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It's actually not about beauty of the math, it's about something which is nowadays called a number sense. It takes a lot of practice to develop an understanding

It's actually not about beauty of the math, it's about something which is nowadays called a number sense. It takes a lot of practice to develop an understanding what these things called numbers are, how these relate to each other, what happens if you combine these with operational signs, how numbers grow and shrink etc. And you are damn right that there is no any use to explain it to the 12 year olds. Or even to 16 year olds.

Izkata 2y ago
Common Core was an attempt at teaching this directly. It gets so much ridicule because so few people have good enough number sense to recognize what they're seeing when shown a demonstration. Of course, since they didn't understand it, it then led to bad examples being created and shared, which just made it worse...
- SkyBelow 2y ago
  It was more than that. It didn't explain the goals well enough to parents, and many teachers didn't have the number sense themselves leading to many of the examples are passed around showing how the whole process is broken. There is also a question of if even works well, as it is somewhat akin to teaching someone the shortcut on how to do something before they have mastered the long way of doing it. Many experts in their fields have shortcuts, but they don't teach them directly to juniors in the field as there is value in learning how to do it the long hard way, as often times shortcuts are limited and only an understanding of the full process provides the knowledge of when best to apply different shortcuts.
  - obscurette 2y ago
    > There is also a question of if even works well ... No, it doesn't. And that's one of the main tragedies in modern discussion about education. A lot of people think that we have to teach the way how experts think. But it doesn't work. Take a look at programming for example. Everything you ever really need to know about programming, can be described in single A4 probably. But it has no any use if you learn. It even makes things worse, because it's a thing you have to pay attention to, but you don't really understand. You have to learn via small babysteps, automate a lot of small things in your brain, practice a lot etc. There is no shortcuts in learning.

Izkata 2y ago

Common Core was an attempt at teaching this directly. It gets so much ridicule because so few people have good enough number sense to recognize what they're seeing when shown a demonstration. Of course, since they didn't understand it, it then led to bad examples being created and shared, which just made it worse...

SkyBelow 2y ago
It was more than that. It didn't explain the goals well enough to parents, and many teachers didn't have the number sense themselves leading to many of the examples are passed around showing how the whole process is broken. There is also a question of if even works well, as it is somewhat akin to teaching someone the shortcut on how to do something before they have mastered the long way of doing it. Many experts in their fields have shortcuts, but they don't teach them directly to juniors in the field as there is value in learning how to do it the long hard way, as often times shortcuts are limited and only an understanding of the full process provides the knowledge of when best to apply different shortcuts.
- obscurette 2y ago
  > There is also a question of if even works well ... No, it doesn't. And that's one of the main tragedies in modern discussion about education. A lot of people think that we have to teach the way how experts think. But it doesn't work. Take a look at programming for example. Everything you ever really need to know about programming, can be described in single A4 probably. But it has no any use if you learn. It even makes things worse, because it's a thing you have to pay attention to, but you don't really understand. You have to learn via small babysteps, automate a lot of small things in your brain, practice a lot etc. There is no shortcuts in learning.