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I think there is another one, Math C that involves day-to-day mental arithmetic which I am terrible at despite being good at Math A and holding engineering degr

I think there is another one, Math C that involves day-to-day mental arithmetic which I am terrible at despite being good at Math A and holding engineering degrees. There might also be another element of Math C which is a feel for numbers and lets you know if an estimate or the value staring at you on the calculator screen makes sense or if it is obviously wrong. I tie my poor mental arithmetic skills partly to never properly learning multiplication tables, at least not all of them and perhaps something lacking in my brain which also means I have a terrible sense of direction. Yet, when it comes to symbol manipulation where the numbers don't matter until the very end, then I am good at that.

Buttons840 2y ago
> I tie my poor mental arithmetic skills partly to never properly learning multiplication tables I thought this too. When you're young the multiplication table seems like a daunting thing to memorize, but after graduating university, it doesn't seem so bad. So I went back and memorized my times tables using Anki. It was pretty easy, but ultimately changed very little and I easily forget them if I stop practicing. I've come to realize that not mastering the times tables were a symptom, not a cause, of my learning difficulties.
- Modified3019 2y ago
  I’ve something similar For whatever reason, 6x7, 6x8, 7x7 and 7x8 are a persistent hole in my ability to memorize. Sure I can temporarily memorize them, but they shortly evaporate back into the void and I’ll have return to quickly having to calculate them out again. I’ve also got this thing where I get mixed up between verbal “eleven” and “twelve”. They sound different, but at the same time somehow sound just similar enough that the boundary that should exist around them as symbols never properly formed. I have to pause and manually match the number to the sound, every time. What’s especially funny to me is I have no such problem distinguishing between onze and douze from French, which I only know a few words of and certainly never hear in real life. I’d like to think the first problem I’d eventually fix if I was using those multiples constantly, but I’m not so sure because the second problem definitely doesn’t improve.
  - jacobolus 2y ago
    I wonder if it would help to remember that etymologically "eleven" comes from "one left" (as in, I counted the first ten and there was still one more) and "twelve" comes from "two left". As for the others, I think remembering these in several different ways is stickiest. For example, you might think of 7·7 = (5 + 2)² = 25 + 2·10 + 4 or perhaps 7·7 = (6 + 1)² = 36 + 2·6 + 1 or 7·7 = 7·(10 − 3) = 70 − 21. If you already know 7·7, then 6·8 = (7 − 1)(7 + 1) = 49 − 1. You can try computing 7·8 by repeatedly doubling: 7, 14, 28, 56. Etc.
    - DataDaoDe 2y ago
      I like the shove it to the nearest 10 approach. It makes a lot of calculations much simpler b/c they can be transformed to a simple multiplication by 10 and a addition or subtraction or two. 1. 6⋅7 = (6⋅10) - (6⋅3) = 60 - 18 = 42 2. 7⋅7 = (7⋅10) - (7⋅3) = 70 - 21 = 49 3. 13⋅19 = (13⋅20) - (13⋅1) = 260 - 13 = 247 4. 58⋅61 = (58⋅60) + (58⋅1) = 3480 + 58 = 3538 If we go up another order of magnitude, then the system starts really grinding to a halt though tbh :)
    - card_zero 2y ago
      The squares of primes become memorable if you've ever tried searching for primes in your head. That's because 7*7 is the smallest product of prime factors that are all larger than or equal to 7: in other words, you can check for the primality of numbers smaller than that by testing for division by 2, 3, or 5 only, because they must divide by one of those or be prime. Because of this pointless mental exercise it also sticks in my mind that 11 squared is 121 and 13 squared is 169 (though the presence of 69 helps with that one).
  - dleink 2y ago
    I'm in the same boat. The multiplication tables for me in that zone are constructs from other principles. :) So, Fives and Nines are easy and I can derive the Sixes Sevens and Eights from those. It's definitely extra steps. I think I'm reasonably good at the sort of mental arithmetic described in another post, Those particular operations just remain as symbols until I absolutely need to define them more precisely. I don't have a problem with 11s and 12s, but 5s and Rs trip me up. The way that our brains process symbols is fascinating. If anyone out there has any literature or reading on this, I'd be interested. Especially, as related to ADHD/Autism.
- rahimnathwani 2y ago
  If anyone else here wants to memorize multiplication facts, this is great: https://mathigon.org/multiply https://mathigon.org/multiply If you want to practice division as well, check out Zetamac or (if you don't want to be timed) my simpler tool: https://math.twilam.com/ https://math.twilam.com/
user_7832 2y ago
Is there any chance you have dyscalculia? Especially as you mentioned having a poor sense of direction. (Folks with neurodivergencies like autism/ocd/adhd etc are particularly more likely to have these.)
fuzztester 2y ago
For improving Math C skills, one approach you can check out is Fermi estimates or Fermi problems. https://en.m.wikipedia.org/wiki/Fermi_problem https://en.m.wikipedia.org/wiki/Fermi_problem
QuarterReptile 2y ago
It takes significant effort to get in the groove of a particular 'day-to-day' math. My job has regularly recurring parts where I spend a lot of time doing one or more of 3 basic skills: setting up integrals and differential equations, converting lots of numbers to binary or hex, and trig-based approximations. When I spend too much time away from one, it really shows. The other day, I tried to do the trig approximations, and it was like getting up after sitting too long with legs crossed. The fluency just wasn't there.
Dr_Birdbrain 2y ago
This is extremely interesting to read. I did learn my multiplication tables correctly, but I was always horrible at mental arithmetic—my elementary school periodically had formal exams for mental arithmetic, and I consistently failed them. It was the only type of task where I ever consistently scored less than 90%, I am also terrible at directions, my parents used to be worried about what would happen to me when I lived on my own—thankfully, Google maps became a thing and nobody notices I am bad at directions anymore. Like you, my learning difficulties are strictly compartmentalized to these two specific domains. I hold a PhD in engineering, and I even have a minor in math, lol.

Buttons840 2y ago

> I tie my poor mental arithmetic skills partly to never properly learning multiplication tables I thought this too. When you're young the multiplication table seems like a daunting thing to memorize, but after graduating university, it doesn't seem so bad. So I went back and memorized my times tables using Anki. It was pretty easy, but ultimately changed very little and I easily forget them if I stop practicing. I've come to realize that not mastering the times tables were a symptom, not a cause, of my learning difficulties.

Modified3019 2y ago
I’ve something similar For whatever reason, 6x7, 6x8, 7x7 and 7x8 are a persistent hole in my ability to memorize. Sure I can temporarily memorize them, but they shortly evaporate back into the void and I’ll have return to quickly having to calculate them out again. I’ve also got this thing where I get mixed up between verbal “eleven” and “twelve”. They sound different, but at the same time somehow sound just similar enough that the boundary that should exist around them as symbols never properly formed. I have to pause and manually match the number to the sound, every time. What’s especially funny to me is I have no such problem distinguishing between onze and douze from French, which I only know a few words of and certainly never hear in real life. I’d like to think the first problem I’d eventually fix if I was using those multiples constantly, but I’m not so sure because the second problem definitely doesn’t improve.
- jacobolus 2y ago
  I wonder if it would help to remember that etymologically "eleven" comes from "one left" (as in, I counted the first ten and there was still one more) and "twelve" comes from "two left". As for the others, I think remembering these in several different ways is stickiest. For example, you might think of 7·7 = (5 + 2)² = 25 + 2·10 + 4 or perhaps 7·7 = (6 + 1)² = 36 + 2·6 + 1 or 7·7 = 7·(10 − 3) = 70 − 21. If you already know 7·7, then 6·8 = (7 − 1)(7 + 1) = 49 − 1. You can try computing 7·8 by repeatedly doubling: 7, 14, 28, 56. Etc.
  - DataDaoDe 2y ago
    I like the shove it to the nearest 10 approach. It makes a lot of calculations much simpler b/c they can be transformed to a simple multiplication by 10 and a addition or subtraction or two. 1. 6⋅7 = (6⋅10) - (6⋅3) = 60 - 18 = 42 2. 7⋅7 = (7⋅10) - (7⋅3) = 70 - 21 = 49 3. 13⋅19 = (13⋅20) - (13⋅1) = 260 - 13 = 247 4. 58⋅61 = (58⋅60) + (58⋅1) = 3480 + 58 = 3538 If we go up another order of magnitude, then the system starts really grinding to a halt though tbh :)
  - card_zero 2y ago
    The squares of primes become memorable if you've ever tried searching for primes in your head. That's because 7*7 is the smallest product of prime factors that are all larger than or equal to 7: in other words, you can check for the primality of numbers smaller than that by testing for division by 2, 3, or 5 only, because they must divide by one of those or be prime. Because of this pointless mental exercise it also sticks in my mind that 11 squared is 121 and 13 squared is 169 (though the presence of 69 helps with that one).
- dleink 2y ago
  I'm in the same boat. The multiplication tables for me in that zone are constructs from other principles. :) So, Fives and Nines are easy and I can derive the Sixes Sevens and Eights from those. It's definitely extra steps. I think I'm reasonably good at the sort of mental arithmetic described in another post, Those particular operations just remain as symbols until I absolutely need to define them more precisely. I don't have a problem with 11s and 12s, but 5s and Rs trip me up. The way that our brains process symbols is fascinating. If anyone out there has any literature or reading on this, I'd be interested. Especially, as related to ADHD/Autism.
rahimnathwani 2y ago
If anyone else here wants to memorize multiplication facts, this is great: https://mathigon.org/multiply https://mathigon.org/multiply If you want to practice division as well, check out Zetamac or (if you don't want to be timed) my simpler tool: https://math.twilam.com/ https://math.twilam.com/

user_7832 2y ago

Is there any chance you have dyscalculia? Especially as you mentioned having a poor sense of direction. (Folks with neurodivergencies like autism/ocd/adhd etc are particularly more likely to have these.)

fuzztester 2y ago

For improving Math C skills, one approach you can check out is Fermi estimates or Fermi problems. https://en.m.wikipedia.org/wiki/Fermi_problem https://en.m.wikipedia.org/wiki/Fermi_problem

QuarterReptile 2y ago

It takes significant effort to get in the groove of a particular 'day-to-day' math. My job has regularly recurring parts where I spend a lot of time doing one or more of 3 basic skills: setting up integrals and differential equations, converting lots of numbers to binary or hex, and trig-based approximations. When I spend too much time away from one, it really shows. The other day, I tried to do the trig approximations, and it was like getting up after sitting too long with legs crossed. The fluency just wasn't there.

Dr_Birdbrain 2y ago

This is extremely interesting to read. I did learn my multiplication tables correctly, but I was always horrible at mental arithmetic—my elementary school periodically had formal exams for mental arithmetic, and I consistently failed them. It was the only type of task where I ever consistently scored less than 90%, I am also terrible at directions, my parents used to be worried about what would happen to me when I lived on my own—thankfully, Google maps became a thing and nobody notices I am bad at directions anymore. Like you, my learning difficulties are strictly compartmentalized to these two specific domains. I hold a PhD in engineering, and I even have a minor in math, lol.