Not for OP, but for typical discussion: A good way of getting people to understand how lecturing is really only introductory is to consider learning a sport. You can get lectured for hours, days, years on technique and strategy and reading the play and knowing your team mates. But pull on the boots or put a racquet in your hand and you're starting from scratch.
"The criticism of practice (called "drill and kill") and the emphasis on sparking interest is very common. But all evidence, from the lab and studies of professionals, indicate that real competence comes with extensive practice. In denying the critical role of practice one is denying children the very thing they need to achieve real competence. The instructional task is not to "kill" motivation by demanding drill, but to find tasks that provide practice while at the same time sustaining interest"
For me it helps that I enjoy perfecting/varying/repeating.
There could be some element of play in math homework. Play is practice that sparks interest. But what is playful math?
“Here’s a character for Pathfinder. Optimize the shit out of it.”
Some of the math learned in high school can be made more fun and playful with applications such as you mentioned, or with contest math designed for high school students. For a few years now I’ve been involved with the CEMC [1] (at my Alma mater) as a grader for the Euclid math contest which I think is quite fun without requiring anything beyond high school math (doesn’t even require calculus).
According to Mentava their program has 5th graders ready for AP math and middle schoolers ready for college computer science.
20 minutes a day.
It’s just another language. A lot of people see it as esoteric wizardry; the debbil in der math, Bobby!
One plus one
1+1
Same thing, less parchment, less writing stick needed. It’s data compression for an era where Walmart didn’t exist
But not in the way teachers/professors teach it. Quite the contrary
I also studied maths as my major (Algebra, to be more precise). Math is infinitely playful. Trying to weasel your way into a hard problem using various results is fun. (Especially if you don't have a fixed deadline that would turn the play into stress.) It is like sitting in an alien workshop and trying very exotic tools that fit other hands.
If you are more of a visual guy, play around with stuff such as fractals. There, you can visualize the intricate structure on your screen. I will never forget the moment when I saw the Mandelbrot set for the first time. Neither probably did Mandelbrot himself; according to the lore, he expected nothing like that and thought that the computer had an error.
It’s like going after a runner’s high though. It takes work to reach that point where you make connections and feel that neurotransmitter rush.
Neurons aren’t special. Electrical state is all over our bodies. Need to use it to trigger the chemistry that builds muscle not just neurons
When I was a sailing instructor, the first day I would always just take kids out on the boat and have fun with very little learning. That gets them invested, and from then on we can teach the necessary skills even when they're boring--tying knots, memorizing vocab, and learning points of sail and right-of-way rules is not what kids think of when they sign up to learn sailing, but it is necessary.
Of course no 12 year old wants to learn geometry or literature when there's no fun, no purpose beyond "this will be useful for you as an adult I promise". They need to be hooked, and then they can go through boring stuff
As far as I understood it, the main limiting factor in education was teachers deliberately holding back knowledge. The main purpose of "problems", and especially of homework, was a show of social submission, designed to persuade the teachers to reveal the next secret. School one essentially one giant hazing ritual.
There's one memory that stands out as the greatest moment in my education. My school had Acorn Archimedes computers, which came with BBC BASIC, and we were allowed to program them during lunch breaks. One of the older students programmed a Space War clone. I very much wanted to write one myself, but I didn't know how to calculate rotations. The older student refused to tell me the secret, which made perfect sense according to my dominance hierarchy model of education.
I begged my math teacher for the secret, and to my surprise he actually explained how to rotate points using trigonometry. This felt like something incredibly subversive, where the teacher was giving me knowledge I hadn't earned. For this reason I still think of that teacher more favorably than any other, despite other teachers objectively doing more for me. I went on to write a superior Space War clone.
Of all the weird misunderstandings kids have about the world, this might be the weirdest I've ever heard.
I'm kinda fascinated, do you recall at what age you believed this? What was the context you grew up in (country, culture, school). Do you recall where the seed of this idea got planted?
I feel this is the most traditional and natural model of education. It's like medieval guilds, where you had literal secrets that would be revealed only after sufficient demonstration of loyalty.
Then in the actual lecture, the teacher would just have a slide deck with exercises. Students tried solving first, then the teacher showed the correct solution. If you got stuck or didn’t understand, you could immediately ask questions, and those questions would also benefit other students’ understanding.
It is hard to understate how much better this method was for grokking the material than the traditional ‘zoning out during the lecture and struggling with the exercises at home’. I don’t understand why all classes aren’t taught this way.
I’m an external examiner for CS students as a side gig. Now that I’ve been one for 8 years, it’s a relatively easy task for me because I’ve been through their curriculum twice every year. I remember the first time, however, and how I subsequently decided I’d better refresh my own… I’m not sure if learning is the right word here, but my own “what I had been taught in CS”. I did so with edx.orc where I took a few Harvard and MIT courses on CS. What struck me about those courses was just how good the video lectures were for me. I have ADHD and bipolar type 2, and I can honestly say I didn’t really do well with CS lectures when I attended university. But these video lectures were so good, that it honestly taught me the first year of introduction and parts of the later courses in a couple of weeks. Sure… I had the foundation with me, but it also made me wonder if you couldn’t just use these lectures everywhere English speaking. Now, I don’t mean to disrespect my own professors but they were terrible at lecturing by comparison. Which isn’t too weird I guess, I imagine it’s natural for some of the top universities in the world to have some of the best lecturers. In this modern age, we can frankly share these awesome video lectures. Lectures you can pause, rewind a bit, rewatch and so on. All the things I would’ve personally benefited from immensely. Then you could have your local professors do the active learning and so on.
I know it’s not likely to happen, but it should.
Having educators is essential for the health of any society. Educators who constantly revise the material, learn it themselves, and teach it to others. Who themselves become informal or formal teachers. This is one of the ways societies deal with change. The educational requirements change with time and place. The teachers themselves are learning all the time. Some are temporarily bad. Some are permanently bad because of bad job incentives or bad evaluation systems.
Replace all this with centrally produced lectures and your society will seriously deteriorate because of the gaps between what needs to be taught at different places and times and what is taught at those places and times will widen considerably.
Please understand that societies are intricate trees and vines, not machines.
I’m not sure a lot of our educators really fall into the latter category. But even if you’re not corporation for the lecture part, at the very least our own educators could do video lectures and make those available. Maybe that might even make some of them improve their teaching styles. When they get to see themselves teach.
Fix those incentives and you won't have to do any of the things you suggest [1]. Good teachers want to teach well, the same way good musicians is always itching to play good music.
[1] Though more but not all lectures should be recorded.
But I could also easily see this backfiring in certain ways. A couple other things that enabled this to be a positive experience:
1) It was a higher level math elective, everyone in that class chose to be a math major and chose to take that particular elective. This avoids having students who simply don't care, which often ruined similar situations in high school in my experience.
2) It was a relatively small class, I think about 15 students, in a relatively small university. Because it was a small school, I already knew most of the other math majors, and the class had a more personable and trusting atmosphere. Even if you didn't know a person, and thought they were stupid or annoying, you didn't want to burn that bridge because you were almost guaranteed to be in a class with them again later. Because of all this, making a mistake was no big deal, even the shyer less-confident students didn't seem particularly nervous.
3) Class attendance and participation was not graded. This made it very clear that doing the problems was for our benefit, it wasn't busy work.
4) You didn't volunteer, and it wasn't an option to sit out. The professor literally was going person-by-person based on how we were seated, starting from a random person each class. This way it wasn't an oppurtunity for know-it-alls to show off, and less motivated and shy students couldn't just disengage
With a slightly different setup it sounds like torture. But as it was, it kept the class engaged and you could immediately apply what you were learning in lecture to cement it.
That was the hardest math class I ever took (discrete and combinatorial mathematics) because--for scheduling reasons--I'd gotten an exception to take it before I'd met the the prereqs, which meant I was a freshman taking this 3000-level elective in parallel with calc 2 lol. If it was with a worse professor I definitely would have failed, I was not at all prepared. I've taken classes with a completely "flipped classroom" and I just don't have the motivation to do well in classes like that, but I also can't focus enough on lectures with no engagement (at least I couldn't back then before I started ADHD medication)
If you only listen to the lecture, and perhaps re-read the notes, you won't learn much. But that's never how a lecture-based course was meant to work!
In my undergrad, it was made clear to us that the learning happens when you do the worksheets, and the discussions around them in the workshops / exercise classes / tutorials / presentations. But the lectures are still there for a reason.
The history of education is littered with the skulls of the failures of pure "discovery learning", sometimes rebranded as "active learning". And apart from a small elite of people who were going to be top of the class whatever you do (short of Vonnegut-style drastic measures), it does. not. work.
The "traditional" method, practiced properly, contains lots of opportunities for practice (which is, naturally, "active") in some sense. It just recognizes that learners sometimes need to be told what to practice, first.
So I guess I don't fully understand the value of lectures, at least not in maths. If I read up on the material, I can go at my own pace.
Of course, everyone learns differently, so YMMV.
The question is therefore not whether lecturing is useful or where does it fit in the overall learning process, but whether those limited hours of prof/TA time are better spent lecturing vs doing something else (e.g. active learning).
There is a trade off between lecturing and active learning, even if you perfectly understand what lecturing is supposed to do.
Which is not bad, but compared to a more coherent program which inspires and empowers students to get interested in the industry and/or maybe in research would be much much much better.
And yes, of course, obviously, of-fucking-course, every year every every stakeholder in this huge circus parrots about this.
And nothing happens. Credentialism and perverse incentives just continue to rob everyone involved of their passions and joy of learning. (Okay, not everyone, but there's a reason that colleges/universities become "easier" https://www.slowboring.com/p/college-students-should-study-m... )
I think this is a misunderstanding of what "lecturing" is supposed to do. It's supposed to _introduce_ you to the material at a high level. Think of it as of skimming a scientific paper. The actual "learning" is something you do on your own after the lecture (although some lecturers require that you _first_ study the subject and then listen to the lecture), and when doing assignments. IOW, it's not a be all end all, and it shouldn't be treated as the only thing you need to learn the material.