I played math games with my grandkids for pocket change. Get it right, I give them a dime. Get it wrong, they give me a dime. It’s cost me at least $100, but they can now accurately do basic math in their heads almost instantly. My grandson went from failing math to excelling in the subject. He can do math faster than using a calculator.
We use an electronic timer. Started with adding single digit numbers. He needs to provide answers before the timer goes off. Right answer adds a dime, but wrong answers or no answer before time expires subtracts a dime. Identified the numbers he had trouble with. We play until he’s taken a couple dollars from me. I always let him win a couple dollars to keep up the interest. Lowered the time until it was down to a second.
Most math is learning and applying a technique. But there is no technique or formula for adding/multiplying single digit numbers - it’s all memory. That’s what I did with my grandkids, and it frees them to learn the techniques without struggling with the basics.
Not to be a naysayer, but there ARE techniques for single digit multiplication and addition. In fact, it’s utilizing some basic principles, like the transitive property.
You can always always breakdown mathematics into smaller bits, like 9+8=(9+1)+7=17, or 7*6=(5+2)*6=30+12=42.
You could even do counting! 1+3 => 1…2,3,4 => 4. Or 3*4 => 3,6,9,12 => 12. There’s lots of shortcuts!
If you can’t break down something, memorizing the answer only teaches you the answer to those problems. Each piece of mathematics is a building block that can be used to help understand another part. You are skipping past the part of why 2+2=4 because it seems forthright and immutable. But, memorizing that means that there may come a time when 2+2 isn’t equal to 4, and without the knowledge of how to get there, could you then solve for 2*3?
This seems silly (and maybe a little abstract), but it’s meant more as an example to show why knowing how to break things down could solve bigger problems later on. Learning multiple ways to solve a problem can be really helpful!
It’s really just meant to show that it can be broken down, not that it is faster (because it isn’t).
Meanwhile almost every job or career uses a calculator to some degree. And those who dont either have no use for them or the math is so simple that you really don’t need a calculator.
" or the math is so simple that you really don’t need a calculator." That was the math they were trying to get you to remember and know how to figure out.
it means basic addition and subtraction, maybe multiplication and division but really if you need to do calculations on a regular basis you will naturally end up leaning to do it in your head if that saves significant time.
I’m not sure if in Maths teachers imaginations, there’s a James bond of maths, out there, and to save the world he has to divide by pi. (in which case they’d pick someone who actually likes maths, anyway) Or, they imagined, either we all collectively or just one of us, has a save the world moment, and it involves solving some maths thing. I don’t think they were quite the heroes they imagined themselves. Or maybe they are and this is all out there, and we just don’t even hear of it.
Are we still acting like this excuse was the actual explanation for why you couldn’t use a calculator?
They just said this. It was easier than trying to explain the nuances of education to kids. The actual reason was “because you have to learn to use your brain to do shit, it’s kind of important.”
Like, this is the equivalent of being upset the gym teacher wouldn’t let you use a segway in class. You’re missing the point.
While I agree that it is good to learn to do math without a calculator, it’s not necessarily the case that the teachers who said “you won’t have a calculator with you all the time” didn’t think that was the exact reason. Also, there’s nothing wrong with just stating the real reason if that’s what they really believed.
and unless you’re carrying one of those solar powered calculators in your pocket, how are you gonna charge your pocket calculator in the post apocalyptic era? You gonna waste guzzoline to run your car to charge your phone?
Neurological pathways need to be reinforced. If you aren’t doing mental math regularly your ability to do it degrades.
Obviously there’s very much a negative cycle at play thanks to the prevalence of modern computing but even then it’s simply a matter of most people not needing to use math much day to day.
To you it’s crazy that the person in customer service wants to give you a correct answer without having to worry about mistakingly not carrying a digit and then customers throwing a hissie fit because “well you said 7531 not 8531 and you’re a representative of the company so I’m going to pick and choose to pay the lower number rather than what I know I owe, get shit on by your manager for it, I don’t care”? Idk man, to me it just sounds like a smart idea - leave no room for error, let the machine be responsible for if you’re tired and can’t mental math for a second. It even shows you the numbers you added, you can double and triple check the result within seconds, no need to go out and prove you attended elementary school.
Thank you. I also can’t stand people who keep saying out loud I’ve never needed a quadratic equation why doesn’t the school teach me how to do taxes. For one thing if you didn’t have to ever use a quadratic then you never understood maths enough to apply it and walk away from the problem. Secondly if school taught you taxes ups be the one complaining the most about why you have to do taxes in school.
They also tell you this nowadays. All my good teachers taught me the logic to solve problems and the ability to calculate small things fast because they knew they only had to optimize for me getting my phone out of my pocket.
It literally doesn’t matter; you can’t make proper use of the calculator without knowing how to do the problems without it anyway, so this is just stupid bullshit lazy people throw at you to justify not putting effort into anything
Yeah. You’ll probably have access to a calculator these days, but that doesn’t mean it’s not worth knowing some basic arithmetic. Playing around with arithmetic is a good way to gain an understanding of the fundamentals and have a better sense of what the operations mean and how they work, which helps even when you do have a calculator.
Theres a few schools of thought when it comes to teaching math. Theres the camp that thinks that you should see 285 X 342 and figure out in your head its 97,470. Then theres the other group that goes, well we just need to teach them the concept and then the students apply it. Its people in the first camp that said you’d never have a calculator and just isn’t a realistic take on the world anymore. Very rarely do I have to sit down and remember what sin(30) is, but I can still do the trig work I’ve needed in my day job as a software developer.
Naa it’s just bad explanation on why. Use a calculator but a brain will know if you put it in right. Kind of like that scene om starship troopers and the Knife.
This was the dumbest fucking take even before everyone had an always-on pocket computer with them at all times.
Outside of insane scenarios during which you would have everything you need at your immediate disposal, the option always existed to say “I need a calculator for this, brb.”
My father had a Casio watch with built-in computation capabilities in the 80s, and in the socialist state of East Germany at that, so you could definitely carry an arithmetic calculator with you anywhere!
One of my professors, at uni, put it best. You should be able to second guess your calculator.
Also, it’s often faster to do an approximate calculation in your head, rather than getting out a calculator (or phone) and plugging the numbers in.
112 x 9.
By approximation, it’s 100ish by 10ish, so around 1000. This can often be enough. (E.g is a current below 1500mA?)
The calculator should give 1008. If it claims it is 10,080, or 12.4, you know you’ve screwed up, and should recheck your calculations. If you can’t do it in your head, then you can’t check for issues.
the thing is: the calculator will always get it right.
our brains use all kinds of shortcuts and patterns so it’s not even that rare for mental calculations to end up completely wrong, or you get the right answer but write the wrong thing, which is less likely to happen if you see the digits in front of you and copy them.
I’ve heard complaints of senior software engineers who, though they do all carry calculators in their pockets and even usually have laptops open in front of them in the meetings, avoid doing math of any kind (simple order of magnitude multiplication, for example) in front of other people. Which makes group decision-making super obtuse.
So, maybe there is something for teachers to do along the lines of let’s get confident and quick at doing this math however you want to do it. I hope things are changing in this direction.
They are. A lot of the new math curriculum my kid took in elementary school was exactly about that. Estimating, quick ways to calculate things, and sort of an underlying grasp of what it all means vs just memorizing multiplication tables or something. So much better than the bullshit way they taught me 40 years ago.
IMO memorizing those multiplication tables was one of the most useful things they taught in elementary school. They are teaching tricks now that separated the kids who were good at math from the ones who weren’t (since the ones who were good could figure out a lot of these tricks on their own to get through the grind of pages of questions quicker), but knowing my multiplication tables was and still is an essential part of doing quick math in my head.
As a senior software engineer with a degree in electrical engineering, I’ll 99% of the time pull up a python shell to do simple arithmetic. Or Google “1 day in minutes”
What they should be saying is that it’s like exercise.
Just because you know how to run or you know how to do a pull-up, you won’t necessarily be able to do so to the extent needed in a pinch. You have to stay in shape. You have a car, but the car could break down and you might have to walk a mile to the nearest gas station.
Likewise, with math, we run into situations all the time where being able to do simple math in your head you can prevent you from getting screwed.
Like at a car dealership, some will show you different payments and ask you if you want to get the premium insurance or skip the premium insurance and go with the lower payment.
Most will choose the lower payment. If you did the quick math* in you head though, you’d quickly see that the “lowest payment” is off and has a minimal car warranty bundled in.
Grocery shopping. I’ve seen where the price per ounce on the shelf doesn’t match the actual price per ounce.
Should you take the more distant job? It pays $5 more an hour, but is it worth driving 15 extra miles?
Should you take the delivery job that pays $20 an hour but will put an extra 50-100 miles a day on your car? It’s not just gas. Cars are a finite resource. Can you figure out the depreciation per mile?
When you buy a house: Should you buy a house now if it’s cheaper but interest rates are high or buy later when interest rates go down but the price may go up? How much money does each 0.25% in APR really mean to me? (Example: For a $400,000 house, a 0.25% APR difference is $83 a month or $1000 just that first year (not including compounding). With compounding, it can mean an extra $62 a month for the life of the loan for all 360 payments or $22,000! An extra 1% is quadruple that!)
If you think you would keep a house for only 5 years, which loan makes more sense? Pay a bit more in closing for a lower APR or pay nothing extra but get a higher APR? How many years in does the first loan come out ahead?
Quick loan payment estimation (without compounding for short loans (<6 years):
Takes a while to read, but with practice, it’s quick to do in your head:
Take loan amount, number of years, and APR:
Ex. 10K at 6% for 5 years.
Think of it as a geometry problem. You have a triangle with one side at 10k (starting loan amount) on the y axis and 0 days (x axis) and the tip will be at 60 months (5 years) and $0.
At the halfway point (30 months 2.5 years) the principal balance (not counting interest) should be about $5000. So on average we can calculate $5000 * 6% APR for 5 years (or 30% total without compounding)
Original loan amount + non-compounded interest =
$10000 + ( $5000 * 30% ) = $11500
$11,500 divided by 60 payments = $191.66 /mo
0% interest would be $10,000/60 or $166.66
This already gets us really close to the real answer.
I threw the loan values into an online calculator and it came up with $193.33 for the monthly payment.
$193.33 - $191.66 = $1.67 difference or 99.1% of the real answer.
This % difference due to compounding will vary based on the APR and and loan term but not the loan amount. So if you know which terms and APR you qualify for, you can figure this out ahead of time. For our 6% APR for 5 years example we know to add 1%.
If the sales person presents us with a significantly different monthly payment, then we know they snuck something in. I’ve personally run into this where all the payment options had a different service plan and/or extended warranty snuck in.
Also it’s good to know that the interest will cost us $26 a month vs 0% APR or paying in cash. Which helps us figure out if it makes sense to buy now (do we get $26 of benefit a month for having it now) vs waiting.
On a semantics level it may be even more true now. Of course you’re not going to have an actual calculator in your pocket, why would you when you can have a smartphone
Talking about supercomputers in your pocket… am I the only one who finds extremely funny when people ask for directions with their smartphone in their hand? Or ask for anything that can be easily solved by just using the device they’re already holding? In the past I used to send “Let Me Google That For You” links, but I think I need a “Just use your smartphone!” T-shit or something. :P
Edit: while I find the situation funny, I want to clarify that I never mock people, or be rude to them. I try to go out of my way to help them, since you never know why they don’t do the obvious thing.
That’s absolutely true. One person asked me for directions once with Google Maps open and pointing where they had to go. Clearly this person was unable to understand the app.
It should be noted that while chat services that many use require low bandwidth, sometimes on throttled speed it’s not enough to even make a basic Google search.
It is likely that the person you are talking to already used up their high speed mobile internet and now is running on throttled. Searching something up can take a minute or two in that state. Opening up a website or navigation becomes straight up impossible.
I totally understand that. As I said, I never know the reason, so I don’t judge. It’s just that the situation is funny, in the “we have the tools, but still can’t solve the problem” kind of way. :D
My parents and grandparents will routinely give me directions to the restaurant we’re all going to. In the past I tried to stop them as I can never remember them anyway and certainly don’t use the same landmarks. Now I just nod my head and pretend like I got it all on the first try and then just use Google maps like a sane person.
I mean I agree, but also can see the advantage of asking someone who seems like a local if you’re confused about the transit system or if you took a wrong turn and just want to get some place without further hassle.
For people whose childhood didn’t have an internet, it makes sense. Many are more comfortable getting information the way they used to. Even though I grew up in the 80s, I prefer to avoid having to interact with people when possible, so being able to use the internet for information was a godsend.
am I the only one who finds extremely funny when people ask for directions with their smartphone in their hand
Depends on the context.
If I’m hanging out with friends, in a city or area I’m relatively familiar with, and somebody suggests going to a restaurant or something I don’t know, I might just casually ask “Where is it? How are we getting there?” or something like that. Because there’s a good chance I don’t need to pull out my phone, open an app, type something in, make sure it’s the right location (being buried beneath the ad results), and following the steps the whole time, when a simple “just head to where the BDSM dungeon is, it like 2 doors down”
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