of individual interactions that go on when people are all learning something at the same time. Tidbits that they each share with one another. And emotion that social interactions evoke is a powerful motivator for mental rewiring.
But I don’t want to dismiss your insights. I’m curious what the difference is that I’ve experienced. Certainly just putting random people together isn’t nearly as beneficial as grouping by ability, or motivation to learn the topic is useful. Maybe that is a necessary requirement for effective group learning?
But I don’t want to dismiss your insights. I’m curious what the difference is that I’ve experienced. Certainly just putting random people together isn’t nearly as beneficial as grouping by ability, or motivation to learn the topic is useful. Maybe that is a necessary requirement for effective group learning?
I have studied in streamed classes (in a school that was very selective anyway) so closely grouped by ability.
I did find working with friends in small groups effective at postgraduate level (although we organised it ourselves) and I would have done better to have done more of that. However this was a small group, not a class.
Classrooms and lecture rooms do not promote interactions. On the other hand one to one tuition is continuous interaction, hopefully with someone who is a better model for interaction that other kids, and who is encourages interaction.
I think we are talking about four different things here. Self teaching, 1:1, small groups, and classrooms. 1:1 and learning oneself are far more effective than classrooms. I cannot compare with small groups, and they are used at some universities (e.g. the tutorial system at Oxford and Cambridge), but my feeling is that it will be highly effective for the right people and the right subject. Then again, those universities require a lot of ability and motivation to get into, so maybe that is why it works for them.
I did find working with friends in small groups effective at postgraduate level (although we organised it ourselves) and I would have done better to have done more of that. However this was a small group, not a class.
Classrooms and lecture rooms do not promote interactions. On the other hand one to one tuition is continuous interaction, hopefully with someone who is a better model for interaction that other kids, and who is encourages interaction.
I think we are talking about four different things here. Self teaching, 1:1, small groups, and classrooms. 1:1 and learning oneself are far more effective than classrooms. I cannot compare with small groups, and they are used at some universities (e.g. the tutorial system at Oxford and Cambridge), but my feeling is that it will be highly effective for the right people and the right subject. Then again, those universities require a lot of ability and motivation to get into, so maybe that is why it works for them.
As a university level educator that also has assistants that learn through practise I must say I find the question: "Is tutoring better than practise?" useless. Better at what? In which field?Thst surely highly depends at what the goal, the subject, the individual students character, the available time and teaching resources are.
That means the question is so context-dependent that any potential answer would only bring insight with that specific context in mind.
That being said, I am a huge fan of practise paired with theory (this is what a good tutor would do). Many people only start to care about theory once they have encountered the problems theory helps with have been encountered in the wild. And getting people to care is one of the first things any educator has to achieve.
There are many who start with the base assumption that theory is worthless, but I'd argue having accurate mental models will greatly improve the speed and quality of the work. Additionally this helps to learn faster, as the question why aomething went wrong in practise can be answered faster and more accurately.
That means the question is so context-dependent that any potential answer would only bring insight with that specific context in mind.
That being said, I am a huge fan of practise paired with theory (this is what a good tutor would do). Many people only start to care about theory once they have encountered the problems theory helps with have been encountered in the wild. And getting people to care is one of the first things any educator has to achieve.
There are many who start with the base assumption that theory is worthless, but I'd argue having accurate mental models will greatly improve the speed and quality of the work. Additionally this helps to learn faster, as the question why aomething went wrong in practise can be answered faster and more accurately.
> I find the question: "Is tutoring better than practise?" useless.
Yes, on further reflection, you're right. My statement was spurred by the claim that practice had "exaggerated significance" in the article relative to practice, which is kind of a hard thing to quantify and argue about.
And I definitely wasn't trying to say that theory isn't important! I love theory - I don't actually like working the problems - and think that it's important, it's just that I've realized that lots of theory is much less effective without practice, even in a highly abstract field like math.
The interplay between abstract (abstract explanation; theory) and concrete (concrete examples in the course of explanation; practice) is fascinating to me.
Based on your experience, do you have any insight for whether, in the course of verbal/written instruction, it's better to start with concrete instances of a concept, and then give the abstract concept itself, or vice versa?
Yes, on further reflection, you're right. My statement was spurred by the claim that practice had "exaggerated significance" in the article relative to practice, which is kind of a hard thing to quantify and argue about.
And I definitely wasn't trying to say that theory isn't important! I love theory - I don't actually like working the problems - and think that it's important, it's just that I've realized that lots of theory is much less effective without practice, even in a highly abstract field like math.
The interplay between abstract (abstract explanation; theory) and concrete (concrete examples in the course of explanation; practice) is fascinating to me.
Based on your experience, do you have any insight for whether, in the course of verbal/written instruction, it's better to start with concrete instances of a concept, and then give the abstract concept itself, or vice versa?
> Based on your experience, do you have any insight for whether, in the course of verbal/written instruction, it's better to start with concrete instances of a concept, and then give the abstract concept itself, or vice versa?
The abstract concept is meaningless without the concrete examples.
It is only mathematicians, who are accustomed to the abstract theorem being the final goal, who get confused about this. It's only possible to consider the "theorem first" approach as reasonable to the extent that you, or the students, already have the requisite concrete foundations to understand it. Which is to say: to the extent that it is not really "new".
The abstract concept is meaningless without the concrete examples.
It is only mathematicians, who are accustomed to the abstract theorem being the final goal, who get confused about this. It's only possible to consider the "theorem first" approach as reasonable to the extent that you, or the students, already have the requisite concrete foundations to understand it. Which is to say: to the extent that it is not really "new".
Well yes and no. If I give people a 16 mm camera, a roll of film and a black sack, the likelyhood they will make a positive learning experience is limited. That means some theory is needed first, especially if you have varying levels of knowledge and confidence within a group.
That doesn't mean theory has to be boring or abstract. It just means some things need explaining and some people profit from having had them explain to them. In some cases this may even be a legal requirement, letting a student use a table saw or a turning machine without explaining the ways in which it may kill them can land you in jail.
That doesn't mean theory has to be boring or abstract. It just means some things need explaining and some people profit from having had them explain to them. In some cases this may even be a legal requirement, letting a student use a table saw or a turning machine without explaining the ways in which it may kill them can land you in jail.
You could say that all words are abstractions, and therefore my statement is false because almost all teaching uses words... obviously this is not what I meant. Some interpretive generosity about where to draw the lines between what counts as abstraction or concretion in a particular context is required.
With that said, I actually think you could teach someone (say, who didn't speak your language) how to use a film camera merely by demonstration. It would take longer than if you could use words, but would be doable.
And I would argue that this kind of operational ability (with no explicit theory) is usually where the bulk of the actual learning goes on, and is usually what we mean when we talk about competence. Sometimes it's shocking the theory that really talented people don't have in a domain... I'm thinking of things like poker, competitive programming, even competitive mathematics. Obviously such people have some sort of theory, but it may be largely implicit, learned almost entirely by doing, and different-looking from the accepted or academic theories of that domain.
With that said, I actually think you could teach someone (say, who didn't speak your language) how to use a film camera merely by demonstration. It would take longer than if you could use words, but would be doable.
And I would argue that this kind of operational ability (with no explicit theory) is usually where the bulk of the actual learning goes on, and is usually what we mean when we talk about competence. Sometimes it's shocking the theory that really talented people don't have in a domain... I'm thinking of things like poker, competitive programming, even competitive mathematics. Obviously such people have some sort of theory, but it may be largely implicit, learned almost entirely by doing, and different-looking from the accepted or academic theories of that domain.
Hmmm, this seems reasonable, but I personally am extremely annoyed when I ask someone "what is thing x?" and they start by saying "let me give you an example" instead of a general description of the thing first.
Is this because I'm starting to think like a mathematician? Or because I'm conflating a deep, theory-first explanation of a concept with a surface-level summary that is then followed by concrete examples? Or something else?
Is this because I'm starting to think like a mathematician? Or because I'm conflating a deep, theory-first explanation of a concept with a surface-level summary that is then followed by concrete examples? Or something else?
An example would be helpful (ironically), but I think it's because you already have fluency in many abstract concepts (rooted in a lifetime of concrete application and examples), and in this situation the abstraction is usually much faster to work with, and you're annoyed because the example is effectively a long-winded explanation.
I'm not saying a mature mathematician is wrong to ask for an abstract definition first. For them, that might work well. But it's wrong to conclude from that experience that the abstraction is somehow more primary, or that it could exist in isolation. They've just forgotten the process that got them there.
I'm not saying a mature mathematician is wrong to ask for an abstract definition first. For them, that might work well. But it's wrong to conclude from that experience that the abstraction is somehow more primary, or that it could exist in isolation. They've just forgotten the process that got them there.
I agree.
It's a constant dance between theory and practice.
Practicing and getting constant feedback is so important (and sadly underrated in school). It still strange to me how we empathise rote learning in school and have the experimentation away from experts (homework).
For example in orbital mechanics it was experimentation that got me to actually understand all the retrograde burns, plane changes and Hohmann transfers, almost exactly like the xkcd comic https://xkcd.com/1356/ (though without the job at NASA part of course)
For example in orbital mechanics it was experimentation that got me to actually understand all the retrograde burns, plane changes and Hohmann transfers, almost exactly like the xkcd comic https://xkcd.com/1356/ (though without the job at NASA part of course)
> getting constant feedback
Concur. However, how many teachers and students are willing to engage in candid critique of the student’s work?
Concur. However, how many teachers and students are willing to engage in candid critique of the student’s work?
This is extremely interesting, because while I'd never heard of the '2 sigma problem' [1] before, one university class I had seems to have been largely modeled on it, but with a very different angle. It was a 'self paced' electrical engineering course where we were given a textbook and free to advance through it at our own pace - kind of farcically, since you needed to complete at least 2 chapters per week to finish by the end of the semester.
Moving forward to the next chapter required, exactly as described in that paper, the completion of a problem set and then a score of at least 90% on a test demonstrating mastery of the previous chapter, sometimes accompanied by also demonstrating that skill in a lab. But far from 1 on 1, this entire class was effectively 0 on infinity. The teaching assistant/proctors that we engaged with were there only to grade your work and provided minimal feedback.
And indeed it was one of the most educational 'classes' I ever took. But I think this challenges the concept that it has anything to do with 1 on 1 attention. But rather the outcome seems practically tautological - a good way to get people to perform to the point of mastery is to require that they perform to the point of mastery. Of course, at scale, all you're really doing is weeding out the people that are unable to achieve mastery. And indeed that class was considered a weed out course.
[1] - https://en.wikipedia.org/wiki/Bloom's_2_sigma_problem
Moving forward to the next chapter required, exactly as described in that paper, the completion of a problem set and then a score of at least 90% on a test demonstrating mastery of the previous chapter, sometimes accompanied by also demonstrating that skill in a lab. But far from 1 on 1, this entire class was effectively 0 on infinity. The teaching assistant/proctors that we engaged with were there only to grade your work and provided minimal feedback.
And indeed it was one of the most educational 'classes' I ever took. But I think this challenges the concept that it has anything to do with 1 on 1 attention. But rather the outcome seems practically tautological - a good way to get people to perform to the point of mastery is to require that they perform to the point of mastery. Of course, at scale, all you're really doing is weeding out the people that are unable to achieve mastery. And indeed that class was considered a weed out course.
[1] - https://en.wikipedia.org/wiki/Bloom's_2_sigma_problem
I had such a self-paced course in the '70s based on the book "Fundamentals of Logic Design" by Charles Roth, Jr. It should be noted that the book was specifically written for self-paced study, and as such acted as a sort of tutor by carefully laying out a sequence of reading short segments, answering short questions about the material, then doing more involved problems. I found this course to be very effective and motivating for me, especially given the undergraduate class sizes.
Wow, care to share your alma mater? That was the exact book we also used - some decades later, 5th edition for my class! Absolutely wonderful book. Wow, what a wave of emotions I got when looking at that book's cover again!
And yeah that course and book gave me a serious love of electrical engineering to the point I even considered swapping majors (it was part of the CS curriculum for us), and in hind sight I rather wish I did, but hey - wisdom to pass onto the kids.
And yeah that course and book gave me a serious love of electrical engineering to the point I even considered swapping majors (it was part of the CS curriculum for us), and in hind sight I rather wish I did, but hey - wisdom to pass onto the kids.
That was at UT Austin, where Dr. Roth was a professor. Another thing about that course - the problems that were given by the TAs for the 90% proficiency checks seemed pretty challenging and weren't in the book. You really had to know your material, yet there were no big surprises.
Haha, it's a small world isn't it? It was EE316k for us, and yeah, sounds like he set the precedent and people carried it on forward perfectly.
Mastery Learning, which Bloom advocates for in the two sigma problem paper, is an alternative to 1 on 1, not a way to achieve it.
What you describe seems to be a very poor implementation of mastery learning. But if the tutor is completely disengaged even 1 on 1 tutoring is unlikely to have good effects.
What you describe seems to be a very poor implementation of mastery learning. But if the tutor is completely disengaged even 1 on 1 tutoring is unlikely to have good effects.
A couple things come to mind reading this. Maybe your professor knew the material was engaging in itself or the textbook was exceptionally well written that any added structure on top was likely to complicate it. The second possibility was that maybe they knew it was a fundamental course that students must engage with anyway.
Regarding the lack of feedback, maybe grade was sufficient. Sometimes enough is best.
I feel like whats most important in teaching is that the teacher has integrity. If you can control the teacher in any way, that loses the dynamic. In fact, his idiosyncratic method might indirectly increased his integrity score, which we subconsciously evaluate on teachers before we allow ourselves to engage.
Regarding the lack of feedback, maybe grade was sufficient. Sometimes enough is best.
I feel like whats most important in teaching is that the teacher has integrity. If you can control the teacher in any way, that loses the dynamic. In fact, his idiosyncratic method might indirectly increased his integrity score, which we subconsciously evaluate on teachers before we allow ourselves to engage.
maybe with AI and things like guided learning from gemini we all can get a 1-1 instructor.
As I understand it, the (medieval?) tutorial system is still used at some universities, notably Oxford and Cambridge.
https://en.wikipedia.org/wiki/Tutorial_system
Much of graduate education in the US seems similar.
https://en.wikipedia.org/wiki/Tutorial_system
Much of graduate education in the US seems similar.
1:1 classroom instruction removes a number of teachers from the labor pool equal to the number of students. Apprenticeships remove only a small fraction of that from the labor pool (because the practitioner spends only part of their time teaching/supervising the apprentice and then makes the apprentice go practice the skill) and partially makes up the lost labor with the labor from the apprentices- apprentices are expected to do actual productive work, not just learn.
> 1:1 classroom instruction removes a number of teachers from the labor pool equal to the number of students.
It does require more teachers, but not 1:1. Students being taught 1:1 learn a lot faster, and can be set work to do unsupervised. From my experience I think less than an hour a seek (sometimes a lot less) of tuition time (plus a bit more for marking, and another few hours of study by the student) is sufficient to cover a subject 1:1 (and it can often me a lot less) for teenagers (specifically for GCSEs - British exams sat in schools at 16).
it does require a significantly higher ratio than classroom teaching usually does, but its a long way from needing 1:1.
It does require more teachers, but not 1:1. Students being taught 1:1 learn a lot faster, and can be set work to do unsupervised. From my experience I think less than an hour a seek (sometimes a lot less) of tuition time (plus a bit more for marking, and another few hours of study by the student) is sufficient to cover a subject 1:1 (and it can often me a lot less) for teenagers (specifically for GCSEs - British exams sat in schools at 16).
it does require a significantly higher ratio than classroom teaching usually does, but its a long way from needing 1:1.
It doesn't have to be a crisis time-wise.
In music you usually have a small amount of one-on-one instruction and then you practice. In tennis you usually have a small number of one-one-lessons and then you practice and play matches.
You could probably do the same for maths. You're given some problems to try to solve and given two hours, then once you've made a serious attempt you get individual tutoring for an hour, then you go back to solving problems and there's a short one-on-one question session at the end, let's say 30 minutes. Then you have a 5 hour study session with 1.5 hours of teacher time, so he can have around three students.
In music you usually have a small amount of one-on-one instruction and then you practice. In tennis you usually have a small number of one-one-lessons and then you practice and play matches.
You could probably do the same for maths. You're given some problems to try to solve and given two hours, then once you've made a serious attempt you get individual tutoring for an hour, then you go back to solving problems and there's a short one-on-one question session at the end, let's say 30 minutes. Then you have a 5 hour study session with 1.5 hours of teacher time, so he can have around three students.
I think another nuance is
apprenticeship is learning by/while doing
the classroom is learning by simulated doing
apprenticeship is learning by/while doing
the classroom is learning by simulated doing
Yeah, while the article makes good arguments about learning by doing and context-rich environments, it probably understates how much of the effectiveness comes down to just personalized guidance
If it wasn't for all the pitfalls and hallucinations (and even then there is probably something to be had already) LLMs would be perfect for this. Limitless customizable one-on-one tutoring. I would have killed for something like it when I was in school, instead the choices were expensive tutor (not an option) or else good luck, hope you pay attention in the back of the 30 student classroom.
Interestingly the Bloom study (1984) that describes the "two sigma problem" looked at three types of learning.
a) Group Instruction: Baseline
b) Mastery Learning, ensuring students master the material before moving on: One sigma improvement (outperform 68% of students in group setting)
c) 1 on 1 Tutoring: Two sigma improvement (outperform 98% of students in group setting)
a) Group Instruction: Baseline
b) Mastery Learning, ensuring students master the material before moving on: One sigma improvement (outperform 68% of students in group setting)
c) 1 on 1 Tutoring: Two sigma improvement (outperform 98% of students in group setting)
Irrelevant. The actual key here is training the exact skills you need to do the job. No classroom instruction can ever replicate that.
The best way to learn how to do something is to do it. There's no substitute.
The best way to learn how to do something is to do it. There's no substitute.
You seem to be suggesting he's writing from a place of not knowing about the benefits of one-on-one learning and the "two sigma problem" when this is something he frequently writes about.
I learned in college that I didn't learn anything until I worked the problem sets.
(It always seemed like I learned it, but when faced with the problem sets I discovered I hadn't learned anything yet.)
It's the same with everything. You can watch a yootoob video on rebuilding a carburetor all day, but you don't know nuttin until you take it apart yourself.
I decided to learn to ride a dirtbike. I took some personal instruction from an expert, and promptly crashed. Again and again and again. Finally, my body figured out how to coordinate the controls.
Can't learn how to double clutch downshift from watching a video, either.
(It always seemed like I learned it, but when faced with the problem sets I discovered I hadn't learned anything yet.)
It's the same with everything. You can watch a yootoob video on rebuilding a carburetor all day, but you don't know nuttin until you take it apart yourself.
I decided to learn to ride a dirtbike. I took some personal instruction from an expert, and promptly crashed. Again and again and again. Finally, my body figured out how to coordinate the controls.
Can't learn how to double clutch downshift from watching a video, either.
Teaching is hard and training courses are often terrible. IMO, lessons need to consist of multiple (usually hierarchical) examples of (1) specific thing to learn, (2) high level motivation for doing this thing, (3) specifically when to do the thing, (4) specific causes and effects between your actions and observations during the process.
I did a snowboarding course once, and it was largely useless because they didn’t actually explain any of the mechanics of how the board actually worked beyond seesawing mostly-sideways down the ultra beginner slope. It wasn’t until I had a chance to experiment that I started actually figuring out anything useful.
I absolutely taught myself how to double-clutch from YouTube and Initial D, though. :D (Plus copious practice, of course.)
I did a snowboarding course once, and it was largely useless because they didn’t actually explain any of the mechanics of how the board actually worked beyond seesawing mostly-sideways down the ultra beginner slope. It wasn’t until I had a chance to experiment that I started actually figuring out anything useful.
I absolutely taught myself how to double-clutch from YouTube and Initial D, though. :D (Plus copious practice, of course.)
I taught myself how to ride a bicycle, but was baffled for a long time how the bike stayed up. I did some very careful observation of what my body was doing to make it work, and finally figured it out. I've had some difficulty transferring that skill to the dirtbike, and spend a fair amount of practice time just doing figure eights.
Another weird thing. I've been using the same text editor for 40 years. I no longer remember what the commands are - but I can still edit files just fine. Sometimes I watch my fingers to see what the command actually is.
Another weird thing. I've been using the same text editor for 40 years. I no longer remember what the commands are - but I can still edit files just fine. Sometimes I watch my fingers to see what the command actually is.
> I no longer remember what the commands are - but I can still edit files just fine. Sometimes I watch my fingers to see what the command actually is.
I learned how to solve the Rubik cube some years ago and I found the same thing. I instinctively know the sequence of steps but I would find it very hard to actually write it down.
I learned how to solve the Rubik cube some years ago and I found the same thing. I instinctively know the sequence of steps but I would find it very hard to actually write it down.
> find it very hard to actually write it down
I think this is called the "assumed knowledge problem".
Source: dev who has LARPed as a technical writer.
I think this is called the "assumed knowledge problem".
Source: dev who has LARPed as a technical writer.
Or “unconscious competence”?
I drive a stick car. Shifting gears happens smoothly without any conscious thought. Not with the dirtbike.
Every time, I have to stop and think through it step by step. My recent rides have all been constantly up and down shifting, in order to get it properly into muscle memory. I was annoyed that my car shifting skills did not transfer.
Every time, I have to stop and think through it step by step. My recent rides have all been constantly up and down shifting, in order to get it properly into muscle memory. I was annoyed that my car shifting skills did not transfer.
NASA Video on how hard it can be to learn to surf
https://m.youtube.com/watch?v=wn5KqWwP6uQ
Basically lots and lots of lots of practice.
https://m.youtube.com/watch?v=wn5KqWwP6uQ
Basically lots and lots of lots of practice.
Not sure if you're being witty, but for the unaware, the channel here is that of Tom Sachs, an extremely successful artist who uses the aesthetics of NASA (among other orgs) in order to sort of capture their essence. This is not from NASA.
I'm a little personally split on Tom Sachs as an artist, as he is constantly riding the line between appropriating the aesthetics of respectable institutions and actually emulating their positive qualities.
I'm a little personally split on Tom Sachs as an artist, as he is constantly riding the line between appropriating the aesthetics of respectable institutions and actually emulating their positive qualities.
Just wanted to point out - because I was curious as to why they would post a video about learning to surf - that this is NOT a NASA video. This is from the channel of someone named "Tom Sachs", who happens to be using the NASA logo as his youtube avatar image.
> These films are required viewing for Tom Sachs' studio. They comprise guides to studio practice and documentation of specific projects and installations. The movies represent aspects of the sculptures that exist in time. These films will enhance your experience with the work and are the prerequisite for any studio visit, employment application, or interview. Most were made in collaboration with Van and Casey Neistat.
> These films are required viewing for Tom Sachs' studio. They comprise guides to studio practice and documentation of specific projects and installations. The movies represent aspects of the sculptures that exist in time. These films will enhance your experience with the work and are the prerequisite for any studio visit, employment application, or interview. Most were made in collaboration with Van and Casey Neistat.
thanks!! I’m was unaware of that.
The video is really good tho, not that that excuses the logo issue :(
The video is really good tho, not that that excuses the logo issue :(
My time on a wakeboard transferred fairly successfully to a snowboard.
Medieval craftsmen often ran what we would consider to be sweatshops, with many young (i.e. child) apprentices banging out work and not receiving much instruction in exchange. We're romanticizing and idealizing a past that was, in realty, often quite exploitative.
There are reasons why we started sending children to schools rather than businesses for basic education. There is also little need to reach back to medieval times when comparatively less exploitative (but still imperfect) apprenticeship systems are alive and well in the trades today.
One-on-one practical instruction related specifically to what you want to do is awesome, but there are a lot of difficulties in incentivizing people to supply such instruction.
There are reasons why we started sending children to schools rather than businesses for basic education. There is also little need to reach back to medieval times when comparatively less exploitative (but still imperfect) apprenticeship systems are alive and well in the trades today.
One-on-one practical instruction related specifically to what you want to do is awesome, but there are a lot of difficulties in incentivizing people to supply such instruction.
Even manufacturing without instructions gives you practice. Also you need only so much instructions per practice, getting instructions won't actually help you get better you also need to do it.
The master very much cares about your quality, because if it doesn't look like his quality nobody will buy it. If the quality goes down to much, there will be complaints to the guilt and he looses its ability to do business.
If you have problems with your master you can look for another one. The good always needed to reject prentices, the bad had nobody showing up. In-fact you were required to stay with multiple masters.
If you complain about them not having an 8-hour day, nobody had that in the middle ages. But tradesman were more of the richer people in a city, maybe behind tradesman.
The master very much cares about your quality, because if it doesn't look like his quality nobody will buy it. If the quality goes down to much, there will be complaints to the guilt and he looses its ability to do business.
If you have problems with your master you can look for another one. The good always needed to reject prentices, the bad had nobody showing up. In-fact you were required to stay with multiple masters.
If you complain about them not having an 8-hour day, nobody had that in the middle ages. But tradesman were more of the richer people in a city, maybe behind tradesman.
In medieval setup, no you could not just look for another master. That is not how the society functioned. There was hierarchy and you had your place in it - bottom.
Also, apprentices duties involved also general housework and pretty much any random thing they told you to do. They would beat you if they thought you do not do what they want and you would be serving literally whole day and that was it. And no it was not whole day of learning. Based on book I read, that frequently involved things wife of the master ordered - they had nothing to do with the trade and that was normal.
With eating, you would wait behind the master while their lunch and tend eat whatever remained.
Also, apprentices duties involved also general housework and pretty much any random thing they told you to do. They would beat you if they thought you do not do what they want and you would be serving literally whole day and that was it. And no it was not whole day of learning. Based on book I read, that frequently involved things wife of the master ordered - they had nothing to do with the trade and that was normal.
With eating, you would wait behind the master while their lunch and tend eat whatever remained.
> They would beat you if they thought you do not do what they want
Again, illegal in England.
> Based on book I read,
Well, if you've read a whole book, I guess that makes you an expert.
Again, illegal in England.
> Based on book I read,
Well, if you've read a whole book, I guess that makes you an expert.
> general housework, wife of the master ordered
Yes you were part of the family for better and for worse. I don't see how that is problematic, you weren't working for a different household, you were just part of this household.
> They would beat you
Sure life sucked back than. There is a reason we are not in the middle ages anymore. I would say that was more a problem with the general attitude in society, not specific to masters.
> no you could not just look for another master
But you were required to look for a different master every few years? That claim doesn't make sense to me.
Of course not everything was all roses, it was just different. You didn't had a social net from the state, there wasn't an independent police you could report beatings from the master. On the other hand you had a social security net by the family/household currently living in (meaning your master's in this case) and if you have rows with everyone you can just walk for a day to the next city, where nobody knows you, and start afresh. The latter isn't possible now anymore.
Yes you were part of the family for better and for worse. I don't see how that is problematic, you weren't working for a different household, you were just part of this household.
> They would beat you
Sure life sucked back than. There is a reason we are not in the middle ages anymore. I would say that was more a problem with the general attitude in society, not specific to masters.
> no you could not just look for another master
But you were required to look for a different master every few years? That claim doesn't make sense to me.
Of course not everything was all roses, it was just different. You didn't had a social net from the state, there wasn't an independent police you could report beatings from the master. On the other hand you had a social security net by the family/household currently living in (meaning your master's in this case) and if you have rows with everyone you can just walk for a day to the next city, where nobody knows you, and start afresh. The latter isn't possible now anymore.
> Yes you were part of the family for better and for worse. I don't see how that is problematic, you weren't working for a different household, you were just part of this household.
No you was not part of the family. And this was not part of the family thing either. It was more of the sweetshop with workers who have no choice thing.
> But you were required to look for a different master every few years? That claim doesn't make sense to me.
You was not given choice to shop around or change up however you wanted. That was not a thing. Occasionally you could be asked to move to different master at predetermined set points. But not always. I do not even see what is nonsensical or hard to understand about such setup.
> you had a social security net by the family/household currently living in (meaning your master's in this case)
Your master was not your security net. You would be kicked off and expected go back to your actual family.
> if you have rows with everyone you can just walk for a day to the next city, where nobody knows you, and start afresh
That was definitely not a thing either. They would vet you and your character with where you came from. There was a lot of suspicion about new people. You would have quite a difficult time to establish yourself or even find a living. Being banished was a punishment for a reason - and other village you go to will be very aware newcomer might be a troublemaker they did not wanted elsewhere.
> The latter isn't possible now anymore.
That is significantly easier now.
No you was not part of the family. And this was not part of the family thing either. It was more of the sweetshop with workers who have no choice thing.
> But you were required to look for a different master every few years? That claim doesn't make sense to me.
You was not given choice to shop around or change up however you wanted. That was not a thing. Occasionally you could be asked to move to different master at predetermined set points. But not always. I do not even see what is nonsensical or hard to understand about such setup.
> you had a social security net by the family/household currently living in (meaning your master's in this case)
Your master was not your security net. You would be kicked off and expected go back to your actual family.
> if you have rows with everyone you can just walk for a day to the next city, where nobody knows you, and start afresh
That was definitely not a thing either. They would vet you and your character with where you came from. There was a lot of suspicion about new people. You would have quite a difficult time to establish yourself or even find a living. Being banished was a punishment for a reason - and other village you go to will be very aware newcomer might be a troublemaker they did not wanted elsewhere.
> The latter isn't possible now anymore.
That is significantly easier now.
> No you was not part of the family. And this was not part of the family thing either. It was more of the sweetshop with workers who have no choice thing.
Name it part of the household then. In a modern sweetshop you get some money (or not) generally too less to pay for food and other things. Nobody cares if you die or just don't show up the next day.
As a prentice, you don't get money, but you also don't buy food and you don't pay for a roof. Your master can not afford for you to not show up or be invalid for work, because he can only afford to house and teach so many prentices. He also can't afford you producing low-quality goods, because the goods get sold in his name.
> You were not given choice to shop around or change up however you wanted.
I think this conflicts with that you were required to have served multiple masters as part of your education. When a prentice shows up to a new master, it means the new master gets an already trained workforce while not having to pay for the expenses of the education. Your old master will not be willing/able to afford that loss, so you need to mess up some money before you get kicked out.
> Your master was not your security net. You would be kicked off
When you become invalid indefinitely, yes. When you get sick for some days, your master will get you back to work as soon as possible.
> expected go back to your actual family.
When you show up broke after years, I bet you get kicked out there also. You have better choices moving to a new city or living off the streets.
> That was definitely not a thing either. They would vet you and your character with where you came from. There was a lot of suspicion about new people. You would have quite a difficult time to establish yourself or even find a living. Being banished was a punishment for a reason - and other village you go to will be very aware newcomer might be a troublemaker they did not wanted elsewhere.
Having an influx of new people from the landscape were how the cities operated. Having more people made the city richer and more powerful. It really depended on how skilled you were. If you can claim to be able to do X and you are able to show it, than you have a good chance to find work. If you don't, then good luck dying in the streets.
> That is significantly easier now.
Being a criminal and trying to flee? Good luck with that in the time of surveillance and world-wide police cooperation. Nowadays you can pretty much only double down on being criminal, be convicted or flee to a third-world country, where you will probably die soon/ have a way lower living standard. In the past you also had the opportunity to just switch jurisdiction and stop being a criminal, while not having a different living standard.
Name it part of the household then. In a modern sweetshop you get some money (or not) generally too less to pay for food and other things. Nobody cares if you die or just don't show up the next day.
As a prentice, you don't get money, but you also don't buy food and you don't pay for a roof. Your master can not afford for you to not show up or be invalid for work, because he can only afford to house and teach so many prentices. He also can't afford you producing low-quality goods, because the goods get sold in his name.
> You were not given choice to shop around or change up however you wanted.
I think this conflicts with that you were required to have served multiple masters as part of your education. When a prentice shows up to a new master, it means the new master gets an already trained workforce while not having to pay for the expenses of the education. Your old master will not be willing/able to afford that loss, so you need to mess up some money before you get kicked out.
> Your master was not your security net. You would be kicked off
When you become invalid indefinitely, yes. When you get sick for some days, your master will get you back to work as soon as possible.
> expected go back to your actual family.
When you show up broke after years, I bet you get kicked out there also. You have better choices moving to a new city or living off the streets.
> That was definitely not a thing either. They would vet you and your character with where you came from. There was a lot of suspicion about new people. You would have quite a difficult time to establish yourself or even find a living. Being banished was a punishment for a reason - and other village you go to will be very aware newcomer might be a troublemaker they did not wanted elsewhere.
Having an influx of new people from the landscape were how the cities operated. Having more people made the city richer and more powerful. It really depended on how skilled you were. If you can claim to be able to do X and you are able to show it, than you have a good chance to find work. If you don't, then good luck dying in the streets.
> That is significantly easier now.
Being a criminal and trying to flee? Good luck with that in the time of surveillance and world-wide police cooperation. Nowadays you can pretty much only double down on being criminal, be convicted or flee to a third-world country, where you will probably die soon/ have a way lower living standard. In the past you also had the opportunity to just switch jurisdiction and stop being a criminal, while not having a different living standard.
All the stuff you wrote is purely imaginary and has nothing to do with how people in medieval times actually behaved. You just made it all up, completely, based on what you want history to be.
In particular, if you was too sick or invalid or whatever, you got kicked off. That is it. No one expected the master to care for you or handle your healthcare. It is true you was not paid and worked for food.
If you produced low quality work, you would get simpler jobs (cleaning, wood chopping) for a but, would not learn and would eventually be kicked off too.
> When you show up broke after years, I bet you get kicked out there also. You have better choices moving to a new city or living off the streets.
Generally, they were unwilling to kick you off family, unless you was disobedient. That would be shameful for them. This was your safety net and related social obligations were actually strong.
You was not better off "living in the streets" of a town (which were significantly smaller).
Like, cities had very real limit of how many people they could accommodate before it became impossible. Newcomer with troublemaking potential was not making it richer nor was welcome.
In particular, if you was too sick or invalid or whatever, you got kicked off. That is it. No one expected the master to care for you or handle your healthcare. It is true you was not paid and worked for food.
If you produced low quality work, you would get simpler jobs (cleaning, wood chopping) for a but, would not learn and would eventually be kicked off too.
> When you show up broke after years, I bet you get kicked out there also. You have better choices moving to a new city or living off the streets.
Generally, they were unwilling to kick you off family, unless you was disobedient. That would be shameful for them. This was your safety net and related social obligations were actually strong.
You was not better off "living in the streets" of a town (which were significantly smaller).
Like, cities had very real limit of how many people they could accommodate before it became impossible. Newcomer with troublemaking potential was not making it richer nor was welcome.
> You just made it all up, completely, based on what you want history to be.
I'm sorry, I'm not yet 500 years old, I have only knowledge based on school and it being portrayed in public media. Do you have sources for your differing knowledge.
> No one expected the master to care for you or handle your healthcare.
Yes nobody is going to sue him. However when one of your prentices vanishes, there will be gossip, that's bad for business. Also I argued that this is bad for the master purely for economic reasons (sunken costs), because feeding someone is not cheap especially in the middle ages.
> It is true you was not paid and worked for food.
Yes and this is not something bad at all. It is just a different economy.
> Generally, they were unwilling to kick you off family, unless you was disobedient.
Yes and your father would claim you were disobedient to your master when you have not learned enough, as he has sent you there. That's why I would earlier that it's kind-of like you are now part of the master's family.
I'm sorry, I'm not yet 500 years old, I have only knowledge based on school and it being portrayed in public media. Do you have sources for your differing knowledge.
> No one expected the master to care for you or handle your healthcare.
Yes nobody is going to sue him. However when one of your prentices vanishes, there will be gossip, that's bad for business. Also I argued that this is bad for the master purely for economic reasons (sunken costs), because feeding someone is not cheap especially in the middle ages.
> It is true you was not paid and worked for food.
Yes and this is not something bad at all. It is just a different economy.
> Generally, they were unwilling to kick you off family, unless you was disobedient.
Yes and your father would claim you were disobedient to your master when you have not learned enough, as he has sent you there. That's why I would earlier that it's kind-of like you are now part of the master's family.
> it being portrayed in public media.
I'm not sure why the media would more accurately depict vampires than a blacksmith.
I'm not sure why the media would more accurately depict vampires than a blacksmith.
Is that sarcastic or what do you want to say? Do you claim the media represents vampires or do you claim it represents blacksmiths?
Public media are entertainment made by artists. They did not study history nor are attempting to paint it accurately. They are trying to create something for for their contemporaries, sorta kinda inspired by history.
Their blacksmiths are as accurate as their vampires as sibling puts it. Which is ok, the rest of us are supposed to realise the difference between a fiction , random tech guy or economist blog and actual history.
Their blacksmiths are as accurate as their vampires as sibling puts it. Which is ok, the rest of us are supposed to realise the difference between a fiction , random tech guy or economist blog and actual history.
In a book having a story and then some pages about the historic context, I would expect the context to be somewhat accurate? I also mean stuff like that researchers are sometimes (I think often) unable to determine whether a picture, a music piece was created by the master or by the prentices. I don't expect public media to lie about that.
It's also about common sense economy and human behaviour. I don't think humans change all that much.
Wars and rivalities between cities and between the nobility-dominated land are part of history classes in school. Can you bring actual arguments why my reasoning is wrong, instead of simply claiming it just didn't happened this way?
It's also about common sense economy and human behaviour. I don't think humans change all that much.
Wars and rivalities between cities and between the nobility-dominated land are part of history classes in school. Can you bring actual arguments why my reasoning is wrong, instead of simply claiming it just didn't happened this way?
The romanticism around apprenticeships misses how tricky it is to scale personalized, practical instruction without either underpaying the instructor or pricing out the learner
Very true, but the benefit to one-on-one instruction is so enormous that we should find ways to apply it fractionally if we can’t apply it fully. One thinks eg of the one-room schoolhouses of the 1800s, with younger students learning from older students.
It's still that way. Germany has an apprenticeship system that is supposed to work just like the medieval system: You work in a company for 2-3 years at low pay, but you get trained in return. (Nowadays you spend some of that time in a trade school). The promise often is that if you do good, the company will hire you as a regular employee afterwards.
Unfortunately, experiences vary. The promise works out for some, but others have a shitty boss that does not teach them anything and makes them do menial jobs that do not require or teach any special skills (e.g. cleaning up the workshop or cooking coffee).
Unfortunately, experiences vary. The promise works out for some, but others have a shitty boss that does not teach them anything and makes them do menial jobs that do not require or teach any special skills (e.g. cleaning up the workshop or cooking coffee).
I've deeply studied the apprentice programs in medieval Europe; your claims don't align with guild law, nor the motivations of the guilds themselves (to create protective but longterm market-satisfying services and goods; i.e. to stay in business and prevent cheap knockoffs, at the cost of inhibiting innovation).
Apprenticeships certainly weren't more abusive than the typical alternatives: serf labor, or servant jobs. (One of the key differences between servants and apprentices in medieval England, for instance, was that you weren't allowed to beat your apprentices.)
Often exploitative? Sure. Most power structures are. But it absolutely was a system that guaranteed rights to the worker, which made it rise far above most employment situations of that time.
Apprenticeships certainly weren't more abusive than the typical alternatives: serf labor, or servant jobs. (One of the key differences between servants and apprentices in medieval England, for instance, was that you weren't allowed to beat your apprentices.)
Often exploitative? Sure. Most power structures are. But it absolutely was a system that guaranteed rights to the worker, which made it rise far above most employment situations of that time.
The author is a good writer, able to expand upon (and illustrate) ideas articulately and convincingly. However, quite a lot of this doesn't quite apply to actual practice in education, particularly in science.
High-school and undergraduate science classes tend to pair lectures with labs. Practical work is very much the focus of those labs, and the lab instructors work closely with students who need help. And a postgraduate degree typically involves a student working side-by-side with a professor on practical work.
As for the pyramid model, I think the author makes some good points, especially for the grade-school level. However, it's simply a fact that being comfortable with adding comes in handy before moving on to multiplying.
Good teachers find ways to motivate students, and adjust those ways as the years flow by. They know how to do their job, and I trust them to find the best practices.
One thing I've heard from many teachers, especially those who are notably effective, is that teaching theorists are not of much help. And I see that in the silly trends that higher-ups impose on teachers. That way of teaching multiplication that has worked for generations? No good -- we must scrap it. The practice of teaching students to write cursive? So quaint - time to toss that in the trash bin. Years later, I see the results of these trends, when students come to university.
The problem of teaching theorists coming up with silly ideas is a result, I fear, of the system of educating educators. How do you get a PhD in a subject? You have to come up with a new idea. Nobody got an advanced graduate degree in education by writing a thesis that said "teaching is fine as it is." No, that PhD student has to say "this is broken, and here's how to fix it." But some things just aren't quite broken, not really. Sure, some adjustments might be helpful. More one-on-one tutoring would be great. Although then, the non-theorist immediately sees a problem: we don't have enough teachers, as it is.
High-school and undergraduate science classes tend to pair lectures with labs. Practical work is very much the focus of those labs, and the lab instructors work closely with students who need help. And a postgraduate degree typically involves a student working side-by-side with a professor on practical work.
As for the pyramid model, I think the author makes some good points, especially for the grade-school level. However, it's simply a fact that being comfortable with adding comes in handy before moving on to multiplying.
Good teachers find ways to motivate students, and adjust those ways as the years flow by. They know how to do their job, and I trust them to find the best practices.
One thing I've heard from many teachers, especially those who are notably effective, is that teaching theorists are not of much help. And I see that in the silly trends that higher-ups impose on teachers. That way of teaching multiplication that has worked for generations? No good -- we must scrap it. The practice of teaching students to write cursive? So quaint - time to toss that in the trash bin. Years later, I see the results of these trends, when students come to university.
The problem of teaching theorists coming up with silly ideas is a result, I fear, of the system of educating educators. How do you get a PhD in a subject? You have to come up with a new idea. Nobody got an advanced graduate degree in education by writing a thesis that said "teaching is fine as it is." No, that PhD student has to say "this is broken, and here's how to fix it." But some things just aren't quite broken, not really. Sure, some adjustments might be helpful. More one-on-one tutoring would be great. Although then, the non-theorist immediately sees a problem: we don't have enough teachers, as it is.
I would wager the benefits of this model come mostly from the 2 sigma boost one gets from one on one instruction and not from any sort of optimal skill tree progression a master would impart on a student in a pedagogical environment engineered for optimal knowledge and skill acquisition.
> a pedagogical environment engineered for optimal knowledge and skill acquisition
I'm not sure how many of those we have available to us. Many are compromised by politics, funding, or the need to act as a daycare.
I learned a lot at the various schools I went to, but the amount I learned seemed to correlate more directly with how invested I was in learning than how well the school was funded. Plenty of schools with better per-pupil funding had significantly worse student achievement rates than where I was.
The only real exception to that is not all schools offer the same curriculum. Back in my day, not every secondary / high school had someone who could teach calculus, though now there's districts that are getting rid of calculus entirely to promote anti-racism. Honestly, I think learning calculus in high school was good for me, even if I've really only needed to calculate integrals once in my programming career.
At University, things were much the same. Undergrad courses focused a bit more on synthesizing than memorizing compared to high school, but not really by much.
All of this is to say that I'm not really sure it's fair to knock the apprentice program since we don't directly experience optimal pedagogy elsewhere.
I'm not sure how many of those we have available to us. Many are compromised by politics, funding, or the need to act as a daycare.
I learned a lot at the various schools I went to, but the amount I learned seemed to correlate more directly with how invested I was in learning than how well the school was funded. Plenty of schools with better per-pupil funding had significantly worse student achievement rates than where I was.
The only real exception to that is not all schools offer the same curriculum. Back in my day, not every secondary / high school had someone who could teach calculus, though now there's districts that are getting rid of calculus entirely to promote anti-racism. Honestly, I think learning calculus in high school was good for me, even if I've really only needed to calculate integrals once in my programming career.
At University, things were much the same. Undergrad courses focused a bit more on synthesizing than memorizing compared to high school, but not really by much.
All of this is to say that I'm not really sure it's fair to knock the apprentice program since we don't directly experience optimal pedagogy elsewhere.
> Undergrad courses focused a bit more on synthesizing than memorizing compared to high school, but not really by much.
Sorry about that. At Caltech, we were never given formulas. Everything was derived from scratch. I never memorized anything (but I found after a while I simply knew all the trig identifies!).
Sorry about that. At Caltech, we were never given formulas. Everything was derived from scratch. I never memorized anything (but I found after a while I simply knew all the trig identifies!).
It's not that bad in theory, but it's true that modern "no homework!", "no boring practice!" etc directions have done a lot of damage during last decades. But it answers quite well to common complaints why we are still learn to solve quadratic function in school although almost nobody uses it later in their lives? It's because quadratic function is a simplest way to lay a foundation to understand a tons of broad theoretical concepts about functions – turning points, zeros, decreasing, increasing, symmetry etc.
I'd generalize this even further. Math, especially higher level math, often turns into a sort of puzzle. And solving quadratic equations is the first step going from learning how to execute basic arithmetic to using it in the process of solving a puzzle.
The fact that these puzzles can then be used to do cool things is almost just a fortunate coincidence.
The fact that these puzzles can then be used to do cool things is almost just a fortunate coincidence.
Apprenticeship is generally for the so-called servile arts. The article completely neglects medieval education in the form of the liberal arts, and specifically the trivium and quadrivium. These are experiencing a minor resurgence in various forms in classical education curricula.
> Classes are divorced from the practical applications of learning. Apprenticeships train in exactly the situation you’d want to apply the skill.
Hmm .... Something like in the movie "The Hunt for Red October", the US Navy wanted:
(1) Start with recordings by US submarines of underwater sounds, and write software to estimate the power spectra using the FFT (Fast Fourier Transform) and the Blackman and Tukey, "The Measurement of Power Spectra".
(2) Given ships at sea and a war, how long would the US submarines last? Start with some WWII analysis of search and encounters by Koopmans and do a Monte-Carlo Markov process, generate many independent sample paths and average.
Gee, how could I do those without my academic courses in analysis and probability? And there are more examples, including the crucial, original core math in my startup.
Hmm .... Something like in the movie "The Hunt for Red October", the US Navy wanted:
(1) Start with recordings by US submarines of underwater sounds, and write software to estimate the power spectra using the FFT (Fast Fourier Transform) and the Blackman and Tukey, "The Measurement of Power Spectra".
(2) Given ships at sea and a war, how long would the US submarines last? Start with some WWII analysis of search and encounters by Koopmans and do a Monte-Carlo Markov process, generate many independent sample paths and average.
Gee, how could I do those without my academic courses in analysis and probability? And there are more examples, including the crucial, original core math in my startup.
Apprenticeship is alive and well across Europe, most famously probably in Germany. The majority of young adults there completes one.
https://en.wikipedia.org/wiki/Apprenticeship_in_Germany
https://en.wikipedia.org/wiki/Apprenticeship_in_Germany
> The majority of young adults there completes one.
Are you sure about this? Your quoted article only has data from >20 years ago. I wouldn't be surprised if nowadays more people study at university than do an apprenticeship
Are you sure about this? Your quoted article only has data from >20 years ago. I wouldn't be surprised if nowadays more people study at university than do an apprenticeship
Combining both is also pretty common in my experience. People frist do an apprenticeship, then, for example because their employment situation changed, they go to university.
There are ways for a apprenticeship to qualifiy one to go for university.
In 2024, according to the "Bundesinstituts für Berufsbildung" 486,700 people started their apprenticeship [0]. In the same period (2024-2025) 490,304 people started their first semester at university/college, according to the "Statistisches Bundesamt" [1].
So you are right, theres more new students than apprentices, but its not by a lot.
[0]: https://www.bibb.de/de/201811.php [1]: https://www.destatis.de/DE/Themen/Gesellschaft-Umwelt/Bildun...
In 2024, according to the "Bundesinstituts für Berufsbildung" 486,700 people started their apprenticeship [0]. In the same period (2024-2025) 490,304 people started their first semester at university/college, according to the "Statistisches Bundesamt" [1].
So you are right, theres more new students than apprentices, but its not by a lot.
[0]: https://www.bibb.de/de/201811.php [1]: https://www.destatis.de/DE/Themen/Gesellschaft-Umwelt/Bildun...
Based on my experience and not hard data: Not most, but still quite a few.
Some jobs more or less require an apprenticeship (carpenter and other handy jobs). Doing an apprenticeship for a job and afterwards going to university also happens a lot
So I don't know what medical education is like in other parts of the world, but in Austria it involves a lot of practice. Doctors spend a lot of time practicing medicine under supervision before they are allowed to practice on their own. Specialists work as "assistant doctors" for a few years before they can open their own specialist practice.
It's not a question of theory or practice; you obviously need both to learn advanced skills.
It's not a question of theory or practice; you obviously need both to learn advanced skills.
You mean, they start practicing before learning the theory, or they learn the theory then start practicing :p
Sorry I got confused by the many meanings of practice :)
People back then just needed to learn one skill, say baking. Then they ply that trade for their lives.
Our economy changes so fast that we need more generalized skills to adapt. If you were apprenticed as a telephone operator, what would you have done? So we learn math, science, communication, etc.
Kids are absolutely right - much of it you will never use to make money. But if you learn how to learn, then that will help make you successful no matter where you go.
Our economy changes so fast that we need more generalized skills to adapt. If you were apprenticed as a telephone operator, what would you have done? So we learn math, science, communication, etc.
Kids are absolutely right - much of it you will never use to make money. But if you learn how to learn, then that will help make you successful no matter where you go.
I feel like this article hits on a good observation but draws the wrong conclusion. Education may have very well come to underemphasize practice. However, I think that a pure learning by doing approach throws the baby out with the bathwater. It's also not what I've observed in my (admittedly limited) experience with apprenticship:
I worked as a field service engineer setting up servers and similar systems for a while. The place I was sent wasn't a union job but many of the workers were from the local union. I was very impressed with the apprentices. They would work half their week at our site and the other half attended training at the union hall. It seemed to work well for everyone: they seemed to learn a lot, the union developed it's next generation, and we effectively got an extra worker for half of every week.
It would be interesting to see a model like (half on the job and half in the classroom) that applied to more professions. E.g. in programming, universities seem to neglect the practice while bootcamps seem to neglect the theory.
I worked as a field service engineer setting up servers and similar systems for a while. The place I was sent wasn't a union job but many of the workers were from the local union. I was very impressed with the apprentices. They would work half their week at our site and the other half attended training at the union hall. It seemed to work well for everyone: they seemed to learn a lot, the union developed it's next generation, and we effectively got an extra worker for half of every week.
It would be interesting to see a model like (half on the job and half in the classroom) that applied to more professions. E.g. in programming, universities seem to neglect the practice while bootcamps seem to neglect the theory.
This really speaks to me.
I teach SwiftUI to people. I've written books and teach classes. The books don't work nearly as well (because many people just read it instead of actually practicing SwiftUI). The classes I teach ("workshops") are extremely hands on, I try to defer my explanations to after the exercise as much as possible. The feedback is often very positive, and I can tell afterwards that people have really grasped stuff. I know I'm just trying to confirm my biases here as well, but to me, there's nothing better than doing stuff first and then analyzing it.
I teach SwiftUI to people. I've written books and teach classes. The books don't work nearly as well (because many people just read it instead of actually practicing SwiftUI). The classes I teach ("workshops") are extremely hands on, I try to defer my explanations to after the exercise as much as possible. The feedback is often very positive, and I can tell afterwards that people have really grasped stuff. I know I'm just trying to confirm my biases here as well, but to me, there's nothing better than doing stuff first and then analyzing it.
Granted I've been out of school for decades. The textbooks were always an accessory to classroom instruction and not intended for stand-alone learning. Math students quickly figured out that the most important thing was doing the problems, the text was essentially a reference, and the classroom was for guidance through the concepts, and for motivation.
Of course the humanities classes were about books, so learning how to study the books themselves was a major part of the practice.
Programming seems to lend itself particularly well to self learning because the computer allows for endless trial-and-error practice.
Of course the humanities classes were about books, so learning how to study the books themselves was a major part of the practice.
Programming seems to lend itself particularly well to self learning because the computer allows for endless trial-and-error practice.
I think I'd prefer overview, exercise, details. You need some kind of mental framework. I guess you don't just dive right in, otherwise you wouldn't be getting good feedback ;)
What I really hate is explaining the solution before explaining the problem. It's a terrible way to teach and it's quite common. I like to say that there are two bad ways to teach: The cookbook (do this, then do that) and the maths textbook (solutions without problems or context). The good way is a combination of them with some additional things that neither of them has, like motivating examples, relevant anecdotes etc.
What I really hate is explaining the solution before explaining the problem. It's a terrible way to teach and it's quite common. I like to say that there are two bad ways to teach: The cookbook (do this, then do that) and the maths textbook (solutions without problems or context). The good way is a combination of them with some additional things that neither of them has, like motivating examples, relevant anecdotes etc.
I think this article shows nicely what we in modern days get wrong about education, even though it's premise is wrong in my opinion. These are just my opinions, and I am not an educator by trade, so take it for what it's worth.
This article starts with the premise that we go to school to learn how to work. In a world where that is the case, yeah, apprenticeships are far better. It happens that many people look at schooling that way, but I don't believe that's even the correct way to think about schooling.
School originally was not about learning to do a job. It was about learning how to learn. That's why writing papers and doing homework used to be such a big deal, because while you might have been stuffing your brain with knowledge about, say the history of bronze-age Europe, what you were really doing was learning how to find facts, how to organize them, and how to take useful notes.
The problem is that in the past 80 years or so, we've started to see school as training to work. Whether it's primary school teaching us to be good factory workers, or college teaching us to be good office workers. College and university came to be viewed as a way for poor children to move up the social ladder. But to do that, you need a good job. And the best way to get that good job is to teach you to do it in university. So you end up in a situation where schools don't teach students how to learn, and since group instruction is a bad way to learn how to do a job, they don't really teach students how to do a job either. And in some countries you pay out the nose for the privilege.
This article starts with the premise that we go to school to learn how to work. In a world where that is the case, yeah, apprenticeships are far better. It happens that many people look at schooling that way, but I don't believe that's even the correct way to think about schooling.
School originally was not about learning to do a job. It was about learning how to learn. That's why writing papers and doing homework used to be such a big deal, because while you might have been stuffing your brain with knowledge about, say the history of bronze-age Europe, what you were really doing was learning how to find facts, how to organize them, and how to take useful notes.
The problem is that in the past 80 years or so, we've started to see school as training to work. Whether it's primary school teaching us to be good factory workers, or college teaching us to be good office workers. College and university came to be viewed as a way for poor children to move up the social ladder. But to do that, you need a good job. And the best way to get that good job is to teach you to do it in university. So you end up in a situation where schools don't teach students how to learn, and since group instruction is a bad way to learn how to do a job, they don't really teach students how to do a job either. And in some countries you pay out the nose for the privilege.
It's just an ad for a series of self-help books.
Exactly. I want a self help apprenticeship
I find it telling that right in the first paragraph it says “People in the middle ages lit cats on fire for fun” as a fact, while it is, in the most charitable interpretation, something historians disagree on (and in the least charitable interpretation, it smells like bullshit from a mile).
I certainly am skeptical of someone taking Wikipedia as the Truth.
I certainly am skeptical of someone taking Wikipedia as the Truth.
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I'm not sure if concerete seeing/doing is the only, or even most effective, way to learn.
I've often learned by recalling the concepts from a lecture, reasoning about the material, and imagining what some of the problems would look like while sketching out solutions in my head. It's not any easier than doing the homework, but it is more convenient and flexible. And it can sometimes help with physical skills.
Theory is still important because it communicates how other people understand what they do. But it's certainly not a replacement for reasoning and experience.
I've found the best model of learning is to... not have a "learning process" in the first place. I try to understand as much as possible from as many angles as possible. This means big concepts, minutae, my ideas, other people's philosophies, imagined scenarios, hands-on-experiences, tangentially related concepts, and so on. Being able to answer questions or do the task is more of a side-effect than the intent.
I've often learned by recalling the concepts from a lecture, reasoning about the material, and imagining what some of the problems would look like while sketching out solutions in my head. It's not any easier than doing the homework, but it is more convenient and flexible. And it can sometimes help with physical skills.
Theory is still important because it communicates how other people understand what they do. But it's certainly not a replacement for reasoning and experience.
I've found the best model of learning is to... not have a "learning process" in the first place. I try to understand as much as possible from as many angles as possible. This means big concepts, minutae, my ideas, other people's philosophies, imagined scenarios, hands-on-experiences, tangentially related concepts, and so on. Being able to answer questions or do the task is more of a side-effect than the intent.
This is a very utilitarian view of learning. Mass education isn't meant just to teach you marketable skills, it's quite explicitly designed to create a shared understanding of the world, a nation. Plus in "medieval" times people also went to church a lot where someone lectured you from a book, with similar goals in mind.
> in "medieval" times people also went to church a lot where someone lectured you from a book,
The idea of church as "someone lecturing you from a book" describes only a few christian denominations, few of which were active/existant in medieval times.
I agree that many churches in the US are "20 minutes singing followed by a 1 hour sermon", which is what you describe, but there are also many denominations where the focus is on the liturgy and the sermon is a side note.
liturgy is basically a spiritual practice you do as a group.
say that week's prayer (from the prayer book)
read the psalm, call-and-response (so the congregation is talking half the time)
say the confession of sins
say the Lords prayer
someone reads 1-2 sections from the bible
a quick sermon
eucharist/communion
The idea of church as "someone lecturing you from a book" describes only a few christian denominations, few of which were active/existant in medieval times.
I agree that many churches in the US are "20 minutes singing followed by a 1 hour sermon", which is what you describe, but there are also many denominations where the focus is on the liturgy and the sermon is a side note.
liturgy is basically a spiritual practice you do as a group.
say that week's prayer (from the prayer book)
read the psalm, call-and-response (so the congregation is talking half the time)
say the confession of sins
say the Lords prayer
someone reads 1-2 sections from the bible
a quick sermon
eucharist/communion
Most parts of the liturgy are teaching. Scripture readings might compare with text book reading; the Lord's Prayer and other formulaic recitations are often taken from Scripture.
The eucharist is more "ritual" than "overt teaching" but it is meant to call to mind one loaf -> one body and the cost of forgiveness.
The earlier poster's point was more "with similar goals in mind" (i.e., "to create a shared understanding of the world, a nation") rather than emphasizing the mechanism (I think). "Marketable skills" is different from social/civic skills/responsibility.
The eucharist is more "ritual" than "overt teaching" but it is meant to call to mind one loaf -> one body and the cost of forgiveness.
The earlier poster's point was more "with similar goals in mind" (i.e., "to create a shared understanding of the world, a nation") rather than emphasizing the mechanism (I think). "Marketable skills" is different from social/civic skills/responsibility.
Which doesn't take away from your main point. A liturgically oriented church does build community.
It seems that the author prefers to ignore the fact that, throughout history, apprenticing has been reserved for the common people, while teaching was reserved for their masters, the rich and the powerful.
Having both is better, but at some point you need to learn the theory.
Having both is better, but at some point you need to learn the theory.
I think even more so apprenticeships were for skilled workers or somewhat "middle-classes". Majority that is farmers well either you worked with your parents or seek employment from someone else in various farming jobs. Sure they trained you to do that, but it was not so much complex jobs but labour.
Much of Europe still has apprenticeship programs for the trades. The loss of this in the US and the UK shows in the quality of work: anyone can claim to be a carpenter, or painter, or whatever: whether or not they have any training.
Fortunately this model is still partially used for some careers like medicine and veterinary practices where you have a mandatory internship of at least a year before you can be admitted as a practicing GP or Vet.
And pilots. Lots of "hours" required for the different grades.
And physicists. Good degree programs involve labs, undergrad, and graduate research.
When you really think of it is doctoral programs in academia apprenticeships? At least in fields where you do need laboratories and such...
That's a good way to think about it, though one still has to ask: "An apprenticeship in what?" Optimally thesis means you're given a nebulous problem within an area of interest and asked to manage a project to solve it and communicate the results. My own field, physics, is particularly loose in terms of what tools you might need to adapt and create.
I've done an apprenticeship in IT and CS, the first two years of it felt more intense than my 4 years of university education. We used to have waves of exams every 6 weeks for the first year. Then on the second, every 8/12. Was crazy but it was thrilling. 16yo me was incredibly happy to have gone to trade school instead of high school.
Wish I practiced programming more than just trying to understand the perfect way to code or theories behind. Such a waste of time :(
FWIW, this is exactly how you learn craftsmanship professions in Germany today. You become a apprentice of a Master for 3 years and learn as you work together, alongside theoretical learning.
> Human beings, it appears, are nearly unique in the animal world for being able to learn something by watching somebody else do it.
This is just blatantly wrong. If nothing else I myself have shown dogs how to solve problems, but here's a link to Wikipedia for good measure.
https://en.wikipedia.org/wiki/Social_learning_in_animals
This is just blatantly wrong. If nothing else I myself have shown dogs how to solve problems, but here's a link to Wikipedia for good measure.
https://en.wikipedia.org/wiki/Social_learning_in_animals
octopuses learn by observing other octopuses
See for yourself
https://www.youtube.com/watch?v=GQwJXvlTWDw
or if you prefer,
https://www.sciencedirect.com/science/article/abs/pii/B97801...
See for yourself
https://www.youtube.com/watch?v=GQwJXvlTWDw
or if you prefer,
https://www.sciencedirect.com/science/article/abs/pii/B97801...
Honestly, it's not worth your time, a lot of presumptions, false premises and incomplete hypothesis. Also, apprenticeship didn't disappear, it's still very much in use in many countries. The focus is just different. Classroom education allows a plethora of secondary skills to be trained without the pressure of performance. For some, it's essential.
compulsory education is a main pillar of the twisted power structure in our society.
power in society comes from a knowledge gap, and powerful people have all the incentives to sustain it. consequently education is a battleground, and we, the honest people, have pretty much lost the battles for about a century now.
the OP only makes sense when also considering this aspect of the question.
power in society comes from a knowledge gap, and powerful people have all the incentives to sustain it. consequently education is a battleground, and we, the honest people, have pretty much lost the battles for about a century now.
the OP only makes sense when also considering this aspect of the question.
School teaches you about things; apprenticeships teach you to do things. Huge difference.
That’s essentially the difference between education and training
He's right, but it has been known for decades that learning by doing is the most efficient way of learning. The reason it is not panacea is because it is hard to measure. A test is easier to administer than reviewing source code to determine whether someone can build web sites well. Learning by doing also requires more freer forms of education, hence it is resisted by Conservative politicians who'd rather have the students learn more discipline (i.e., if you aren't suffering you aren't working hard).
Moreover, a country that emphasizes learning by doing over education focused on test taking will likely score worse on international student assessments, such as PISA. For the simple reason that if students are better at doing their own research, writing reports, etc., they are probably also worse at test taking.
There's too much paranoia and prestige involved in education. It would be better if education was based on the science of education, rather than the whims of politicians, but it's not... it's like the prerogative to control the young generation is too important to let people like "professors in pedagogy" decide. Cause what the fuck do they know? I was a kid once and I learned things in school, kids these days suck, yadda, yadda.
Moreover, a country that emphasizes learning by doing over education focused on test taking will likely score worse on international student assessments, such as PISA. For the simple reason that if students are better at doing their own research, writing reports, etc., they are probably also worse at test taking.
There's too much paranoia and prestige involved in education. It would be better if education was based on the science of education, rather than the whims of politicians, but it's not... it's like the prerogative to control the young generation is too important to let people like "professors in pedagogy" decide. Cause what the fuck do they know? I was a kid once and I learned things in school, kids these days suck, yadda, yadda.
The author constructs a straw man in a simplified universe that is utterly unrealistic and then proceeds to defeat this straw man. Most real teaching is not done as it is described in the text. That is why there is nothing readworthy in it. It is probably a hidden form of marketing to buy the books they are selling.
I like that we talk about practice, and we need to add this to our learning. Even more now, when apprenticeships are a dying practice and everyone is vibe-working.
But dismissing theories, and just saying “most theories are wrong, anyway” smells too strongly of anti-intellectualism, and it just rubs me in the wrong way. I don't like this trend at all.
Theory is as important as practice. The two depend on each other.
But dismissing theories, and just saying “most theories are wrong, anyway” smells too strongly of anti-intellectualism, and it just rubs me in the wrong way. I don't like this trend at all.
Theory is as important as practice. The two depend on each other.
Simply put, the author doesn't know what he's talking about.
This nostalgia for the "good old days" should have a name.
This comparison of "medieval learning" and "modern learning" is tougher than "Wilt Chamberlain" versus "Michael Jordan." The amount of knowledge and usage of high abstractions is incomparable. Imagine what we've learned in the last 500 years, and then forget it all and teach children that. They'll finish school in one year.
If your goal is to create a capable laborer for a specific job that won't change in their lifetime, apprenticeships are the way to go. However, if your goal is to teach a person many abstract ideas not specifically related to a particular job, it won't work.
3. It's a popular idea to teach with real-world examples and learn by doing ("general abstractions" vs. "hyperspecific things," "do and watch" vs. "study"). But how many things that you study in school can you touch or do? If you throw away the last 500 years, then yes, what's left you can definitely touch. For example, the author refers to "economic reasoning." Okay, let's create a real-world example and have the student either do it or watch how someone else does it. Hard, right?
4. We can actually use "real-world examples" and "do and watch" for almost anything students are learning. For example, we could go with the class to a nuclear power plant and 'do and watch' there. There are two issues: many things will not be allowed for students, and it would take years to finish just one year of school. We may call not using it "an embarrassment," but there is a reason for it.
5. "Human beings, it appears, are nearly unique in the animal world for being able to learn something by watching somebody else do it." This is simply not true.
6. "It’s often not so important to understand the reasons why you should do something as it is to see it being performed correctly." We do so much of this in real life unintentionally. Imagine a world where we do it intentionally. What would happen if things changes faster and faster? Who would pay all of these "real-world example" learners during their transition?
7. "Most theories are wrong anyway." You may read this and skip the other parts.
8. He got the pyramid model wrong. Putting a base first doesn't mean learning all of math first, then physics, then chemistry, then biology. A biology base may be about the differences and similarities of animals and plants, and the types of animals.
9. "...this must mean we have an ironclad theory of how scientific knowledge is produced. Except we don’t." Yes, we actually have a scientific method. He probably couldn't "do and watch" it, so it fell out of his sight.
This nostalgia for the "good old days" should have a name.
This comparison of "medieval learning" and "modern learning" is tougher than "Wilt Chamberlain" versus "Michael Jordan." The amount of knowledge and usage of high abstractions is incomparable. Imagine what we've learned in the last 500 years, and then forget it all and teach children that. They'll finish school in one year.
If your goal is to create a capable laborer for a specific job that won't change in their lifetime, apprenticeships are the way to go. However, if your goal is to teach a person many abstract ideas not specifically related to a particular job, it won't work.
3. It's a popular idea to teach with real-world examples and learn by doing ("general abstractions" vs. "hyperspecific things," "do and watch" vs. "study"). But how many things that you study in school can you touch or do? If you throw away the last 500 years, then yes, what's left you can definitely touch. For example, the author refers to "economic reasoning." Okay, let's create a real-world example and have the student either do it or watch how someone else does it. Hard, right?
4. We can actually use "real-world examples" and "do and watch" for almost anything students are learning. For example, we could go with the class to a nuclear power plant and 'do and watch' there. There are two issues: many things will not be allowed for students, and it would take years to finish just one year of school. We may call not using it "an embarrassment," but there is a reason for it.
5. "Human beings, it appears, are nearly unique in the animal world for being able to learn something by watching somebody else do it." This is simply not true.
6. "It’s often not so important to understand the reasons why you should do something as it is to see it being performed correctly." We do so much of this in real life unintentionally. Imagine a world where we do it intentionally. What would happen if things changes faster and faster? Who would pay all of these "real-world example" learners during their transition?
7. "Most theories are wrong anyway." You may read this and skip the other parts.
8. He got the pyramid model wrong. Putting a base first doesn't mean learning all of math first, then physics, then chemistry, then biology. A biology base may be about the differences and similarities of animals and plants, and the types of animals.
9. "...this must mean we have an ironclad theory of how scientific knowledge is produced. Except we don’t." Yes, we actually have a scientific method. He probably couldn't "do and watch" it, so it fell out of his sight.