I kinda took that to the extreme when I was young. Used to loathe anything practical - experiments, programming, applied math etc cuz you know they weren't "pure" and engaging enough. I would also have a hardtime processing/registering something if I'm not able to derive it analytically from first principles. It felt like cheating if I have to use a formula without fully understanding how it was derived haha.
I was the other way around. Only when I found utility in something could I finally grasp the subject properly.
I remember how I was taught derivatives and integrals in HS, I knew how to do them but I was confused as hell. I asked the professor and once explained some uses it all clicked into place.
Same. I really struggle to learn anything which I can't see a practical use for.
Just as an example, in high school learning trigonometry was really difficult for me, like why would I even care about finding an angle in a triangle, etc.?
Only once I studied physics or game dev, this has started to become relevant, and then studying it got SO MUCH easier.
It's mindboggling to me that every teacher doesn't just debut the subject with videogames as a reference.
"Alright everyone, let's make a video game character out of triangles".
"Let's make a little cannon that you can change the angle of. How do you calculate the angle? Funny you should ask.."
"Now let's learn how you'd make the fireball move up and down as it travels. That's a sine wave!"
Every single student understands the basic concept of a game visually, even if they don't play them regularly. It's just a perfect frame of reference and context for applying the concepts in 2D, and then in 3D. And it's so easy to help the students understand how easily those concepts get extrapolated to other things (engineering, sports, whatever).
Totally! One of the first thing I did after learning Newton's law of gravity, was to write down a small simulation of planets in orbit and how they "dance" around each other. This little exercise totally blew my mind and the code was really simple to code.
There's probably an untapped opportunity here, but ed-tech is such a difficult industry.
I'm sure someone actually working in ed-tech will correct me, or perhaps even laugh me out of the room, but I still believe in what I figured out around highschool: that edtech, particularly "educational games", have it all backwards.
Kids aren't stupid. If you take the usual boring curriculum with choreful exercises, and try to "make it more fun" by half-heartedly sprinkling in some colors, characters and cheesy stories, it will backfire spectacularly - kids will see you're just trying to trick them, and not even putting much effort into it.
The right way is the reverse: you need to make something honestly, inherently fun, but design it so that it educates users/players as a side effect. Take Kerbal Space Program: it's not designed to be an educational game, but it's fun, and models real-world physics well enough that you get 12 years old researching and understanding the math of orbital mechanics, all because they'd like to do better than "point roughly half-turn ahead of the Moon and go full throttle", and they'd like to not run out of fuel on the way. Or, look how Minecraft is tricking kids into learning electronics, boolean logic, low-level programming, etc.
(I'd mention Factorio, but I think it's a wash - any gains society gets from the game educating kids are cancelled out by the amount of productivity loss the mere exposure to this game inflicts on software devs.)
(EDIT: or, remember Colobot? A very simple third-person perspective game that had you find and refine resources to build robots, which then you used to kill some big bugs. The twist being, instead of controlling the robots like in a shooter, you had an option to program them in a Java-like DSL, inside the game. It was a great way to organically learn programming. The IP owners later made a "fork" of the game, Ceebot, that was pretty much the same, except it focused on teaching you to program robots instead of having fun exploring and shooting stuff. Predictably, that simple change of focus made the game flop.)
It doesn't even have to be a game: leave a kid in front of Google Earth, and they'll learn geography much faster and much more thoroughly than they would from a globe or a book. Not because the software is better at teaching, but because the kid is just messing around with a virutal model of Earth, and learning stuff along the way.
Etc. Etd.
I think it's a tough sell to adults, particularly parents and educators - that if you want to motivate kids to learn, you need to... stop trying to motivate them to learn. Give them something that's honestly fun, involving or benefiting from real-life knowledge and skills, but actually trying to teach them - and then trust that they'll pick that knowledge up on their own.
They call these kind of games "chocolate covered broccoli" and I totally agree.
I think games, have lots to teach, but that most of the time they are a catalyst for learning or inspiration to learn, but on their own, they will rarely actually teach you. It's hard to put the finger on it, as for example, I'm not a native English speaker, but I learned and practiced most of my English from playing video games, and they were the catalyst to make me WANT to learn English, but they didn't exactly *teach* me English.
Another part of it, is I bet if you sample today's scientists and engineers at places like NASA, you'd probably find that a lot of them loved watching Star Trek/Star Wars as kids. So while sci-fi hasn't taught them how to work with Schrodinger's equation, it probably had a major part of what sparked their motivation to get started. Games probably do that too, and then some, thanks to interactivity.
Thank you! Not only I 100% agree with you, you've also managed to provide a few terms and phrases I've been missing, which could've cut my previous comment down to 1/4 of its size, without loss of meaning. Specifically:
- "chocolate covered broccoli"
- "catalyst for learning"
- "inspiration to learn"
> I learned and practiced most of my English from playing video games, and they were the catalyst to make me WANT to learn English, but they didn't exactly teach* me English.*
English is my second language, and I've also learned most of it from video games. Mostly from exposure, but initially through focused effort - I still vividly remember that time when I was maybe 10 or 12 years old, when I made screenshots from loading screens in Star Trek: Generations, and printed them out on paper, one by one, directly from MS Paint, to take back into my room and meticulously translate the story text on those screens, looking up every single word in an English->Polish dictionary. I also remember keeping that dictionary around when playing Fallout 1. The need to understand the stories and dialogues in games is what bootstrapped my English.
> I bet if you sample today's scientists and engineers at places like NASA, you'd probably find that a lot of them loved watching Star Trek/Star Wars as kids. So while sci-fi hasn't taught them how to work with Schrodinger's equation, it probably had a major part of what sparked their motivation to get started.
I agree. And Star Trek is, in fact, what got me interested in STEM. I owe my entire career and most of who I am as a person, to early exposure to captain Picard and the adventures of Enterprise-D.
(A lot of my early STEM self-education was driven by trying to understand the so-called "technobabble", which - at least in TNG - actually made sense. Probably because, in those days, they had proper scientific advisors.)
> Games probably do that too, and then some, thanks to interactivity.
Yup. I mentioned KSP for a reason - not only have I read the accounts of parents impressed by how much advanced math and physics their 8-12 years old kids can pick up, just for the sake of getting better at the game, but myself I also learned these things for the same reason. While Star Trek is what got me interested in space in the first place, KSP is what got me to finally grok how orbital mechanics and rocketry work in reality. It also made me no longer able to fully enjoy any space travel fiction, except for diamond-hard sci-fi.
I should probably give KSP a try again. I guess there's an initial threshold I got to power through first, as I got a bit exhausted after the first mission hehe.
I'm actually working now on a game of my own, with themes of science, and it's indeed a game-first approach rather than an educational game, but I do hope to maybe inspire some ideas and motivation with at least a few players.
I totally believe there's a lot of untapped potential in this area, and advancing towards cracking learning motivation + capabilities could have a huge impact.
> I should probably give KSP a try again. I guess there's an initial threshold I got to power through first, as I got a bit exhausted after the first mission hehe.
What made all the difference for me was a mod (Kerbal Engineering ...something?) that calculated ∆v for each stage as you were building your rocket. Coupled with a ∆v "subway map" of the game's solar system, this solved the problem of running out of fuel half-way through the mission. I eventually learned how to do the math on my own, but I would've given up long before that happened, if not for this mod. It's been some time since I last played KSP, but I hear that this functionality is now built into the stock game.
Good luck with your game! Give me a shout if and when you need someone to play-test it :).
Back when I studied these videogames were much simpler. I was explained instead calculating areas and volumes for various functions and that was enough for me to get it. The thing is that not everyone was confused and some can take in theory without a practical application. They’re different modes of thinking and I appreciate both, I just happen to fall in the practical group.
In primary and secondary school, I had troubles with math - mostly caused by me not doing homework exercises and generally avoiding work (probably an early indication of an issue that took 20 more years to diagnose...). It all changed when I got interested in gamedev - suddenly, I've caught up with most of the material I was bad at, quickly learned trigonometry beyond the secondary school program, and then some basic vector and matrix algebra - and I distinctly remember it all starting with a simple problem: how to make a sprite rotate and move in circles?
Couple decades later, I still have a kind of theory+applications mindset: I always seek to generalize and abstract, but I feel lost when presented with a new abstraction without any context. Over the years, I realized I learn and understand things most effectively by seeking out answers to the question: why?. Not in the sense of, "what will I ever use this for?", but in the sense of "why was this invented?", "what were the problems people who invented it were trying to solve?". I trace the topic back in time until I find the point where the "why" and "how" are both apparent, and then go forward from there.
I would love to have some sort of statistics on what the proportion of this feeling is. My suspicion is that the practical approach is probably about 90% of the population (who is willing to learn math at all). Would be helpful in trying to figure out how to tune learning programs. (I say this as one who is perfectly content to learn the theory directly and with little-to-no practical motivation, but my impression is I'm very much in the minority on that.)
I was going to say that the curriculum is tuned in favor of those who can just learn by theory, but then I realized that's not even true. It's tuned in favor of those who will simply swallow it without any idea what it is for; it is neither contextualized in terms of what it is practically good for, nor is it contextualized in terms of theory. It's just... there.
I’d be curious to see that as well. I loved math until it became too abstract for me to grasp so I lost interest in it. And that worked pretty well as a self selection for the field, well, a large part of it. I wouldn’t want to be in the academia anyways…
> I really struggle to learn anything which I can't see a practical use for.
That's a close-minded, ignorant world view. Much of the world's most important advancements were made before any practical use could be seen. Why do you think that way?
> Much of the world's most important advancements were made before any practical use could be seen.
In a sense, yes. But usually this was kind of accidental - as in, people making those breakthroughs weren't doing it because they loved manipulating abstract symbols, or believed that someone, somewhen will find it useful; rather, they had some immediate-term reason for doing the work - a problem to solve, a person to impress, or just doing it for shits and giggles - and only later it turned out their work was the key to something transformative.
I have a similar "mental make" as GP too. Over the years I realized that for me, it's not about practical use to me - it's about knowing why something was invented, what problems the inventors were trying to solve. Learning the historical motivation "grounds" the concept for me, and makes it much easier to understand.
It's just the way my mind works and motivated. Motivation is a very elusive feeling that I did not find easy ways to manipulate.
It's not as if I'm totally blocked from learning stuff with no clear purpose, but it will require much more mental capacity that is often difficult to muster in the day-to-day routine.
Another example, is I did try to learn what I perceive as totally theoretical math such as "prove that there are infinite primary numbers" which was a nice idea to entertain, but it didn't really make me want to dig in further.
On the other hand, learning about linear algebra in the context of machine learning, suddenly got Linear Algebra a lot more interesting and easy to learn.
Makes sense. Somewhat related --- I find procrastination to be a very similar feeling. I know what I should do, but I feel compelled not to do it, for whatever reason.
I think procrastination and what you are describing are slightly different, though, because procrastination stems from stress and emotions for me, whereas with what you describe, it doesn't sound like you have to be stressed to experience it.
You are shadowboxing - fighting an argument nobody is making. Someone is describing their personal experience of the world, not arguing that this is the best way to think about the world. It's an opportunity to learn about the ways that people learn things differently, if you can be curious and kind about it.
Same. I studied derivatives and integrals twice. First time in HS, and it was just a bunch of random rules I had to learn by heart to be able to do these calculations that were required to pass the tests.
Second time was during the first year at university. Here the professor explained that derivatives are needed to calculate the speed with which something changes. Since we were studying economics, interest rates and growth rates made great intuitive examples. Or that integrals permit us to calculate the area under a graph, thus making it possible to calculate for ex the total expected value of something over time. When I saw the utility out of this mathematical tools, studying how to apply them became of great interest!
Same. There's an infinite things to learn, if you can't argue for the usefulness of any piece of information and if that use isn't related to my own goals I will stop you from communicating said information
Same here. A lot of concepts seemed didn't matter if cannot be reflected in real world. That has changed for me though. Abstract things and first principle, zero knowledge actually quite interesting to me now.
Congrats. I’ve made some progress on the abstract axis but still with some faint endgoal to make some progress in the practical realm I feel more grounded in.
I think the parent comment + yours (and others off parent) provides a perfect encapsulation of one of the dimensions of teaching / learning: what's often referred to as "style"*. One way to summarize, specifically, might be something like "inductive" vs. "deductive".
As my experience has ... accumulated ... through the decades, I've come to feel that these sorts of differences / preferences likely don't have much impact on ultimate (potential) "level"**. And, I think you see this and related notions of "what mathematics 'actually is'" echoed (in a very fractal-like way, +1 to the universe in achieving a consistency we'll never rival) across the development of individual mathematicians as well as through the history of mathematics [1-6].
These distinctions are important in "pedagogy" - can be very helpful for teachers and students to be aware of and work at, especially at the more "basic" levels. This can make a massive difference in how an individual's arc unfolds - with extremes of "F this subject" vs. "I'm willing to accept low pay in exchange for torturing myself with this material for the rest of my life!" But, aside from trying to be mindful of the differences - and all involved, ideally, trying to USE awareness of knowledge and "EQ" and all of that in making the mutual learning enterprise work for everyone involved, many other aspects of the differences can just be outlets for time-wasting if focused on IMO (/ experience).
* AFAIK, not really my field though and it has been ~15 years since I did any significant reading / study in the area - for the sake of 'full disclosure'
** The effects end up more in details of notes, problems and areas people are drawn to more or less, etc.
[2] Polya's "How to Solve It", in particular, I think of (from the intro): "The title of the very short second part is 'How to Solve It.' It is written in dialogue; a somewhat idealized teacher answers short questions of a somewhat idealized student.") - many options for accessing / buying, but, for this text, it's in the (unfortunately images) here - https://math.hawaii.edu/home/pdf/putnam/PolyaHowToSolveIt.pd...
> I would also have a hardtime processing/registering something if I'm not able to derive it analytically from first principles.
I still find it easier to understand something if I understand it from the ground up instead of in an ad-hoc way. For example, I found it easier to reason about probability once I had seen a rigorous definition for what a probability distribution is. I guess the reason is that it gives me a way to sanity check my intuition.
I still struggle with the fact that in software development, you get hundreds of technologies thrown at you and you barely have any time to understand them all fully. It makes me sometimes feel not very confident in what I do. I feel that I could understand e.g. Kubernetes better, if I had real in-depth (not just superficial) knowledge about networking. A lot of the time I'm just missing crucial information like "what problem are we trying to solve?", "why does this technology work the way it works?", etc. Something like Kafka is another example.
I had a hardtime remembering if I didn't understand.
But I tried an experiment at uni (once...) to learn a subject solely by rote. I could typically recall about 7 out of 10 items. I was astonished I could do it at all.
Unfortunately, I lost all my usual strengths in that subject: unable to generalize, unable to justify, unable to adapt.
Re: software technologies: non-leaky abstractions are the way to understand without details. Algebras are a great example: arithmetic, concatenation, boolean, Kleene, relational. Although they still leak (overflow, PCRE, etc), an idealized core plus ad-hoc crap beats all-crap. jq has an algebra of , and | operators (though it doesn't call it that)
\aside git: I wonder if git internals can be interpreted as an algebra (absent in UI)? TBF I tried to design a programming language around git internal operations (tree navigation and construction), but it was tedious to use. Maybe something analogous to a declarative SQL over relational algbra would solve this?
> I would also have a hard time processing/registering something if I'm not able to derive it analytically from first principles.
This really resonates with me. I always had a really hard time with anything where I just had to memorize formulas, but I didn't have any issues if I could derive it myself. For this reason I actually struggled a lot more with algebra in HS than I did with calculus in college. I don't know if it's just the teachers I had growing up or if it's a more broad issue with how the curriculum is structured, but I didn't even realize you could derive things from first principles until I took calculus in college.
Yep kinda like that. I call it Answer guided monkeying around :) I try and see if I can arrive at the answer using Monte Carlo simulations and then try to work around that. Often times they give valuable insights and help uncover symmetries etc that aren’t obvious.
...Used to loathe anything practical - experiments, programming, applied math etc cuz you know they weren't "pure" and engaging enough. I would also have a hardtime processing/registering something if I'm not able to derive it analytically from first principles. It felt like cheating if I have to use a formula without fully understanding how it was derived...
Hello, 'undergraduate me'.
"haha" indeed. The universe is still experiencing California-splitting [1], planet-slapping [2] spasms of laughter at my ... stupidity [3] (speaking only for myself, here, of course).
Exactly my experience! Can tell you how often I was on the brink of failing school/college because I wanted to derive as much as I could from first principles - under time pressure in an exam! I did myself no favors.
I now find I learn better by being the opposite - finding a problem to solve and using math as a tool.
I kinda took that to the extreme when I was young. Used to loathe anything practical - experiments, programming, applied math etc cuz you know they weren't "pure" and engaging enough. I would also have a hardtime processing/registering something if I'm not able to derive it analytically from first principles. It felt like cheating if I have to use a formula without fully understanding how it was derived haha.