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I remember when I was little, I was told that I wouldn't always have a calculator on me. This turned out to be false, but being able to do mental arithmetic is

I remember when I was little, I was told that I wouldn't always have a calculator on me. This turned out to be false, but being able to do mental arithmetic is still an extremely valuable skill. The usability of your pocket calculator is really bad in comparison, and what the mental arithmetic gives you is a general automatic numeracy where you can ballpark the answer to numerical problems much faster than using a tool. This becomes a qualitative difference because you'll do more of those mental checks as a matter of course that you would never pull out a calculator for. Kind of like how git made merges so painless that they're now a standard part of most people's development flow. That's the kind of qualitative impact that mental arithmetic can give you. I admit that this is a point that's difficult to get across, and schools generally don't do a great job of it...

dylan604 6y ago
yes, being able to calculate the tip for your bar tab without needing to dig into a purse to find your "calculator" is a nicety. Being able to calculate the savings from the 20% sales price is also a useful trick. My favorite is just being able to round up the prices of items at the grocery store, and keep a running total in my head. I know I'm a nerd, but the concept calculating the tip by doubling the value after moving the decimal place one position to the right of the total flabbergasts me on how difficult it is for others to grasp. That's like 6th grade level math (at least it was when I learned it).
nickysielicki 6y ago
Don't you feel like you would have improved at this regardless of whether your schooling put a concerted effort into it? I've forgotten a lot of things from school -- doing math in my head isn't one of them because I use it all the time. Is that evidence that it's a good investment of time for 1st graders, or is it evidence that you would have learned it anyway due to the utility of it?
mkasberg 6y ago
Agreed! To build on your point - I used to teach Algebra 1 in a Title 1 school. What many people don't realize about "memorizing math facts" in elementary school is that if someone doesn't have a basic level of numeracy, it's really hard to learn more advanced concepts (like solving for x in a simple equation). You can't understand solving for x if you don't fundamentally understand how two numbers change when I subtract 5 from each of them, and you also don't have free working memory in your brain for learning if you're using all your working memory to do the subtraction. It's an anecdotal observation, but it's something that isn't often talked about in conversations about "memorizing facts". I guess what I'm trying to say is it's useful to be able to calculate a tip without a calculator or tally a grocery bill. But more importantly, it'll be a big hurdle to learning slightly more advanced math concepts if you can't do some of the basics in your head.

dylan604 6y ago

yes, being able to calculate the tip for your bar tab without needing to dig into a purse to find your "calculator" is a nicety. Being able to calculate the savings from the 20% sales price is also a useful trick. My favorite is just being able to round up the prices of items at the grocery store, and keep a running total in my head. I know I'm a nerd, but the concept calculating the tip by doubling the value after moving the decimal place one position to the right of the total flabbergasts me on how difficult it is for others to grasp. That's like 6th grade level math (at least it was when I learned it).

nickysielicki 6y ago

Don't you feel like you would have improved at this regardless of whether your schooling put a concerted effort into it? I've forgotten a lot of things from school -- doing math in my head isn't one of them because I use it all the time. Is that evidence that it's a good investment of time for 1st graders, or is it evidence that you would have learned it anyway due to the utility of it?

mkasberg 6y ago

Agreed! To build on your point - I used to teach Algebra 1 in a Title 1 school. What many people don't realize about "memorizing math facts" in elementary school is that if someone doesn't have a basic level of numeracy, it's really hard to learn more advanced concepts (like solving for x in a simple equation). You can't understand solving for x if you don't fundamentally understand how two numbers change when I subtract 5 from each of them, and you also don't have free working memory in your brain for learning if you're using all your working memory to do the subtraction. It's an anecdotal observation, but it's something that isn't often talked about in conversations about "memorizing facts". I guess what I'm trying to say is it's useful to be able to calculate a tip without a calculator or tally a grocery bill. But more importantly, it'll be a big hurdle to learning slightly more advanced math concepts if you can't do some of the basics in your head.