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> Memorizing the multiplication table is a useless waste of time and I recognized as much when they tried to make me do it and I refused. Nobody needs to know 8

> Memorizing the multiplication table is a useless waste of time and I recognized as much when they tried to make me do it and I refused. Nobody needs to know 8x7 off the top of their head. ) Me too! I thought I was so smart as a kid, realizing that stuff I didn't want to do was useless. However, I was wrong. An over-dependence on calculators due to a lack of arithmetic fluency has sabotaged all my encounters with mathematics ever since. I had a hard time understanding and developing any kind of fluency because I was forced to push everything through a black box that also distracted me. I now realize that memorized facts are the foundation for knowledge and advanced thinking. Dismissing memorization, especially of fundamental facts, is like choosing not to use RAM because you can always swap to disk.

jimmaswell 8y ago
Except memorizing multiplied numbers is not foundational knowledge for any higher math, knowing what the concept means is. Learning this involves working through some examples but it doesn't mean you need to know an entire table. Not knowing 7x8 never held me back in higher math/math-relevant classes like Calculus I-III, Discrete Math, Linear Algebra, Physics I-II, Chemistry, Macroeconomics, Computer Science (anything from basic programming to language processing or algorithm proof), Music Theory. Had a fun and mostly easy time in all those. Once in a blue moon on a test I'd have to do a multiplication and count it out (8x5, add 5 8 times) because it was a product in a derivative or something and that class had an (unrealistic for the real world) no-calculator policy. In fact I'm pretty sure mathematicians are notorious for poor arithmetic. Additionally to your point, I think forcing arithmetic memorization on students is harmful because it makes math seem boring and hard.
- photojosh 8y ago
  Do the memorisation by spaced repetition and make it competitive, and it takes almost no time to learn them. Of course if the kids begrudge it, they’ll hate it and fail to work at it.
- rdtsc 8y ago
  > Except memorizing multiplied numbers is not foundational knowledge for any higher math But my point wasn't that it's foundation in general, category theory, set theory, etc are foundational, but that it's important to start from it. Just because something is foundational doesn't mean it's a good starting point. > it doesn't mean you need to know an entire table. Kids at an young age are usually very good at memorizing things and once they have memorized then they can build on that and learn new tricks, relationships, abstract and foundational principles. > Not knowing 7x8 never held me back in higher math/math-relevant classes like Calculus I-III, Neither did me either. Embarrassed to say, I had forgotten a lot of it. But I would have been struggling early on in the 4-9th grades if I didn't know how to add or multiply numbers then. I would have been wasting time on tests doing it the slow way, instead of thinking of more interesting problems. So to summarized, yes, it is not foundational but it all depends on age, it's better to take advantage of what the brain already knows how to do well at that particular state in time. > In fact I'm pretty sure mathematicians are notorious for poor arithmetic. Could be but if they are poor they would be left behind in early grades and might never becomes the mathematicians they are. There is also a bit survivorship bias in the sense that if there mathematicians who are poor ar arithmetic, they'd stand out and become memorable, but those that are good are not noticeable because they are expected to be good with numbers.
photojosh 8y ago
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).

jimmaswell 8y ago

Except memorizing multiplied numbers is not foundational knowledge for any higher math, knowing what the concept means is. Learning this involves working through some examples but it doesn't mean you need to know an entire table. Not knowing 7x8 never held me back in higher math/math-relevant classes like Calculus I-III, Discrete Math, Linear Algebra, Physics I-II, Chemistry, Macroeconomics, Computer Science (anything from basic programming to language processing or algorithm proof), Music Theory. Had a fun and mostly easy time in all those. Once in a blue moon on a test I'd have to do a multiplication and count it out (8x5, add 5 8 times) because it was a product in a derivative or something and that class had an (unrealistic for the real world) no-calculator policy. In fact I'm pretty sure mathematicians are notorious for poor arithmetic. Additionally to your point, I think forcing arithmetic memorization on students is harmful because it makes math seem boring and hard.

photojosh 8y ago
Do the memorisation by spaced repetition and make it competitive, and it takes almost no time to learn them. Of course if the kids begrudge it, they’ll hate it and fail to work at it.
rdtsc 8y ago
> Except memorizing multiplied numbers is not foundational knowledge for any higher math But my point wasn't that it's foundation in general, category theory, set theory, etc are foundational, but that it's important to start from it. Just because something is foundational doesn't mean it's a good starting point. > it doesn't mean you need to know an entire table. Kids at an young age are usually very good at memorizing things and once they have memorized then they can build on that and learn new tricks, relationships, abstract and foundational principles. > Not knowing 7x8 never held me back in higher math/math-relevant classes like Calculus I-III, Neither did me either. Embarrassed to say, I had forgotten a lot of it. But I would have been struggling early on in the 4-9th grades if I didn't know how to add or multiply numbers then. I would have been wasting time on tests doing it the slow way, instead of thinking of more interesting problems. So to summarized, yes, it is not foundational but it all depends on age, it's better to take advantage of what the brain already knows how to do well at that particular state in time. > In fact I'm pretty sure mathematicians are notorious for poor arithmetic. Could be but if they are poor they would be left behind in early grades and might never becomes the mathematicians they are. There is also a bit survivorship bias in the sense that if there mathematicians who are poor ar arithmetic, they'd stand out and become memorable, but those that are good are not noticeable because they are expected to be good with numbers.

photojosh 8y ago

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).