5 ms·

Herbert Simon - "The criticism of practice (called "drill and kill") and the emphasis on sparking interest is very common. But all evidence, from the lab and s

by qp11 2y ago

Herbert Simon - "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"

wumbo 2y ago
As a software engineer, musician, and now taking on martial arts, yes. 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.”
- chongli 2y ago
  Math gets more playful and fun the more you study. The most fun I’ve had with math was when working through difficult proofs in logic, analysis, abstract algebra, and geometry. 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). [1] https://cemc.uwaterloo.ca/contests/contests.html https://cemc.uwaterloo.ca/contests/contests.html
  - nordstreem 2y ago
    Not an endorsement but a criticism of how schools teach math: https://www.mentava.com/ https://www.mentava.com/ 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
  - raverbashing 2y ago
    > Math gets more playful and fun the more you study. But not in the way teachers/professors teach it. Quite the contrary
- inglor_cz 2y ago
  I am programmer, musician (singer), author and I used to do some martial arts when I was younger, though I had approximately 0 talent for them. 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.
  - wumbo 2y ago
    On the visual note, 3Blue1Brown math visualizations are amazing. 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.
- plokiju 2y ago
  to me, programming is playful math. I think I would have enjoyed math a lot more as a kid if we learned programming alongside the traditional math lessons
nordstreem 2y ago
Yeah need that muscle memory and not just the eyeball/ear memory 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
ein0p 2y ago
Yep, and in a lot of fields things only get to the “fun” stage after much perspiration and effort. I’d say nearly all fields that are of practical utility are that way if you’re trying to make a dent in them.
Micanthus 2y ago
But you also need students to be interested to do the practice in the first place. A big problem with modern schooling is they don't usually make a serious effort to convince students to be interested in the first place--apart from the occassional teacher going above and beyond the curriculum. 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
- ein0p 2y ago
  It’s sort of like any other difficult skill in that yes you need to be interested in the skill to make the effort to acquire it, but no you’re not going to be interested in 90% of the work it takes to acquire it, and some perseverance and discipline will be required. Kids need to be at peace with that.
mrob 2y ago
Teachers should explain this point to students. When I was in secondary school, the teachers called the practice tasks "problems". But they obviously already knew the answers, so the problematic nature of the tasks was entirely artificial. The name felt like they were gloating about being permitted to force you to do pointless work. Calling the tasks "exercises" and explaining the analogy to physical exercise would have been much better.
- dvdkon 2y ago
  My teachers never called practice tasks "problems", and I still didn't like doing repetitive tasks like "do 20 long-form divisions". I think students do understand that doing something over and over will make you better at that task, and it doesn't motivate them much.
  - mrob 2y ago
    That's not the mental model I had, and I doubt I'm the only one. I believed knowledge to be something you either had or didn't have. I understood that it was possible to learn things incorrectly, and to forget things (hence the necessity of revision), but I had no appreciation of "fluency" as a concept until I was an adult. 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.

by qp11 2y ago

wumbo 2y ago

As a software engineer, musician, and now taking on martial arts, yes. 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.”

chongli 2y ago
Math gets more playful and fun the more you study. The most fun I’ve had with math was when working through difficult proofs in logic, analysis, abstract algebra, and geometry. 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). [1] https://cemc.uwaterloo.ca/contests/contests.html https://cemc.uwaterloo.ca/contests/contests.html
- nordstreem 2y ago
  Not an endorsement but a criticism of how schools teach math: https://www.mentava.com/ https://www.mentava.com/ 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
- raverbashing 2y ago
  > Math gets more playful and fun the more you study. But not in the way teachers/professors teach it. Quite the contrary
inglor_cz 2y ago
I am programmer, musician (singer), author and I used to do some martial arts when I was younger, though I had approximately 0 talent for them. 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.
- wumbo 2y ago
  On the visual note, 3Blue1Brown math visualizations are amazing. 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.
plokiju 2y ago
to me, programming is playful math. I think I would have enjoyed math a lot more as a kid if we learned programming alongside the traditional math lessons

nordstreem 2y ago

Yeah need that muscle memory and not just the eyeball/ear memory 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

ein0p 2y ago

Yep, and in a lot of fields things only get to the “fun” stage after much perspiration and effort. I’d say nearly all fields that are of practical utility are that way if you’re trying to make a dent in them.

Micanthus 2y ago

But you also need students to be interested to do the practice in the first place. A big problem with modern schooling is they don't usually make a serious effort to convince students to be interested in the first place--apart from the occassional teacher going above and beyond the curriculum. 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

ein0p 2y ago
It’s sort of like any other difficult skill in that yes you need to be interested in the skill to make the effort to acquire it, but no you’re not going to be interested in 90% of the work it takes to acquire it, and some perseverance and discipline will be required. Kids need to be at peace with that.

mrob 2y ago

Teachers should explain this point to students. When I was in secondary school, the teachers called the practice tasks "problems". But they obviously already knew the answers, so the problematic nature of the tasks was entirely artificial. The name felt like they were gloating about being permitted to force you to do pointless work. Calling the tasks "exercises" and explaining the analogy to physical exercise would have been much better.

dvdkon 2y ago
My teachers never called practice tasks "problems", and I still didn't like doing repetitive tasks like "do 20 long-form divisions". I think students do understand that doing something over and over will make you better at that task, and it doesn't motivate them much.
- mrob 2y ago
  That's not the mental model I had, and I doubt I'm the only one. I believed knowledge to be something you either had or didn't have. I understood that it was possible to learn things incorrectly, and to forget things (hence the necessity of revision), but I had no appreciation of "fluency" as a concept until I was an adult. 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.