7 ms·

I'm a firm believer that resources which raise the bar for math and computing education are huge catalysts for innovation. The fact that resources like BetterEx

I'm a firm believer that resources which raise the bar for math and computing education are huge catalysts for innovation. The fact that resources like BetterExplained, Paul's Math Notes, 3Blue1Brown's YouTube Channel, Ben Eater's YouTube channel, and the entire body of high quality MOOCs are just available for free over the Internet is probably one of my favorite accomplishments of the human race in the 21st century. While researchers, inventors, startup founders, and all other types of entrepreneurs are pushing the envelope on what's possible, there are literally thousands of creators and educators who are doing their best to bring some of that knowledge to the common man. My own experience with academia has lead me to believe that there problems that are truly difficult and complex, but there are also problems which are described as difficult because so many people were exposed to the topic through a resource (typically another person) who had little experience (or interest) in effectively teaching the subject.

parksy 6y ago
Definitely agree - I struggled beyond basic integration in High School, and my "why" and "what is it" type questions about calculus were met with annoyed "read the book" replies and young me lost interest in higher maths at a time when my mind was more plastic. As an adult having these personalities enthusiastically breaking down the fundamentals and using analogies to help cement the concepts intuitively has been a taste of what I imagine having a brilliant and engaging math professor would be like.
- jhoechtl 6y ago
  For me it clicked once it understood that integration is the area "beyond" the "curve".
Barrin92 6y ago
It's a good goal from just a humanistic standpoint and because learning should be recreational but from an innovation standpoint it's honestly likely overrated. Innovation is the result of very particular institutions and resources being coordinated and people networking and clustering tightly, which is why, despite incredibly dispersion of knowledge over the internet, innovation and VC money actually still is so geographically concentrated. I think these online learning resources are good but the expectations should be correct, they're not tools to kickstart innovation, which is much more tacit and reliant on close interaction between people rather than knowledge.
- mathnmusic 6y ago
  Internet has some amazing learning resources these days. Not just articles like these and videos, but also interactive explorables. Even my 7yo was able to understand basic aspects of game theory and complex systems with the help of explorables made by NickyCase, MeltingAsphalt etc. Most recently, I taught myself to not just solve 4x4 Rubik's cube but understand its connections to ideas in abstract algebra such as commutators. I feel extreme gratitude for all the people who create such enlightening material and offer it freely, without asking for a paid subscription to their Udemy course. It inspired me enough that I started creating a DMOZ-style catalog of learning resources as a FOSS project: https://github.com/learn-awesome/learn https://github.com/learn-awesome/learn
sinfulprogeny 6y ago
I wholeheartedly agree on the point about decentralizing and modernizing education, and thank you for reminding me of this. We still have a massive bias towards academic institutions to work against, but the fact that knowledge is so easily accessible, and of such a high quality, is pretty amazing.
- enriquto 6y ago
  Why do you think academic institutions are something to work against to? I'm in academia and here everybody is enthralled and really happy about the explosion of high-quality, freely available learning resources. The only kind of complain that I have ever heard (and very rarely so) is because some of this material is supported by videos in a platform with shitty terms of service.
  - ai_ja_nai 6y ago
    it's the bias that has to be worked against, not the institution
    - enriquto 6y ago
      But who has that bias? Is it you? People in academia certainly not. It would be absurd. As if medical doctors and nurses would be against the education of the population for lifesaving techniques and for healthy eating.
      - tauist 6y ago
        > medical doctors > healthy eating Wrong example, lol
DoreenMichele 6y ago
because so many people were exposed to the topic through a resource (typically another person) who had little experience (or interest) in effectively teaching the subject. I used to homeschool and one of my sons had terrible baggage about math by the time I pulled him out of public school when he was 11. And somewhere along the way, I learned that a lot of elementary school teachers are women who weren't doing well in math and got encouraged to go become an elementary school teacher because, basically, sexism is alive and well and the world goes "Oh, I know what a woman who can't cut it in college is qualified for: Dealing with small kids all day!" So a lot of elementary school teachers are women who suck at math and were also never told 'Get over it and get a degree you want.' Instead, they were told 'Oh, go teach kiddies. That's what you are qualified for.' And I know this is a gender difference in terms of the world treating men and women differently -- a social difference, not a biological one -- because I'm a woman who is good at math (or was at one time) and was married to a man who was terrible at it. No one ever told him (a career soldier) "Oh, go become an elementary school teacher!" Instead, he got his wife to tutor him in college math even though he found it so difficult he threw his pencil across the room one day when I showed him the right way to do it and then I told him "You can be nice or go find another tutor."
- tails4e 6y ago
  I agree in general its an issue when basics are being thought by any person who does not really understand what they are teaching. They end up tecaching the rote method and not the intuition. Happens all the time in maths.
  - DoreenMichele 6y ago
    I think the larger issue here is that a lot of elementary school teachers are people who have a math phobia because their difficulties with math derailed their career dreams. So they not only are bad at teaching it, the primary thing they teach their students is that "Math is scary stuff and something to be feared." And they teach it to really young kids who are very impressionable and don't have some means to avoid being brainwashed into believing it. My one and only goal with homeschooling my son was to get him past the math phobia he had developed and teach him "Math is your friend." He's genuinely bad with numbers, but he no longer has a math phobia and has a better grasp of the concepts than a lot of people, even though he can't calculate anything in his head and routinely asks me or his brother to calculate it for him. A math phobia is crippling and many people never get over it.
ganafagol 6y ago
I'm split on this. On one hand I appreciate these kinds of posts because they bring math with intuition to broader masses. On the other hand, it makes people believe that they have understood what's there to understand and move on. In a sense, they contribute to the Dunning-Kruger effect. The article illustrates this quite well. The intuition is presented well, but is no substitute for actually learning math. The first two questions in the end: > Why is one function reversed? > Why is convolution commutative? With having studied math "properly", it's immediately obvious that they are answers to each other. Defining it with the "reversal" on one function is what makes the operation commutative by introducing a somewhat hidden symmetry and that's a quite common trick in mathematics. The other two questions are also quite clear with some actual math background. Not M.Sc. level math, just some proper calculus. You just need to sit down and do the math, which can take half a page of pen-on-paper. That's what math is, you need to work it. Again, don't get me wrong, I appreciate the effort. But those types of posts don't make you more fluid in math than reading a popular science article about Alpha Centauri makes you an astronomer or an expose about Covid-19 makes you an epidemioloist. It's popular science and can't replace the actual study of the subject.
Konohamaru 6y ago
> and the entire body of high quality MOOCs are just available __for free__ over the Internet nobody alerted me to these

parksy 6y ago

Definitely agree - I struggled beyond basic integration in High School, and my "why" and "what is it" type questions about calculus were met with annoyed "read the book" replies and young me lost interest in higher maths at a time when my mind was more plastic. As an adult having these personalities enthusiastically breaking down the fundamentals and using analogies to help cement the concepts intuitively has been a taste of what I imagine having a brilliant and engaging math professor would be like.

jhoechtl 6y ago
For me it clicked once it understood that integration is the area "beyond" the "curve".

Barrin92 6y ago

It's a good goal from just a humanistic standpoint and because learning should be recreational but from an innovation standpoint it's honestly likely overrated. Innovation is the result of very particular institutions and resources being coordinated and people networking and clustering tightly, which is why, despite incredibly dispersion of knowledge over the internet, innovation and VC money actually still is so geographically concentrated. I think these online learning resources are good but the expectations should be correct, they're not tools to kickstart innovation, which is much more tacit and reliant on close interaction between people rather than knowledge.

mathnmusic 6y ago
Internet has some amazing learning resources these days. Not just articles like these and videos, but also interactive explorables. Even my 7yo was able to understand basic aspects of game theory and complex systems with the help of explorables made by NickyCase, MeltingAsphalt etc. Most recently, I taught myself to not just solve 4x4 Rubik's cube but understand its connections to ideas in abstract algebra such as commutators. I feel extreme gratitude for all the people who create such enlightening material and offer it freely, without asking for a paid subscription to their Udemy course. It inspired me enough that I started creating a DMOZ-style catalog of learning resources as a FOSS project: https://github.com/learn-awesome/learn https://github.com/learn-awesome/learn

sinfulprogeny 6y ago

I wholeheartedly agree on the point about decentralizing and modernizing education, and thank you for reminding me of this. We still have a massive bias towards academic institutions to work against, but the fact that knowledge is so easily accessible, and of such a high quality, is pretty amazing.

enriquto 6y ago
Why do you think academic institutions are something to work against to? I'm in academia and here everybody is enthralled and really happy about the explosion of high-quality, freely available learning resources. The only kind of complain that I have ever heard (and very rarely so) is because some of this material is supported by videos in a platform with shitty terms of service.
- ai_ja_nai 6y ago
  it's the bias that has to be worked against, not the institution
  - enriquto 6y ago
    But who has that bias? Is it you? People in academia certainly not. It would be absurd. As if medical doctors and nurses would be against the education of the population for lifesaving techniques and for healthy eating.
    - tauist 6y ago
      > medical doctors > healthy eating Wrong example, lol

DoreenMichele 6y ago

because so many people were exposed to the topic through a resource (typically another person) who had little experience (or interest) in effectively teaching the subject. I used to homeschool and one of my sons had terrible baggage about math by the time I pulled him out of public school when he was 11. And somewhere along the way, I learned that a lot of elementary school teachers are women who weren't doing well in math and got encouraged to go become an elementary school teacher because, basically, sexism is alive and well and the world goes "Oh, I know what a woman who can't cut it in college is qualified for: Dealing with small kids all day!" So a lot of elementary school teachers are women who suck at math and were also never told 'Get over it and get a degree you want.' Instead, they were told 'Oh, go teach kiddies. That's what you are qualified for.' And I know this is a gender difference in terms of the world treating men and women differently -- a social difference, not a biological one -- because I'm a woman who is good at math (or was at one time) and was married to a man who was terrible at it. No one ever told him (a career soldier) "Oh, go become an elementary school teacher!" Instead, he got his wife to tutor him in college math even though he found it so difficult he threw his pencil across the room one day when I showed him the right way to do it and then I told him "You can be nice or go find another tutor."

tails4e 6y ago
I agree in general its an issue when basics are being thought by any person who does not really understand what they are teaching. They end up tecaching the rote method and not the intuition. Happens all the time in maths.
- DoreenMichele 6y ago
  I think the larger issue here is that a lot of elementary school teachers are people who have a math phobia because their difficulties with math derailed their career dreams. So they not only are bad at teaching it, the primary thing they teach their students is that "Math is scary stuff and something to be feared." And they teach it to really young kids who are very impressionable and don't have some means to avoid being brainwashed into believing it. My one and only goal with homeschooling my son was to get him past the math phobia he had developed and teach him "Math is your friend." He's genuinely bad with numbers, but he no longer has a math phobia and has a better grasp of the concepts than a lot of people, even though he can't calculate anything in his head and routinely asks me or his brother to calculate it for him. A math phobia is crippling and many people never get over it.

ganafagol 6y ago

I'm split on this. On one hand I appreciate these kinds of posts because they bring math with intuition to broader masses. On the other hand, it makes people believe that they have understood what's there to understand and move on. In a sense, they contribute to the Dunning-Kruger effect. The article illustrates this quite well. The intuition is presented well, but is no substitute for actually learning math. The first two questions in the end: > Why is one function reversed? > Why is convolution commutative? With having studied math "properly", it's immediately obvious that they are answers to each other. Defining it with the "reversal" on one function is what makes the operation commutative by introducing a somewhat hidden symmetry and that's a quite common trick in mathematics. The other two questions are also quite clear with some actual math background. Not M.Sc. level math, just some proper calculus. You just need to sit down and do the math, which can take half a page of pen-on-paper. That's what math is, you need to work it. Again, don't get me wrong, I appreciate the effort. But those types of posts don't make you more fluid in math than reading a popular science article about Alpha Centauri makes you an astronomer or an expose about Covid-19 makes you an epidemioloist. It's popular science and can't replace the actual study of the subject.

Konohamaru 6y ago

> and the entire body of high quality MOOCs are just available __for free__ over the Internet nobody alerted me to these