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Thats the kind of BS math they shouldn't bother teaching. Most of math is about concepts, and if 5 year olds can grapple with super-basic calculus how about tea

Thats the kind of BS math they shouldn't bother teaching. Most of math is about concepts, and if 5 year olds can grapple with super-basic calculus how about teaching 10 year olds proof-based math and concepts (closer to college level) than memorization? Its kind of dumb how arithmetic is seen as a precursor to math when its really not. You could do an ENTIRE college-level course in linear algebra or calculus or graph theory or even combinatorics perfectly well even if you have no idea what 11*15 is off the top of your head and have to look it up every time. Its just a ridiculously backwards approach to teaching. We don't teach CS by testing people on memorizing syntax and API calls - they are rightly relegated to "google it when you need it, eventually you'll remember it". Of course algorithms are more interesting and building things is more fun so we focus on that. Current way of teaching math is just a historical accident IMO. No real reason it couldn't be conceptual and interesting from the start if there wasn't so much inertia around current systems.

tttt5 9y ago
Being able to recognize that 11 * 15 = 10*15 + 15 may be related to success in higher level math courses like linear algebra and calculus.
- noir_lord 9y ago
  I never learnt my times tables when I was little I just learnt how to do the multiplications in my head on the fly. Years later when I worked in a shop I used to cost complex print jobs in my head and co-workers though it was magic. The way maths is taught in the UK is largely how and very rarely why.
Ntrails 9y ago
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.
ashark 9y ago
> Thats the kind of BS math they shouldn't bother teaching. Most of math is about concepts, and if 5 year olds can grapple with super-basic calculus how about teaching 10 year olds proof-based math and concepts (closer to college level) than memorization? The times tables are BS math? The thing I've used IRL literally hundreds (thousands?) of times more than I've ever used anything from, say, calculus? The thing that yes I could use a calculator for but damn would it get annoying because I use it so often? That's what we should stop teaching? Math things I use a lot in actual real life: basic arithmetic (drilled skills/knowledge!), basic algebra, factions/percentages (converting one to the other, and scaling other numbers by them—the basic arithmetic stuff is also vital here), and generally how triangles work. That's... almost all of it, actually. Some high-school-level stats stuff from time to time, I guess.
njarboe 9y ago
If you don't know up to 9x9, then doing basic algebraic problems become vary cumbersome. Factoring and simplification becomes a chore and one can't get into a good flow if you are typing in 2x5 into a calculator. On the other hand, I can't imagine anywhere that would expect one to know 11x15 off the top of ones head.

tttt5 9y ago

Being able to recognize that 11 * 15 = 10*15 + 15 may be related to success in higher level math courses like linear algebra and calculus.

noir_lord 9y ago
I never learnt my times tables when I was little I just learnt how to do the multiplications in my head on the fly. Years later when I worked in a shop I used to cost complex print jobs in my head and co-workers though it was magic. The way maths is taught in the UK is largely how and very rarely why.

Ntrails 9y ago

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.

ashark 9y ago

> Thats the kind of BS math they shouldn't bother teaching. Most of math is about concepts, and if 5 year olds can grapple with super-basic calculus how about teaching 10 year olds proof-based math and concepts (closer to college level) than memorization? The times tables are BS math? The thing I've used IRL literally hundreds (thousands?) of times more than I've ever used anything from, say, calculus? The thing that yes I could use a calculator for but damn would it get annoying because I use it so often? That's what we should stop teaching? Math things I use a lot in actual real life: basic arithmetic (drilled skills/knowledge!), basic algebra, factions/percentages (converting one to the other, and scaling other numbers by them—the basic arithmetic stuff is also vital here), and generally how triangles work. That's... almost all of it, actually. Some high-school-level stats stuff from time to time, I guess.

njarboe 9y ago

If you don't know up to 9x9, then doing basic algebraic problems become vary cumbersome. Factoring and simplification becomes a chore and one can't get into a good flow if you are typing in 2x5 into a calculator. On the other hand, I can't imagine anywhere that would expect one to know 11x15 off the top of ones head.