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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 8x7

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. What's really important is estimation techniques to tell if something passes a sanity check, like reducing things to powers of 10/etc and seeing if they're close to the result you got on a calculator, like how 123x456 should be close to 50000 (100x500)

CamperBob2 8y ago
How in the world are you supposed to estimate products of large numbers if you don't know the products of small ones?
- jimmaswell 8y ago
  You'll pick up on a few as you go along and that's all you need.
  - grimjack00 8y ago
    So, you'll memorize them.
    - jimmaswell 8y ago
      A few that you need, on an ad-hoc basis, instead of front-loading a bunch of calculations you're probably never going to use.
      - Dylan16807 8y ago
        Memorizing every combo of 2-9 x 2-9 is only 36 numbers. That doesn't seem like a big waste of time to me. If you do common ones like 2, 3, 5, and squares, that already covers most of them and you only have 10 left to remember them all.
CharlesColeman 8y ago
> 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.
opportune 8y ago
I do mental math all the time. Nobody needs to memorize tons of math but it's laughable that you would take that to such an extreme that you can't do basic multiplication without a calculator.
- jimmaswell 8y ago
  Can you give the example of the last mental math calculation you did? I almost never do it and I still almost never did it even when I was in college taking higher math. Tip calculation is all I can think of.
  - opportune 8y ago
    I work in big data/cloud stuff so I do estimates all the time to figure out what size resources I need/how long something will take. Less than 5 minutes ago I did mental math to see how long a job would take (I knew how long it would take for one read, and I had 2 days of reads over 3 data sources each with 8 data partitions => 48 reads each taking about 90 seconds => about 1.25 hours). Tip is another thing. And I like to "min/max" grocery shopping so I typically do mental math when shopping to maximize things like grams of protein/$.
  - toomanybeersies 8y ago
    I do rough division all the time in my head, for instance figuring out how much each can of beer costs if a slab of 24 is $60. Or on the flip side, how much it's going to cost me to get a round of 4 beers at $8 each. It's just a general life skill.
    - jelliclesfarm 8y ago
      I can be claustrophobic..I don’t like being in a closed car..so when I am at traffic stops..I convert alphabets to numbers and numbers to alphabets of the license plates..and sometimes I add the numbers together to check if it’s a prime number. Calms me the fuck down.
  - jelliclesfarm 8y ago
wrycoder 8y ago
You may be a bit embarrassed when you get older and a medical practitioner gives you a cognition test. Start with 100 and repeatedly subtract seven, announcing the results.
- jimmaswell 8y ago
  I'm certain they have different tests for people who don't have such arithmetic down.
  - wrycoder 8y ago
    Actually, that's on a standard cognition test. Other questions include identify pictures of animals, "what date is today", "Remember these five words (and get asked them at the end of the test), an "a is to b as c is to" question, etc. The assumption is that people over 50 in the USA can do simple arithmetic, because they all went to elementary school. Sadly, that assumption may have to change.
Viliam1234 8y ago
The opposite extreme is when a smart child cannot solve a math problem, because despite having interest and some cool insights, and making a few hopeful steps, they predictably fail at one of the "2 + 3 = ?" steps. Also, smart kids who hate memorizing are often really bad at languages. Which are mostly memorization; there is no way to derive the language from the first principles. But I guess if one's first language is English, this is not a big problem. I get it: memorizing stuff doesn't signal how smart you are. But at some moment, the lack of factual knowledge is going to overcome the advantage of being smart. You will start making logically correct conclusions from factually wrong premises, and you will be proud that you didn't fill your brain with garbage.
- jimmaswell 8y ago
  I had a hard time getting in the habit of learning French but I adapted to it when I had to. However, as I've mentioned in another comment, shoddy arithmetic in particular was never an issue for me in real math contexts.
- jelliclesfarm 8y ago
  I agree. That’s why there I some truth to the stereotype of Chinese kids being better in Math. Mandarin has 5 tones and having a keen ear to identify each tone and then recognizing it and memorizing it and matching sound to meaning is an enormous advantage. Also...teaching music..to recognize diff sounds/tones..musical notes(Bach would do) also gives mandarain/language/math students an edge.
toomanybeersies 8y ago
I sort of both agree and disagree with you. Being able to do mental arithmetic for small numbers is actually a very useful life skill. Sure, everyone has a calculator in their pocket these days (despite what my maths teacher told me), but that overhead of having to pull your phone out does slow you down. But I don't believe that rote learning your times tables up to 12 is the way to do it. Mental arithmetic should be incorporated into the curriculum in a more integrated way. The problem is that school systems love testing and grading people. And it's quick and easy to grade people on their times tables by giving them a speed test to see how many equations they can complete in 5 minutes. You can say that little Jimbo is doing his times tables at a third grade level because he knows his 2, 3, 5 and 10 times tables. It's a terrible method of testing student progress though, I managed to get all the way to high school and was in the top stream class and never learned my times tables. The actual concept of multiplication tables is an important concept for children to learn though, as it does help solidify fundamental mathematical concepts.
jimmaswell 8y ago
Addendum: I highly recommend this reading material, A Mathematician's Lament: https://www.maa.org/external_archive/devlin/LockhartsLament.pdf https://www.maa.org/external_archive/devlin/LockhartsLament....
theoh 8y ago
The example of approximating 123 x 456 with 100 x 500 tends to undermine your point a little. It's too simplistic and the answer isn't even within 10%. 120 x 500 gives a much better approximation, and just needs you to know 12 x 5 = 60. Better still would be 125 x 460, which is 1/8 x 46 x 100000. That's within 3% of the true answer, and all it takes is quickly dividing 46 by 8. It's very helpful to be on good terms with numbers less than about 100, which is why the multiplication table is taught. It's useful for reverse calculations (like 46 / 8) as well as forward ones. Decimal equivalents (1/8 = 0.125) are worth learning as well. The key to being able to quickly approximate things is to populate your mind with memorized values. They work as landmarks (so the 7x8 example, in conjunction with the decimal equivalent of 1/8, means that you know almost immediately that, e.g. 55 x 125 is close to 7000).

CamperBob2 8y ago

How in the world are you supposed to estimate products of large numbers if you don't know the products of small ones?

jimmaswell 8y ago
You'll pick up on a few as you go along and that's all you need.
- grimjack00 8y ago
  So, you'll memorize them.
  - jimmaswell 8y ago
    A few that you need, on an ad-hoc basis, instead of front-loading a bunch of calculations you're probably never going to use.
    - Dylan16807 8y ago
      Memorizing every combo of 2-9 x 2-9 is only 36 numbers. That doesn't seem like a big waste of time to me. If you do common ones like 2, 3, 5, and squares, that already covers most of them and you only have 10 left to remember them all.

CharlesColeman 8y ago

> 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.

opportune 8y ago

I do mental math all the time. Nobody needs to memorize tons of math but it's laughable that you would take that to such an extreme that you can't do basic multiplication without a calculator.

jimmaswell 8y ago
Can you give the example of the last mental math calculation you did? I almost never do it and I still almost never did it even when I was in college taking higher math. Tip calculation is all I can think of.
- opportune 8y ago
  I work in big data/cloud stuff so I do estimates all the time to figure out what size resources I need/how long something will take. Less than 5 minutes ago I did mental math to see how long a job would take (I knew how long it would take for one read, and I had 2 days of reads over 3 data sources each with 8 data partitions => 48 reads each taking about 90 seconds => about 1.25 hours). Tip is another thing. And I like to "min/max" grocery shopping so I typically do mental math when shopping to maximize things like grams of protein/$.
- toomanybeersies 8y ago
  I do rough division all the time in my head, for instance figuring out how much each can of beer costs if a slab of 24 is $60. Or on the flip side, how much it's going to cost me to get a round of 4 beers at $8 each. It's just a general life skill.
  - jelliclesfarm 8y ago
    I can be claustrophobic..I don’t like being in a closed car..so when I am at traffic stops..I convert alphabets to numbers and numbers to alphabets of the license plates..and sometimes I add the numbers together to check if it’s a prime number. Calms me the fuck down.
- jelliclesfarm 8y ago

wrycoder 8y ago

You may be a bit embarrassed when you get older and a medical practitioner gives you a cognition test. Start with 100 and repeatedly subtract seven, announcing the results.

jimmaswell 8y ago
I'm certain they have different tests for people who don't have such arithmetic down.
- wrycoder 8y ago
  Actually, that's on a standard cognition test. Other questions include identify pictures of animals, "what date is today", "Remember these five words (and get asked them at the end of the test), an "a is to b as c is to" question, etc. The assumption is that people over 50 in the USA can do simple arithmetic, because they all went to elementary school. Sadly, that assumption may have to change.

Viliam1234 8y ago

The opposite extreme is when a smart child cannot solve a math problem, because despite having interest and some cool insights, and making a few hopeful steps, they predictably fail at one of the "2 + 3 = ?" steps. Also, smart kids who hate memorizing are often really bad at languages. Which are mostly memorization; there is no way to derive the language from the first principles. But I guess if one's first language is English, this is not a big problem. I get it: memorizing stuff doesn't signal how smart you are. But at some moment, the lack of factual knowledge is going to overcome the advantage of being smart. You will start making logically correct conclusions from factually wrong premises, and you will be proud that you didn't fill your brain with garbage.

jimmaswell 8y ago
I had a hard time getting in the habit of learning French but I adapted to it when I had to. However, as I've mentioned in another comment, shoddy arithmetic in particular was never an issue for me in real math contexts.
jelliclesfarm 8y ago
I agree. That’s why there I some truth to the stereotype of Chinese kids being better in Math. Mandarin has 5 tones and having a keen ear to identify each tone and then recognizing it and memorizing it and matching sound to meaning is an enormous advantage. Also...teaching music..to recognize diff sounds/tones..musical notes(Bach would do) also gives mandarain/language/math students an edge.

toomanybeersies 8y ago

I sort of both agree and disagree with you. Being able to do mental arithmetic for small numbers is actually a very useful life skill. Sure, everyone has a calculator in their pocket these days (despite what my maths teacher told me), but that overhead of having to pull your phone out does slow you down. But I don't believe that rote learning your times tables up to 12 is the way to do it. Mental arithmetic should be incorporated into the curriculum in a more integrated way. The problem is that school systems love testing and grading people. And it's quick and easy to grade people on their times tables by giving them a speed test to see how many equations they can complete in 5 minutes. You can say that little Jimbo is doing his times tables at a third grade level because he knows his 2, 3, 5 and 10 times tables. It's a terrible method of testing student progress though, I managed to get all the way to high school and was in the top stream class and never learned my times tables. The actual concept of multiplication tables is an important concept for children to learn though, as it does help solidify fundamental mathematical concepts.

jimmaswell 8y ago

Addendum: I highly recommend this reading material, A Mathematician's Lament: https://www.maa.org/external_archive/devlin/LockhartsLament.pdf https://www.maa.org/external_archive/devlin/LockhartsLament....

theoh 8y ago

The example of approximating 123 x 456 with 100 x 500 tends to undermine your point a little. It's too simplistic and the answer isn't even within 10%. 120 x 500 gives a much better approximation, and just needs you to know 12 x 5 = 60. Better still would be 125 x 460, which is 1/8 x 46 x 100000. That's within 3% of the true answer, and all it takes is quickly dividing 46 by 8. It's very helpful to be on good terms with numbers less than about 100, which is why the multiplication table is taught. It's useful for reverse calculations (like 46 / 8) as well as forward ones. Decimal equivalents (1/8 = 0.125) are worth learning as well. The key to being able to quickly approximate things is to populate your mind with memorized values. They work as landmarks (so the 7x8 example, in conjunction with the decimal equivalent of 1/8, means that you know almost immediately that, e.g. 55 x 125 is close to 7000).