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The formal language of math is intensely optimized for rapidly communicating with yourself 90 seconds in the future, when doing a proof or calculation, turning

The formal language of math is intensely optimized for rapidly communicating with yourself 90 seconds in the future, when doing a proof or calculation, turning paper into working memory. It does seem silly to use the same language for communicating with others across unkniwn but deep chasms of context. Its remarkable that it works at all

lazystar 1y ago
its silly. itd be like introducing first year programming students to advanced maps/filters/anonymous function syntax, instead of the easier to understand for loops and if/else statements. math's "no true scottsman" approach to teaching only hurts itself in the long run.
- jpc0 1y ago
  I'm not sure if it would be easier to explain a map / filter to a first year student vs implementing the patten manually using a for loop and if statement... Seems like a pretty easy example to make practically, for map have a collection of things, say balls or black. Pick up each one and do a thing to them, paint them blue for example. For filter do the same except have two different colour balls, if they are yellow they get thrown away, of they are blue they get put in a bucket. A for loop doing exactly the same you would need to explain the topic at hand, as well as explain iterating an index etc...
  - renerick 1y ago
    Explaining loops is independent of the concepts of collections though. It's also more general, since map/filter/reduce use some kind of loops under the hood anyway, the fact that probably shouldn't be ignored in education process. Unless of course you go with pure functional recursive iterator, but good luck explaining that one. Maps and filters also require understanding of higher order functions and the very idea of passing function around as a value. I would argue that implementing map/filter with a loop and then demonstrating how this pattern is generalized as .map()/.filter() functions is better and more accessible
imtringued 1y ago
The strangest part about mathematics culture is that there is a culture of vibing the notation. Nobody in school ever tells you that there are glossaries on Wikipedia that tell you the meaning of the symbols. You're supposed to figure it out yourself using vibes. The way mathematic notation is taught is inherently unstructured. You're expected to just get it.
Viliam1234 1y ago
For the purposes of education, it is important to keep in mind that "optimized for performance of a highly trained person" and "optimized for understanding of a complete beginner" are two different things. I often see people make the mistake of trying to teach inappropriately abstract things to small children, because that's what the pros do, and we want the little kids become pros as soon as possible. Problem is, trying to skip the fundamentals is only harmful in long term. First kids need to learn what all that stuff means, and then we can proceed to teach them the shortcuts.

lazystar 1y ago

its silly. itd be like introducing first year programming students to advanced maps/filters/anonymous function syntax, instead of the easier to understand for loops and if/else statements. math's "no true scottsman" approach to teaching only hurts itself in the long run.

jpc0 1y ago
I'm not sure if it would be easier to explain a map / filter to a first year student vs implementing the patten manually using a for loop and if statement... Seems like a pretty easy example to make practically, for map have a collection of things, say balls or black. Pick up each one and do a thing to them, paint them blue for example. For filter do the same except have two different colour balls, if they are yellow they get thrown away, of they are blue they get put in a bucket. A for loop doing exactly the same you would need to explain the topic at hand, as well as explain iterating an index etc...
- renerick 1y ago
  Explaining loops is independent of the concepts of collections though. It's also more general, since map/filter/reduce use some kind of loops under the hood anyway, the fact that probably shouldn't be ignored in education process. Unless of course you go with pure functional recursive iterator, but good luck explaining that one. Maps and filters also require understanding of higher order functions and the very idea of passing function around as a value. I would argue that implementing map/filter with a loop and then demonstrating how this pattern is generalized as .map()/.filter() functions is better and more accessible

imtringued 1y ago

The strangest part about mathematics culture is that there is a culture of vibing the notation. Nobody in school ever tells you that there are glossaries on Wikipedia that tell you the meaning of the symbols. You're supposed to figure it out yourself using vibes. The way mathematic notation is taught is inherently unstructured. You're expected to just get it.

Viliam1234 1y ago

For the purposes of education, it is important to keep in mind that "optimized for performance of a highly trained person" and "optimized for understanding of a complete beginner" are two different things. I often see people make the mistake of trying to teach inappropriately abstract things to small children, because that's what the pros do, and we want the little kids become pros as soon as possible. Problem is, trying to skip the fundamentals is only harmful in long term. First kids need to learn what all that stuff means, and then we can proceed to teach them the shortcuts.