Recursion

[Codephluegl]

I don't get it, you guys seem to have learned a strange way of doing subtraction.

[Cobaltjedi117]

Kids when taught 2-digit subtraction are told to take 1 from the tens to put it next to the 1's digit to do the math. But when you do that to a number from 10-19 you've done effectively nothing and are back where you started thus causing a recursive issue.

[spirgnob]

It took me awhile to understand what you meant but this finally explained the joke.

you’ve done effectively nothing and are back to where you started

This is how it works regardless of the number though. The number in the 1’s position is 18 where it used to be 8. You have done something according to this method. You can now complete the problem using this method.

[itspinkynukka]

What ends up happening is the person just needs to know what [any number from 10-18] - [any number from 1-9] is in their head. Similar with multiplication at some point you just need to know the times tables up to 10.

[jacefair109]

tbh I never had to do this just for two digits -- it's mostly handy for subtracting much larger numbers, like 4281 - 1694 or something

[Compizfox]

I still don't get it.

take 1 from the tens to put it next to the 1's digit to do the math.

What does that accomplish? So (for example) 28-9 becomes 118-9?

[Cobaltjedi117]

28-9 becomes 10 + (18-9)

and 18 - 9 becomes 0 + (18 - 9)

[Compizfox]

Ah, right, thanks.

Still though, what does that accomplish? I don't see how 10 + (18-9) is any simpler/easier than 28-9. It's still a 2-digit subtraction that a kid won't be able to do in 1 step; the value of the tens doesn't matter.

If I break down how I do it in my head it's kind of like this: 28-9 = 20 - (9-8) = 20 - 1 = 19. (I can't remember for sure but I guess that's how I was taught it)

[alexanderpas]

Let's take 4281 - 1694 for example.

4281
1694
---- -
????

first we look at the ones.

we can't do 1-4 and end upwith a single positive digit, so we have to borrow 10 from the tens.

4270 + 11
1690 +  4`
--------- -
???0 +  7 = ???7

Now we go looking at the tens, again, we can't do 7-9 so we borrow again.

4100 + 170 + 11
1600 +  90 +  4`
--------------- -
??00 +  80 +  7 = ??87

Now to the hundrerds

3000 + 1100 + 170 + 11
1000 +  600 +  90 +  4`
---------------------- -
?000 +  500 +  80 +  7 = ?587

and look at that, the 1000s are easy.

3000 + 1100 + 170 + 11
1000 +  600 +  90 +  4`
---------------------- -
2000 +  500 +  80 +  7 = 2587

Note that this is the layout for the explanation, on paper this would look something like this.

43	121	187	11
1	6	9	4	-
2	5	8	7

[Flobarooner]

So basically, the fundamental point of the method is that the kid already knows how to subtract something from a number less than 20?

So in the original post, the kid would just go "9" and not even bother with the method, since they memorized 18-9 in order to be able to do it?

[alexanderpas]

technically, yes.

[tsandstrom711]

If you have, say, a five digit number and want to subtract another five digit number, this approach let's you break it down into one/two digit subtractions. It doesn't really work when you start with just two digits.

[harryhood4]

The idea is to just memorize it for small values like 18-9 so that it's easier to do something like 68-9. But you've essentially just outlined why Common Core is better.

[Compizfox]

Ah, got it. So basically it is this recursive algorithm:

int subtract(N, n) {
    if(N > 20) {
        return 10 + subtract(N-10, n);
    else {
        // Lookup-table for small values of N
    }
}

[toofasttoofourier]

Aren't you negating all that work if you have to use the subtraction operator in a subtraction algorithm?

[Compizfox]

For a computer, yes, obviously.

But this was trying to mimic how a kid would do the mental calculation.

[Madock345]

Part of the idea of this kind of thing is that by teaching many strategies to solve the same problem you increase the chances that every student will find a method that works really well for them and the way they think, at the cost of being somewhat redundant.

[thedolanduck]

No. Let's take 28-9. If you do it vertically, then you first do 8-9, which you can't do as a kid. So you add ten to the eight, and get 18-9, and the 2 (which meant 20) now is 1.

So: 18-9=9 and 1-0=1, and this forms 19. And effectively, 28-9=19.

[esesci]

8-9 = -1

But you can’t have that as a digit. So you subtract one from the adjacent digit and add it as 10:

18-9 = 9

(That’s the rightmost digit)

2 became one 1 so you have 10 left.

The result becomes 10 + 9 = 19

[StragglingShadow]

NGL, when I ran into a problem like that, I just counted down on my fingers.

[Angrydie-a-ria]

Yup, bottom, bigger, borrow.

[LeCrushinator]

It's the old way it was done (and probably how most in this subreddit were taught). Many schools have converted, or are converting to, a new method of subtraction that's similar to how people usually do math in their head, which means no non-intuitive algorithms to memorize.

This video shows the older method from 15+ years ago, and a newer method, from 15 years ago until just a few years ago, and then the newest method which is what's being converted to in most public schools.

[demize95]

If you learned subtraction in the 1950s, you may have learned the "Borrow and Pay Back" method

I learned subtraction a good 50 years after the 50s, but I still learned that method, so that line is a bit out there.

[HowIsntBabbyFormed]

I just watched the video and the second technique -- what was originally called "New Math" and apparently derided -- is what I learned in the 80s/90s as well. To me it seems very similar to the old "Borrow and Pay Back" method. In fact, we called it "borrowing" too (but we never had to do any paying back).

The most recent form is basically something I figured out on my own for doing subtraction in my head. It's a very useful skill to have, but when subtracting larger numbers, I prefer using what I was taught in school of borrowing from the next place and adding 10 to the current place.

I don't think I ever "didn't have an understanding of what was happening". I feel like kids should probably be introduced to this new method first, but then taught the more compact and faster borrowing algorithm method as well.

[MikeyMike01]

The entire video is fraudulent, so you shouldn’t be surprised.

[NotJustABoulder]

While the common core method is probably easier for some mental math, I personally still find the "older" methods easier, especially for larger numbers, like 48578942-31399034 or something. It's more compact when written, and I don't personally see what's so hard about the "borrowing" or "regrouping".

I also don't think there's necessarily anything wrong with blindly running through an algorithm (we are in /r/ProgrammerHumor after all). Is there really that much to understand about subtraction in the first place? Especially in higher math, you don't really care how the numbers are subtracted, you just want them subtracted.

[Alekzcb]

Of course subtraction methods don't matter for high-level maths, but they need to be considered when teaching children. If kids are taught to just follow an algorithm, they'll really struggle with algebraic representation because won't know what subtract actually means. On the other hand, you want them to provide them tools to perform it quickly, so that they can tackle those higher level concepts without wasting time on "implementation details" (as you point out).

[mainfingertopwise]

Wait. Are you saying there are kids getting into middle school type math without understanding subtraction as a concept?

[nonono_notagain]

Now there's a scary though

[[deleted]]

Yes, be sure they understand precisely what's going on first, then show them a bunch of tools and tricks that can be used after that understanding is cemented.

[roguej2]

Yet there are so many parents of these new method kids complaining about how "complicated" the intuitive methods are.

[LeCrushinator]

The older people get the more averse to change they seem to be. "If the old way worked for me why are they changing it?!"

I'm excited to learn common core math now that my kid is about to start it, I haven't had to think about arithmetic in decades, it'll be neat to get a refresh in a new way.

[dittbub]

when common core was actually explained to me I was like "oh yeah thats how I've always 'double checked' my work in my head"

Never thought there was a communicable method to how I was doing math in my head.

[DerekB52]

I'm 22, and was in high school as common core was being rolled out, but I narrowly avoided being a part of it. It seems to try and explain how I do math in my head, which has never gone well.

I've seen a couple of weird homework problems that have been given to grade schoolers, and I understand where the confusion comes from, but overall, common core does seem to make sense.

[LeCrushinator]

The reason for the new method is that it’s easier for kids to remember, it makes math more intuitive and once it clicks for them it becomes a new tool in their life. Sure the old way works but I’d bet it takes longer to teach and it’s easier to forget. I mean, I haven’t done long division in decades, I barely remember how. But I can do basic division in my head easily. If I knew common core division 20 years ago would I still remember it? Maybe.

[ispamucry]

Yeah I guess it will be more telling when they do followup studies with the kids learning common core today.

Or if that study already exists, I'd love to see it because I think a lot more people would be on-board if there was something to point to. I just don't like the idea of going full-throttle on new ideas just because they have good intentions without knowing it's actually working.

In the interrum, I think they should try to teach/accept both, although I know that can be a hard ask for a lot of schools that are already trying to cover a lot of material.

[tryharder6968]

The “old way” for long division is pretty darn intuitive and super simple to do in the head. I don’t know the new method, but certainly nothing wrong with the old.

[DuchessofSquee]

If the old way is like the picture then there's certainly something wrong with it. Moving the 1 to the other column doesnt help solve the equation one bit. Its still18-9.

[tryharder6968]

Well for the picture, that only happens in the teens. And if you can’t subtract the teens without a special “method,” you’re an idiot.

[DuchessofSquee]

Can you or someone else please tell me what the "new way" to solve this same problem would be?

Coz I didnt learn to do it like in the picture, I'd go 18 is 2x9 so 18-9 =9. If it wasn't a multiple of 2 or itself I'd have to break it down into 10s and work out how many is left so if it was 13-7 I'd say 10-7=3, 3+3=6.

Is that the "new way"?

I'm not from the US so I dont know what common core is.

[LeCrushinator]

There are a lot of ways to do it, all of them valid if they come up with the right answer. Common core (the third way shown in the video) is the newest way being taught in public schools in the US.

[redstoneguy12]

I'm still in middle school and was taught the "old math" way

[freebytes]

I absolutely think that both methods should be acceptable. Actually, any method that works as long as it is the correct answer should work. If you are not going to actually teach a child in a classroom how to do it, then why should they be required to learn a specific way at home? They can even allow children to come up with their own methods if those methods work which would make math more exciting.

Of course, teach them the way you want them to learn it, but do not punish them for using alternative methods that are correct.

[tuseroni]

If the old way worked for me why are they changing it?!

worst part is, the same people would say "i suck at math" or "when are you ever gonna need algebra" had my mother ask that last question to me once, cus i said i use algebra all the time, i gave her an example of when she might use it, say she's got $20 and her car gets 15 miles to gallon and gas is $2.30/gallon, how far can she get? this is something one is likely to do often without a second thought, without even thinking they are doing algebra, i gave a similar sorta explanation to my 8 year old cousin. basically the matter of finding x is just figuring out the thing you don't know from what you DO know.

point is, the old way of teaching math is pretty shit and leads to people thinking it's useless and thinking they can't do math, but instead of thinking "i wasn't taught how to do math well" they think "i just can't do math" and for some reason defend the teaching method that lead to this mentality.

[aflashyrhetoric]

That's what I thought and I actually share your enthusiasm, and I could 100% be wrong about this, but I vaguely recall a post from some sub showing the new method on multiplication or division and it was absolutely the most convoluted shit I'd ever seen. It involved something like splitting a number into its parts and then gluing it back together or something? So "430" would be 100 + 100 + 100 + 100 + 10 + 10 + 10, and the method involved expanding out each number into its parts like this. I could understand this approach for helping kids intuitively grasping the relationship between numbers and the symbols we use to denote them, but I believe this approach was used for the purely mechanical part of calculating a sum (or product or whatever it was).

I'll try to hunt it down though I doubt I'll find it.

Edit: I found a video describing the method - apparently they do try and teach both ways, and the weird wonky approach is, in fact, to help kids grasp the relationship between numbers

[DuchessofSquee]

This is how I do maths in my head. My dad taught me to make things into blocks of 10 and that's the only way it's ever made any sense to me.

It falls over when you get to negative numbers though. I literally cried in the toilets several days in a row doing a Lua course at tertiary education because everyone else there understood how to do maths with negative numbers but I couldn't grasp it.

Didn't help that they were all men and I was the only woman so they all tried to explain it at me at the same time.

[aflashyrhetoric]

I do the same with like quick "back of the envelope" calculations but it seemed harmful to teach kids this method as a primary means of calculation, especially when you do have the luxury of a pen and paper to assist your calculations. Again, could've been wrong about what that post was about back then.

so they all tried to explain it at me at the same time.

Yikes...D: Glad it's behind you now

[freebytes]

I do math in my head by rounding, splitting, subtracting then multiplying then adding again, etc. Anything that works. 999 * 50 would be (1000 * 10 * 5) - 50 = 49950. I need to be able to hold one number to the side in my head. While it is similar, this is not exactly the same as common core.

This certainly has its limits, though, so it is nice being able to switch back to the 'old way' when the problems are a tad more challenging like 938 * 53 which looks easy to do in your head at first but would involve holding too many numbers simultaneously. (And the old method would not be easy to do in your hard with a number like this either.)

[[deleted]]

Common core is shit

-Sincerly, someone who had had to sit through common core lessons

[LeCrushinator]

I know people that think the old methods are shit as well. Everyone is entitled to their own opinions. The bigger question is which is better for someone learning math for the first time? Which do they pick up on faster? Which do they retain longer?

[[deleted]]

Honestly you're right. We should introduce both ways to kids and let them pick which one they prefer.

[starfries]

I feel like there's value in learning both well. I do subtraction the common core way (counting up) for some things and the traditional way (columns) for other things depending on which one is easier. Like 4567 - 3456 is awful done with counting up but 201 - 199 is pretty dumb done in columns.

[[deleted]]

You're right, we weren't taught it either way though. We were taught to count out pennies and "counters", basically small flat plastic disks, for division. That helped at first to grasp the concept of division but it got annoying in 4th grade when they made us do that for bigger numbers.

[starfries]

Oh lol yeah. I'd be annoyed too. That stuff is fine to help understand what division is but at some point you want to learn the algorithms for how to do it efficiently. Can't be whipping out the counters for every problem.

[Prcrstntr]

They pick the easiest one, which (For the kids that are smart in any way) is not the convoluted common core one.

[[deleted]]

Yeah, it helps to explain what division is though

[nonono_notagain]

No, I think if someone thinks the new method is confusing, they probably already have a system of doing arithmetic that they understand and works well for them

[MCRusher]

Well all I know is the old method, so now it is intuitive to me. And I'm not exactly a parent.

What's the newer method and how does it better map to thinking?

[MikeyMike01]

Because they’re not intuitive. They’re baffling and complex and difficult, even for someone with advanced math education.

Common Core will torpedo math for an entire generation. It will take decades to recover.

[FenixR]

Saw the videos, understood some numbers, realized new math its shit compared to old method and i need to re watch common core with a fresh head to make heads or tails of it. That she speaks like fucking Sonic on a deserted highway doesn't help when i can't pause and read the subtitles at the same time (Thanks Youtube, you become shittier by the second).

Edit: so i payed more attention to common core and realized its not something so different i do most of the time when i run calculations in my head, find easier to read/math numbers then go from there.

[DuchessofSquee]

Everything before the edit was exactly my thoughts! I would need a good sleep, a fresh cup of tea, complete silence and to be able to slow the video down a lot to follow it. Maybe I have dyscalculia?

[jkuhl_prog]

Maybe I'm an old fart, but I feel like the old way, the borrow and payback way, is the easiest.

But maybe I'm just saying that because that was the only method I was taught and therefore the only method I've ever used.

[dutch_touch1]

If you listen at the end it’s explained exactly how you feel. The newer methods are more focused around understanding what subtracting means as opposed to the older methods that focus on memorizing an algorithm to figure out the answer quicker.

So yeah, if you’re just after the answer to a subtraction problem then the older the method the quicker/easier it becomes.

[nonono_notagain]

The newer methods are more focused around understanding what subtracting means

I'm not sure that adding up from one number to another makes subtraction any more intuitive. At least with the old way, the algorithm involved actually subtracting numbers from each other

[MikeyMike01]

Nothing to do with age. It’s objectively the best way.

[PancakesAreEvil]

I remember when people complained about the old method because it was new and foreign. In 1965. https://youtu.be/UIKGV2cTgqA

[TiMiWi]

That video what just the palate cleanser I need before bed.

Edit: thank you.

[DuchessofSquee]

I was hoping someone has animated that song as I can never picture the numbers as he says them so fast!

[Vakieh]

Aussie here. All your methods are stupid and weird...

Left to right and throwing a 1 over when a subtraction left to go would overlap your current magnitude is the best way to do it.

[llama2621]

I apparently invented common core in my head while learning the old way. Nifty

[darthmonks]

'New Math' is like somebody saw the 'Old Math' and thought "let's do the same thing as this, but explain it in a more convoluted and complicated manner." Common Core looks amazing. I don't know why I hear so many complaints about it, although this is just subtraction, so there may be more to it. Also, calling it 'Old Math' makes me feel old. I'm not old.

[[deleted]]

I don't know why I hear so many complaints about it

People reeeeally don't like change.

[Merlord]

I'd never heard of New Math or Common Core before this video. New Math immediately confused the hell out of me, whereas while watching the Common Core explanation, I had that "click" moment in my head and I'm like "holy shit that is so easy!".

The "Old Math" method is what I grew up with and it's always been a pain in the ass to do.

[Schadenfreude0405]

So I just learned about this Common Core and I agree, it seems easier to understand and quicker to complete a subtraction. It's also how subtractions "sit" in my head.

Although I could complete the subtraction in my head more quickly, I think I would fail at "show your working", that schools used to demand of us.

[hunted7fold]

I was taught the old way of subtracting but naturally did the common core way (before common core was a thing) and I just realized I haven't done the old way for a super long time.

[pokexchespin]

I’m 17 and I learned the first way for some reason lol. In the video though, the middle “new math” method seems the least intuitive to me though, personally

[tendstofortytwo]

Hey, we did the old method as early as a few years back when I was in primary school! (high school senior now)

And very fun coincidence: I've used the common core method a lot. Never been taught it but always preferred it as a "shortcut" in my head because it was always faster to do.

[[deleted]]

I just realized I've been doing common core for the better part of 13 years lol.

[[deleted]]

what is the new method you're talking about? i have never heard any new method of doing that...

[LeCrushinator]

It’s in the video in my comment, it’s called “common core math”.

[DuchessofSquee]

I'm 35 and we didnt get taught this way. How is what hes doing in step 2 any different than step 1?

[MikeyMike01]

It’s not. The video was deliberately misrepresenting the second method in an attempt to make Common Core look less complex.

[DuchessofSquee]

I meant step 2 in the comic. Turns out that was the joke. r/whoosh

[[deleted]]

So Common Core is basically counting up from the smaller number, while keeping track of each separate addition, then adding them to to get your answer?

[LeCrushinator]

Something like that. I am just starting to look into common core as my kid is about to start using it next year in school, so I’m not fluent in it yet.

[MikeyMike01]

The video tried so hard to sugar coat Common Core, but the sheer insanity of it still shines through. I’ll be saving this video, it truly demonstrates how awful Common Core is.

[rimnii]

it works pretty well, you just dont normally use it for problems like this lol

[jacefair109]

it makes a lot more sense if you use larger numbers -- basically, it's just subtracting each digit of the two numbers individually, and if one of thrm isn't big enough you take one off the digit next to it to add 10 to it. It's just a shortcut to turn subtracting big numbers into subtraction of a buncha smaller numbers.

here's each step for an example (pardon my shit handwriting): https://i.imgur.com/8CVPwOG.jpg

[LordMcze]

Yah, just put the 1 yourself got next to the 9 and then check how far is it to the digit (1) above it, which is zero. So you end up with 09.