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Of course understanding fourier transforms isn't reliant on my ability to do 6x7 - but arithmetic as a lifeskill is actually valuable. It's like saying that gr

Of course understanding fourier transforms isn't reliant on my ability to do 6x7 - but arithmetic as a lifeskill is actually valuable. It's like saying that grammar and spelling aren't important because spellcheck will sort it out. Splitting out arithmetic from "Maths" doesn't seem terribly sensible to me. Times tables aren't really problematic, and they do provide opportunities to teach valuable concepts (5x6 = 6x5).

eecc 9y ago
No, you're straying away from the original point which was: there's no need to make rote memorization of arithmetic tricks and multiplication tables a hard prerequisite to everything else about math. Nobody claimed that arithmetic is absolutely useless
- Ntrails 9y ago
  It is never hard blocked on arithmetic though (in the UK at least). A bunch of simple numerical solving will be harder without being able to do multiplication in your head - but certainly someone could get through without. I'm honestly dubious of anyone who claims that the reason people hate maths is because of times tables.
  - zaptheimpaler 9y ago
    Well a lot of people who dislike math do so because they think its all about rote calculation. Not just times tables, even algebra can be seen as a completely syntactic procedure - memorizing a bunch of rules. Another example - if you are taught 10 different "templates" of problems and solutions in calculus class and memorize which equations to apply where, you can solve a lot of problems without ever building any intuition. If someone thinks of math that way, I can understand why it would be boring to them. Thats what I mean by blocked on arithmetic. If every thing is taught as a cookie-cutter process to follow its not surprising that people associate math with blindly following processes.
    - Ntrails 9y ago
      > If every thing is taught as a cookie-cutter process to follow its not surprising that people associate math with blindly following processes. A hammer and a chisel are tools. You can use them to shave a bit of wood off the door, or you can use them to carve a beautiful sculpture. You can do neither without knowing how to use them. I agree that too much of maths teaching is "here are 100 quadratics, go solve them" - which is obnoxious and dull. But "blindly following process" (matrix multiplication, change of variables/base, sum to infinity etc) happened throughout my degree and is a component of higher maths as well. Heck, most of the proofs I remember use "tricks" that any mathematician is expected to just know. I sure as hell don't think children are taught maths well. I remember being taught how to take the derivative of x^2 without the teacher bothering to show where that came from or what it really meant. Heck - children are given the quadratic formula to memorise and basically told "it's magic, learn it" instead of showing them how you can trivially create it by completing the square. But mathematics does involves a ton of following some process or other to get the problem into a format you can do something with. Probably by following a different process that you've done before. I'm not sold that you can simply eliminate that aspect.
      - zaptheimpaler 9y ago
        Seems like we agree. I am only saying current math is too focused on the mechanical processes, so much that many people never even see the other (more important) conceptual side. Times tables don't need to be taught in class - there is nothing to teach. They just need to be memorized by students.
- mannykannot 9y ago
  I think it is undeniable that both a certain level of working memory and of basic algebra is necessary to understand mathematics at the next level. Someone who could actually understand an "entire college-level course in linear algebra or calculus or graph theory or even combinatorics perfectly well", yet be unable to remember a basic multiplication table, or figure out how to calculate 11*15, would have a very interesting pathology.

eecc 9y ago

No, you're straying away from the original point which was: there's no need to make rote memorization of arithmetic tricks and multiplication tables a hard prerequisite to everything else about math. Nobody claimed that arithmetic is absolutely useless

Ntrails 9y ago
It is never hard blocked on arithmetic though (in the UK at least). A bunch of simple numerical solving will be harder without being able to do multiplication in your head - but certainly someone could get through without. I'm honestly dubious of anyone who claims that the reason people hate maths is because of times tables.
- zaptheimpaler 9y ago
  Well a lot of people who dislike math do so because they think its all about rote calculation. Not just times tables, even algebra can be seen as a completely syntactic procedure - memorizing a bunch of rules. Another example - if you are taught 10 different "templates" of problems and solutions in calculus class and memorize which equations to apply where, you can solve a lot of problems without ever building any intuition. If someone thinks of math that way, I can understand why it would be boring to them. Thats what I mean by blocked on arithmetic. If every thing is taught as a cookie-cutter process to follow its not surprising that people associate math with blindly following processes.
  - Ntrails 9y ago
    > If every thing is taught as a cookie-cutter process to follow its not surprising that people associate math with blindly following processes. A hammer and a chisel are tools. You can use them to shave a bit of wood off the door, or you can use them to carve a beautiful sculpture. You can do neither without knowing how to use them. I agree that too much of maths teaching is "here are 100 quadratics, go solve them" - which is obnoxious and dull. But "blindly following process" (matrix multiplication, change of variables/base, sum to infinity etc) happened throughout my degree and is a component of higher maths as well. Heck, most of the proofs I remember use "tricks" that any mathematician is expected to just know. I sure as hell don't think children are taught maths well. I remember being taught how to take the derivative of x^2 without the teacher bothering to show where that came from or what it really meant. Heck - children are given the quadratic formula to memorise and basically told "it's magic, learn it" instead of showing them how you can trivially create it by completing the square. But mathematics does involves a ton of following some process or other to get the problem into a format you can do something with. Probably by following a different process that you've done before. I'm not sold that you can simply eliminate that aspect.
    - zaptheimpaler 9y ago
      Seems like we agree. I am only saying current math is too focused on the mechanical processes, so much that many people never even see the other (more important) conceptual side. Times tables don't need to be taught in class - there is nothing to teach. They just need to be memorized by students.
mannykannot 9y ago
I think it is undeniable that both a certain level of working memory and of basic algebra is necessary to understand mathematics at the next level. Someone who could actually understand an "entire college-level course in linear algebra or calculus or graph theory or even combinatorics perfectly well", yet be unable to remember a basic multiplication table, or figure out how to calculate 11*15, would have a very interesting pathology.