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This is exactly what I tell my kids right now as they learn the tables by rote: knowing the answers instantly by drawing from your subconscious makes it vastly

This is exactly what I tell my kids right now as they learn the tables by rote: knowing the answers instantly by drawing from your subconscious makes it vastly easier to solve harder problems later on. Making it competitive between the two of the kids helps too... after all, sports is “just” being better at getting the ball in the goal better than the other team, right?

jimmaswell 8y ago
Higher math isn't harder arithmetic, it's increasingly more abstract and sometimes doesn't even involve numbers. A student with their times tables down isn't going to do any better in a calculus course than one who relies on a calculator.
- CamperBob2 8y ago
  Statistics, on the other hand... (Which is what most people ought to be taking anyway instead of calculus.)
  - jimmaswell 8y ago
    What about statistics exactly? Bayes' theorem etc are enlightening and the numbers never gave me a problem.
- eitally 8y ago
  I don't believe you're correct. As my 2nd & 4th graders' teachers tell them, they need to learn a set of level-appropriate "math facts" ... but they're not forced to start by memorizing those facts (my son, for example, has a printed multiplication table up to 15x15 to reference while practicing decomposition of 3 & 4 digit multiplication problems). I truly appreciate the Common Core principle of focusing on teaching methods over facts, and -- at least in my children -- it is apparent that it sets them up for problem solving success IRL. YMMV. It's not a perfect curriculum and is still tailored to the lowest common denominator student, but I do think there's value there. And again, in a classroom with a strong teacher who can take time for differentiated instruction, there are ample opportunities for advanced students to go beyond or to practice their learned skills by helping their classmates. That said, I think your statement is absolutely incorrect in the context of higher math (and experimental science). The more facts you know -- whether literal facts, axioms, proofs, applied example or theories -- the more facile problem solving will be. This holds true in all disciplines (and not just math & hard sciences, but also engineering, social sciences & business).
- CharlesColeman 8y ago
  > Higher math isn't harder arithmetic, it's increasingly more abstract and sometimes doesn't even involve numbers. A student with their times tables down isn't going to do any better in a calculus course than one who relies on a calculator. IMHO, that's wrong in many cases. For instance: there's arithmetic in algebraic manipulations, and a lot of that is in the times-table memorization range. I definitely had to rely on my calculator in calculus class (and specifically swapped professors to one that would allow the use of one for that reason). There's also the fact that neglecting memorization as a "waste of time" at the start of your math career sets up a bad precedent and bad habits that will continue throughout it, barring substantial corrective effort. I, personally, only stopped having problems due to my deficit when I got to discrete math, which was the one math class I took that didn't involve numbers, like you said.
- chongli 8y ago
  A student with their times tables down isn't going to do any better in a calculus course than one who relies on a calculator. A linear algebra course, on the other hand, is going to make mincemeat out of any student who can't do basic arithmetic in their head at high speed. Gaussian elimination, matrix multiplication, determinants, diagonalization; all of these tasks are extremely arithmetic-intensive. If someone needs a calculator to multiply 8x6 then they are not going to be able to solve a linear system in 4 unknowns on an exam that disallows calculators (which is all math courses at my university, besides stats and act sci).
  - jimmaswell 8y ago
    Such a math course is being taught wrong if passing a test relies on churning through a million arithmetic steps instead of demonstrating understanding. I did fine in my course. Had to use the technique of mentally placing objects around a familiar path to memorize a silly list of matrix properties though.
    - chongli 8y ago
      The computational part was only 60% of the exams. The rest was proofs. For most of us, we needed every mark we could get in the computations because the proofs were really hard.
- photojosh 8y ago
  > Higher math isn't harder arithmetic That's narrowing the argument I made, I said "harder problems", of which higher math is just one aspect. Even sticking to just higher math; you're going straight from arithmetic to... calculus? What about algebra, trig, geometry; all much easier when your arithmetic chops are blazing?

jimmaswell 8y ago

Higher math isn't harder arithmetic, it's increasingly more abstract and sometimes doesn't even involve numbers. A student with their times tables down isn't going to do any better in a calculus course than one who relies on a calculator.

CamperBob2 8y ago
Statistics, on the other hand... (Which is what most people ought to be taking anyway instead of calculus.)
- jimmaswell 8y ago
  What about statistics exactly? Bayes' theorem etc are enlightening and the numbers never gave me a problem.
eitally 8y ago
I don't believe you're correct. As my 2nd & 4th graders' teachers tell them, they need to learn a set of level-appropriate "math facts" ... but they're not forced to start by memorizing those facts (my son, for example, has a printed multiplication table up to 15x15 to reference while practicing decomposition of 3 & 4 digit multiplication problems). I truly appreciate the Common Core principle of focusing on teaching methods over facts, and -- at least in my children -- it is apparent that it sets them up for problem solving success IRL. YMMV. It's not a perfect curriculum and is still tailored to the lowest common denominator student, but I do think there's value there. And again, in a classroom with a strong teacher who can take time for differentiated instruction, there are ample opportunities for advanced students to go beyond or to practice their learned skills by helping their classmates. That said, I think your statement is absolutely incorrect in the context of higher math (and experimental science). The more facts you know -- whether literal facts, axioms, proofs, applied example or theories -- the more facile problem solving will be. This holds true in all disciplines (and not just math & hard sciences, but also engineering, social sciences & business).
CharlesColeman 8y ago
> Higher math isn't harder arithmetic, it's increasingly more abstract and sometimes doesn't even involve numbers. A student with their times tables down isn't going to do any better in a calculus course than one who relies on a calculator. IMHO, that's wrong in many cases. For instance: there's arithmetic in algebraic manipulations, and a lot of that is in the times-table memorization range. I definitely had to rely on my calculator in calculus class (and specifically swapped professors to one that would allow the use of one for that reason). There's also the fact that neglecting memorization as a "waste of time" at the start of your math career sets up a bad precedent and bad habits that will continue throughout it, barring substantial corrective effort. I, personally, only stopped having problems due to my deficit when I got to discrete math, which was the one math class I took that didn't involve numbers, like you said.
chongli 8y ago
A student with their times tables down isn't going to do any better in a calculus course than one who relies on a calculator. A linear algebra course, on the other hand, is going to make mincemeat out of any student who can't do basic arithmetic in their head at high speed. Gaussian elimination, matrix multiplication, determinants, diagonalization; all of these tasks are extremely arithmetic-intensive. If someone needs a calculator to multiply 8x6 then they are not going to be able to solve a linear system in 4 unknowns on an exam that disallows calculators (which is all math courses at my university, besides stats and act sci).
- jimmaswell 8y ago
  Such a math course is being taught wrong if passing a test relies on churning through a million arithmetic steps instead of demonstrating understanding. I did fine in my course. Had to use the technique of mentally placing objects around a familiar path to memorize a silly list of matrix properties though.
  - chongli 8y ago
    The computational part was only 60% of the exams. The rest was proofs. For most of us, we needed every mark we could get in the computations because the proofs were really hard.
photojosh 8y ago
> Higher math isn't harder arithmetic That's narrowing the argument I made, I said "harder problems", of which higher math is just one aspect. Even sticking to just higher math; you're going straight from arithmetic to... calculus? What about algebra, trig, geometry; all much easier when your arithmetic chops are blazing?