Tom Lehrer - New Math (Animated) 

Unfortunately, math education is still stuck on the idea that basic arithmetic needs to be explained to 3rd-graders in depth

@@jonathanccast And thus is the concept of today's Common Core Math curriculum...and yeah I actually agree there. Third graders learning drawn out concepts often, and fifth graders learning these basic math taught in Algebraic equations already. o.O

Wtf but you can explain it in depth without all this extra bs? Using borrowing and carrying the way we did as kids is the SAME SHIT. You can't take 3 from 2 so you *borrow* '1' from the 2nd column (aka the 10s place, so the 1 represents a full *10*) and add it to the 2 in the ones' place to make a 12. Why did we need to start all this fancy "take 10" and other bs strategy that is way more time consuming when both are essentially saying the exact same thing?

@@allykayyy2683 because the other half of the kids in the room didn't realize it was the same thing, so they limited themselves to memorizing the strat without gaining any knowledge, any useful generalization from it but the strat itself. But fuck those dumbasses, amirite.

And they are impressed over rappers instead of this professional nerd singer

As we poison some pigeons in the park. ;-)

This one isn't. Most people today would find the new math way more intuitive.

BosonCollider and yet in the last few years, when I link this video on a Facebook comment thread where parents are loosing their... minds 😏 over their children’s math homework... I’m saddened and amazed at how many people think this song is new and was written with the intent of blasting common core. These parents have forgotten so much of what they were taught, that they don’t even recognize that “new math” of the song is the now “old” math of their childhood. 🤦🏼‍♀️

@@tanya5322 I didn't know that parents had loose minds.

number3Ihatetoontown 😝 aw... crap 🤔 I was always better at math than spelling. Lose/loose Chose/choose Always gave (gives) me trouble because they don’t rhyme in the manner you might suspect based on their spelling. 🤷🏼‍♀️

Very good point, that is to say 'I was going to say that.' Note: I'm very glad I was taught the New Math way, it expanded my mind and allowed me to understand arithmetic as a formal system---I would have been useless at rote-work.

+Cast Iron Chaos the animation is brilliant.

+Ayn Marx it's the same. Any good teacher would explain the logic.

+Cast Iron Chaos yes, my friend. Some folks just don't have a sense of humor. I am a briliant Summa Cum Laude PhD. and if you don't get this, go home and watch it again. Thanks your creativity. I salute you.

@1:04 *you're

Though the thoughts and emotions behind this song are quite relevant.

@@thegardenofeatin5965 ...except the system he is making fun of is the very system that people who complain about common core learned in school. The "thoughts and emotions" behind this song is nothing more than "it's new so I don't like it". I do love Tom Lehrer and I doubt he took this issue very seriously but god this attitude bugs me.

@@Weebusaurus He's not making fun of the math (He's a well accomplished Mathematician) he's making fun of attitudes towards change

Yup. Tom Lehrer. Night time comedic lounge singer. Daytime professor of mathematics at Harvard. 😏👍🏼

this makes me wounder how many ways we have changed math I was born in 1983 and did "old math" the same way as his old math was, never learned the new math he was talking about, or even using different bases till i hit college and computer courses. so was there a time they did weird math and just reverted then decided to go with common core to confuse the millennial (god i hate that term) like me that became parents?

Try playing it at 1.25x speed, and singing along with *that* :))))

He graduated Harvard at 18, so he definitely was gifted.

The man was a genius

@@onthepalehorse And worked in the NSA.

I can't even play the piano

Zachary Sasser Im a teenager so I'm not sure but for the questions it's 3-2=1 10-1=9 9 is the answer now take a 1 away from the 4 or add it to the 7 and you get 7-3=4 10-4=6, carry the one and take one away from the 3 and you get 2-1

This is actually close to how I naturally do math in my head. In the 1 column, you can take 2 off of 3, which leaves 1. that 1 has to go somewhere, so you knock it off a 10 in the 10s column which leaves 9 in the 1 column, and 4-1 = 3 so you now have a 3 in the top of the 10 column since you broke one of those 10s up to make change for the 1. You can take 3 off the 7 in the 10 column, leaving 4 to come off of one of the hundreds (functioning as a 10 if you're currently ignoring the 1s column). This puts a 6 in the 10 column, and 3-1 is 2 so you now have 2 in the hundreds column since you broke a 100 up to make change for the 40 in the 10s column. Then 2-1 is 1. a 1 in the hundreds column, a 6 in the tens column, and a 9 in the 1s column equals 169. The little twist is that I naturally do this in reverse order. 342-100 leaves us 242. 242-70 = 172 (through the knowledge that 40-70 = -30, and 200-30 = 170, plus the 2 we were ignoring). 172 - 3 = 169 (through the knowledge that 2-3 = -1, and 170-1 = 169). Instead of having to carry 1s, you just take 1 off of a column any time you are forced to use it to "make change" for a subtraction in the next column. There's one more abstraction, my brain sometimes conceptualizes math as discrete units like money and change. Think about it like this, you have 342 dollars in bills. You always have the highest denominations possible, where all of your bills start with a 1. You have to pay the guy 173 dollars. You give him a hundred dollar bill. (242 bucks left). You don't have enough 10s to make 70, so you give him another 100 dollar bill and ask for 3 10s back (142 bucks plus the 3 10s is 172) you don't have enough 1s, so you give him 1 of your 10s and ask for 7 1s back. (162 plus 7 1s is 169)

That's also kind of funny, because I've learned to do it both ways. 😂

@@danthony1715 he is 90

@@danthony1715 pretty sure he is dead

*_Where did 64 come in all of this?_*

@@Deedoo_r 64? More like Mario

No,I love this song!

You ask a silly question, you get a silly answer.

I always fall in love with teachers. Makes sense

Holy crap that's amazing

If you think thats funny then you are clearly a German.

Nominative determinism

And Tom Lehrer WAS a teacher... if you think that's funny, you're probably British (ie Lupin the werewolf, etc)

Well given that this song was recorded in 1965, most people alive today learned the "New Math" :-D

Resistors and Sputnik.Ascii anyone?

​@@MichaelMoore99same out of all his songs this is the one I can't laugh at cause I'm too young to understand and it just fucks with my brain😂😂

Not what I teach MY kids:... "A stupid question CERTAINLY needs a sensible answer!"

Parallels with computer jargon: "Garbage in - garbage out"...

He was just taking the piss with the second bit. The answer is correct though, (depending on how you look at it). 342 is 226 in base 10 and 173 is 123 in base 10. Subtracting gives us 103, which in base eight is 147. If anything, he is (perhaps unwittingly) pointing out one of the strengths of the New math technique. Understanding what you're doing in the process can allow you to tackle problems in an unusual format, because the technique requires you to actually think about what you're doing!

It was new math then- I’m pretty sure it’s an old song.

It's like base ten if you're missing two fingers

@@ineedausername9547 it is @SonyKid147

Base 8 means that the numbers go like this: 1,2,3,4,5,6,7,10. Because 8 is the base- where we put the 10. Essentially, the ones place goes up to 7. The tens place is actually groups of 8, the hundreds place is groups of 64: 342-173 in base 8 looks a bit different as a result: one's place: 3 from 2 is 7 base 8. To get this, you should move an 8 over from the "ten's" place: 12 - 3, base 8: 1,2,3,4,5,6,7,10,11,12. Count backward 3, you get 7: 1 2 3 4 5 6 7 *10* *11* *12* "tens" place: We already moved an 8 over for the ones place. So we actually have 3-7 for this spot. Move one from the "hundreds" over, and we get 13-7, base 8. 1 2 3 4 5 6 7 10 11 12, 13 count backward 7, You get 4: 1 2 3 4 *5* *6* *7* *10* *11* *12* *13* "Hundred's" place: You took a hundred away already, leaving 2-1. You get 1. End result: 147. The "counting on your fingers, with 2 gone" bit is a half-serious joke. People count in base 10 because we have 10 fingers.

Pmccrsp Sort of, but this is highly logical. It's basically just including the step that they used to skip through memorization. Common core meanwhile is ridiculous. It adds in steps that make no sense. Plus, it's impossible to teach well with how curricula are set up for it

Can I get a hallelujah

@@catherinestickels2591 it also pigeon holes students. Because if they don't do it step by step in the way they expect.... you don't get the point. Which is silly. Math has rigid rules but you can work around them if as they would say as a negative: "if you learn the algorithms" Well fucking duhhhh.... because the algorithms work.... you wouldn't try to fix a fucking rubick cube using common core right? Same principle.

@@catherinestickels2591 From what I've seen of Common Core (I'm from the UK but saw some of the stuff online), it does actually have logic to it and can help make things simpler, but you need to already understand what you're doing for it to make sense.

So true!

*trouble

O that would be amazing.

Hadassah Rose e still do use this method

I learned it both old and new. We got "new" in fifth grade, for two years.

Actually, New Math come back every other year. My mom was a math teacher, and used to roll her eyes at "the latest sexy math methodology that miraculously doesn't require students to do any work but promises they'll just suddenly 'have math'." Naturally, it's really just a convoluted con that ends up teaching very little over a very long time. Then I grew up to be a foreign language teacher, and found that every other year we have "the latest sexy language methodology that miraculously doesn't require students to do any work but promises they'll just suddenly 'have language'." And I realised how much self-discipline my mom displayed when she complained about this I was a kid.

It's all the same shit. The laws of logic have NOT CHANGED. Maths (not math) works by logic. Mathematical teaching modalities are designed CULTURALLY, and aimed at those who CONCEPTUALLY do not understand logic operators. The rest is only arithmetic and geometry, and no matter how it is taught, it only grasped by the handful who give a damn. The rest will ALWAYS struggle, no matter what you call it.

+Mark Siefert Except that when it comes to the current meme going around of the kid who wrote "5+5+5" rather than "3+3+3+3+3" and thus lost a point on his assignment, it comes off as pretty stupid.

+Joshua Solomon Common Core doesn't address pedagogy. It just discusses curricular goals. So that meme and its populist criticism is misplaced, but hey, everybody loves to attack teachers these days. (Full disclosure: Former math teacher here.) PS - +Mark Siefert: - "Maths?" Do they have CC where they use that word?

+YouMustBe Kidding The problem (from what I've seen) is that Common Core seems to teach both the theoretical and practical at the same time, with the result being that it makes the math look harder than it really is. In one of the videos I saw (which appeared to be pro-CC) they showed a problem subtracting one three digit number from another using the "counting up" method, and by the time they were done it took about half a page for one problem. It would be like teaching chemistry by starting off with creating equations that also mention how many electrons are in each shell of each atom involved. At some point in chem you'll probably need to know that, but you don't need to know it at the start.

exactly!!

+Leo Ix Since no one answered, it's because he assumed a tens place, then subtracted one from the actual tens place. That bit about public/private school was about where you were taught to subtract it from -- the top number or the bottom? Ultimately it doesn't matter. Ends up the same. So, basically, it's the same as what we do -- pull a one from the next column over and subtract. It's just that they did it in their heads and worked in a different order. Same concept, same result, but a slightly different method for getting there. Honestly, I don't understand how "new math" was hard for them. It's not nearly as different as Common Core is today.

Melody Elrod I think Lehrer was a comedic genius but it’s fair to say that the joke hasn’t aged well. Lehrer seemed in his work to always be of the opinion that “if it ain’t broke don’t fix it”. There’s a really cynical sarcasm to his approach and yet he comes off completely genuine because he’s always got a target. I have no understanding of maths in the slightest and had no idea what I was doing at school with it, yet the song still kills me. I think that’s the brilliance of his work

You were a math ed PhD student (your comment is four years old, so I assume you are not a student anymore), and Tom Lehrer was a professor of mathematics at Harvard back in the day. I can't speak to how misguided his math song is, as I personally suck at math, but I assume he had a smidgen of experience with math, given his position.

@@MattHawes "It just takes a smidgen to poison a pigeon in the park."

those who can, do. lehrer did. it didn't stop him teaching well into the 21st century either.

People regularly call this song misguided, but he was probably arguing in favor of new math, as this song was him making fun of the prevailing attitudes towards the change.

You didn't get the sarcasm - if you don't get the right answer, then you don't really understand what you're doing after all.

​@@jlee54 At the same time, teaching children that mistakes (and that's usually the reason for errors when you understand the method) will always be punished is a pedagogical disaster. No, it doesn't matter if you get the wrong answer, because the notebook will be thrown by the end of the school year. More generally, "Did you get the question right?" is not the same as "Do you understand what you are doing; can generalise and abstract what you are doing to other applications; learnt it in such a way that you won't forget it without constant aggressive maintenance?" The latter is my own philosophy on education (especially in mathematical sciences), and may not be the perfect reflection on the idealised aim of education, but it's much closer than the first.

@@jlee54 NO that's completely not the case~! You can understand what you are doing and still make a mistake. This is the rationale behind showing ones working. On the other hand, producing the correct result is in NO WAY an indicator that one knows what they are doing (they may as well have just copied or repeated the answer, or performed a process from memory without any understanding). So you're completely wrong here. It wasn't sarcasm, and you obviously flunked basic maths..

The problem with New Math is not that it was wrong, but that it was designed by mathematicians for kids, most of whom are not big on abstract principles. Too many of them got lost. (I understood it, but I never got good at arithmetic. Fortunately there are calculators. Unfortunately, mental arithmetic is part of the cognitive test for dementia.)

Why is your favourite number base base-13?

@@Anonymous-df8it ah. It’s because of Douglas Adams. The ultimate question about the meaning of life the universe and everything (whose answer is 42) is supposed to be “what do you get when you multiply 6 by 9?” Which is true in base 13. Plus you get to see better how division rules work when you choose a weird or prime as a base.

@@TheAnalogCat May you please elaborate on your final sentence?

@@Anonymous-df8it well, for instance, say you have a base of “n.” If you add up the digits of a number, you can test the divisibility of “n-1” (in base 10 it’s called casting out 9s). Last digit analysis (or last two digits, and so forth) allows you to test for powers of factors of “n” (like how all multiples of 5 end in 5 or 0 in base 10). If you subtract digits from right to left, you can test for “n+1” (e.g. 11*14=154->4-5=1,1-1=0 in base 10). It’s interesting seeing what patterns emerge when you do weird stuff in math.

They didn't use "new math" by the 80s. It gets a lot more confusing.

That Was The Year That Was, 1965

BIG G New math is no different than "old" math in the sense that the same problem still gets the same answer. New math (and common core for arguments sake) try to teach _why_ 13-7=6 instead of just simply learning it by heart. You may know a^2+2ab+b^2=(a+b)^2. But in traditional teachings just just have to learn that and remember it. Now you would start of with what you know: (a+b)^2= (a+b) * (a+b) -> a(a+b) + b(a+b) = a^2+ab+ba+b^2. Rather then just knowing a solution you now know why that solution .

Old math was simple. Memorize basic addition, subtraction, muliplication, and division tables. Then in cases like the video's subtraction, you would just "borrow" from the next tier up so that 2-3 could be thought of as 12-3. Which is one of those easy to memorize solutions.

Elodin11 except “borrowing” was a “new math” concept

Old Way: CCCXLII - CLXXIII

@Khaled Rapp yeah. My mom had a TERRIBLE time in elementary school in the 50s because it was just supposed to be rote memorization and she isn't good at that. Luckily New Math came by when she was in Jr. High, but the damage was done. She was past learning basic math by then.

I figure that was to keep the patter going.

Oh, absolutely, I did that all the time in school.

@@TheWanderingLPer Me too!

That's... Common core.

Ardub23 I learned this "new math" but I pretty much did the same thing as you

I invented that method by myself as well, and was continually told I was wrong, because of course 8 - 5 is not the same as 5 - 8 and thus obviously I had gotten the wrong answer. Obviously. That's what I was told, at least. I was right every time, though. Because 10 - (8 - 5) - 10 = 5 - 8 is true.

Yup... Knowing "why" is often way less important than just getting the answer. Too much redundancy in Mathematical education.

You learned the optimal algorithm, you are a smarty pants :P

That's how I subtract even now.

he was kidding, dude, he's not going to do fractions...

Oh, that wasn't too bad.Short division, and set theory.Try it!

Yes, and primitive was spelt wrong - but the video is fantastic

I think that's the point of the song. A bunch of satire

Heh... you haven't been to a math class since the '50s, have you? New math didn't die, there was just a couple of extraneous bits dropped and the rest stayed. The 'new' way of doing subtraction is what's still taught. Understanding how operations work is still taught. Now, getting the right answer is still important - if you're getting the wrong answer your understanding is off somewhere! But you can't get the right answer reliably unless you actually know what you're doing... try applying the 'old math' algorithm he explained to 2-3 if you don't believe me. You get either 19 or an infinite series of nines. And if you don't understand what subtraction actually is, you'll never know that's wrong.

Yeah, for a long time I had no idea what the 'original' method was, and the beginning of this always confused me. I finally understand it and it feels so much more relevant.

I teach undergraduate mathematics, and I agree with the sarcastically stated sentiment completely. If you understand what you are doing, getting the right answer is relatively trivial. This is especially true with calculators and computers that perform the actual calculation, but require the user to be able to intelligently set up the values and operations in a meaningful fashion. In a simple example, a child that can't tell the difference between 5-3 and 3-5 is in a great deal more trouble than one that cannot solve 5-3 without a calculator. On the other hand, teaching students tricks to solve specific types of problems gets them in a horrible mindset where math is a collection of tricks and techniques that must be memorized and used to get the right answer. These students memorize equations and tricks and procedures. You tell them to solve y=2x+1 when x=2 and they'll all tell you y=5. Tell them to solve for y=2 and your answers will be split between y=5 and "I don't know how to do that." Getting students used to the idea of approaching math as a logical thing that is supposed to make sense at a very young age means they'll be better prepared for algebra and trigonometry. Of course what actually happens is that teachers have just come up with a new set of tricks, because most teachers of young students do not have a background in mathematics. You have a similar deprivation in the physical sciences.

No, what killed it was stupid teachers being hard to fire and impossible to teach a more advanced math that better prepares kids for college level work.

You commie! :P

no, "Common Core" would be the original system, and "New Math" was what you were taught in school.

Haha. I meant that the reason was to show the work, and you don't have to get the answer right - also, that parents couldn't do it.

Nope, "New Math" would be the base-8 example, as well as Boolean algebra, matrices, and modular arithmetic. Things that are now reserved for higher-level math classes, because they're completely unnecessary for the elementary level.

actually, this song was written by a Harvard professor of Mathematics. in the 1950s

Grad student. Not quite a "professor" at Harvard. But he did teach at UC Santa Cruz -- "Math for Tenors"

The first example isn't really "New Math." "New Math" would be the base-8 example, as well as Boolean algebra, matrices, modular arithmetic, etc. Things that are now reserved for higher-level math classes, because they're completely unnecessary for the elementary level.

That part "I guess I have a math brain" is key. For those of us that do not--probably most of us!--insane mathematical acrobatics just turn us off to math forever.

Virtuoso80 I don't even get the old math

every body gets new math. There is no such thing as a "math brain", everyone can learn math if taught correctly.

You are also not in grade school. Making kids who just figured out base 10 do anything in base 8 is not "just the same process". The "New Math" stuff taught in grade school and probably turned off as many kids are route memorization.

I couldn't agree more. He even goes as far as making shit up. "and that leaves 5. Well, 6 actually but it's the idea that counts". Just, no. Math class very much expects you to get the right answer. No number of people who cry "but I'll never use math in real life" can take away from the fact that most of our modern conveniences are thanks to people applying math.

Sherlock Wright For the oblivious (you), he is making a joke by getting the wrong answer and seeing who in the audience would get it. He isn't making anything up, you just are unable to understand.

You're right, look at me, I'm so upset. It's not a joke if there's nothing to be actually ridiculed and the comedian has to pull facts out of thin air.

Warren Bloom He didn't pull fact out of mid-air (however, I think the term you were looking for was thin air). He is actually ridiculing something. Seems like you are the one making things up.

Warren Bloom Um.... do any of you who have replied to Warren's comment, including Warren, himself, realize that Tom Lehrer was a Professor of Mathematics at Harvard University in the 1960's when this song was recorded?

He carried the one. Basically instead of borrowing from the next place up and then subtracting (turning 2 - 3 into 12 - 3 then subtracting to get 9), he did the subtraction first, adding a -1 to the tens place when it went below zero. I like to think of it like a series of dials representing the places, one ticks down by 1 if the one to its right goes past 0 and loops back to 9.

@@BobofWOGGLE I know what you mean, but I'm not old enough to remember using that.

@@number3Ihatetoontown Neither am I lol

@Khaled Rapp It seems counterintuitive because your intuition is at least partially informed by how you learned. It's the same reason common core seems unintuitive to people who grew up with the "new" math, and both seem unintuitive to the people who grew up with the "old" math. Besides, unless we're doing word problems like "bill has 47 apples, he gives 8 to bob..." there's nothing "actually happening" when you subtract numbers. If we are doing word problems, carrying negatives is closer to it than borrowing: If I take 8 apples from 47, I don't take 10 from that 40 to add to the 7, then take 8 from the resulting 17, I take 1 from the 47, then another 1 from the resulting 46, and on until 40, from which I take 1, and now because I've taken 1 from "zero" we loop back around to 9, with a lower 10s count.

Patty Jeddy more explicitly, Tom was a Professor of Mathematics at Harvard Universityand a darn good piano player too ;)

May you send a link?

If you're 23 this isn't new math anymore. You learned this method in school it's just that Tom explains it in an overcomplicated way in the song to make a joke. I'm guessing you were born sometime in 1990 or 1989 right? You would have learned this method exclusively. You just don't reckonize it when it's explained like this.

No, I didn't learn math this way. At all. This is still NEW math to me. XD

SourBitters No. You are absolutely incorrect.

danilianian HOWW???? HOW IS HE INCORRECT?? EXPLAIN PLEASE FOR THE LOVE OF GOD

I'm also 23, and I definitely learned it the new way. But then again, I'm from Belgium. In my opinion, it is quite clear. When looking from the new way, it seems quite confusing that you would substract the upper one from the lower one, and then add a one to the next column (I mean, yes, I understand it, but small children might not). But I guess it just depends on which method you learned in school.

Weird flex but okay

It seems like in the new math, you have to understand how people in the far east do it.

He puts a 1 in front of the 2, making it 12. 3 from 12 is 9 haha

See I thought he might have done it a different way (after thinking about it for awhile). 3 and 2 are 1 number apart and 10-1 is 9. Some for 8 from 4 being 6... It's hard to make that work in my brain though...

In terms of digits, 0 comes after 9, and it goes around in a circle, just like baccarat. Once you cross over that "edge", you carry something from the place to the left. Also, this song came out in the 60's. Nothing to do with Common Core, although Common Core has repopularized the song.

***** It is something that should still be taught, though, especially if you are going to deal with computer arithmetic where this paradigm is important when dealing with the bit size of a primitive, such as an unsigned int.

That is why my young "college" friend, I can still do math in my head 20+ years since the last time I stepped foot in a classroom. That is why when I give a cashier $5 + 4cents for a $4.79 transaction, she looks at me like I am an idiot until I explain the logic behind it. That is why more than 75% of kids failed the new standardized testing in 2013. The solution to the failing US Education system is not a "new" way to solve problems. The solution is actually going back to the old methods of teaching which starts with memorization, good habits, accountability, and more importantly discipline and respect in the classroom, all of which are non-existent today.

Woah woah woah! Not letting that one slip by, those signs are correct thank you madam!

Jared Khan The crocodile eats the bigger number. Think of it that way...

***** Haha that's how my mom taught me, she said the crocodile wants the biggest meal, so he'll go after the bigger number. Of course, I would always draw the < symbol with teeth...

***** Haha, exactly! 'Under 35' therefore 35 is greater than your age.

The Definite Article me too!

1) Doesn't realise the song is made for entertainment purposes. 2) Insults the audience, when in fact it is he who is the moron.

Joshua Kippax Nah, I know it's meant to be funny. I don't actually think Tom Lehrer thinks the things he's implying here. I was more commenting on the way some people seem to be championing this song as a valid argument against what they perceive to be the failings of modern arithmetic education.

***** isnt math pretty much useless anyways? why is this a debate?

grimbladed wiseman well, ignoring the fact I don't believe in the concept of "usefulness", understanding how arithmetic works is not useless (ie new method). Route learning an algorithm to add/subtract/multiply/divide IS useless in the age of computers, (ie old method)

***** but you see... there is a valid argument here in that people don't all learn the same. if you try and impose the same methods on every one because " they're better" some people are going to fall behind. when i was learning subtraction they taught it by adding ten to the number then subtracting and i had a lot of trouble with this. i instead found the difference and subtracted that from ten. that made more sense to me and i got it right more often. the issue is that when you look for one solution to teach something better some people won't get it.

+AmesKtown YEP! only the words used to describe it have changed

The Noble and Mighty Beaver Yeah apparently everyone else is seeing a difference that I'm not seeing.

@@Powerofthepickle The difference is really a conceptual one. In the 'old math' system, you would complete the subtraction before any number was 'carried'. 2 - 3 = ... well, 9, I guess, but because we had to loop around we have to carry this 1 over here now and subtract it from the top (or add it to the bottom). This was handy notationally, but it was very abstract and some students had a hard time following it. New Math™ was meant to help this by increasing comprehension of why that 1 is moving at all. It adds more steps, but in was less abstracted in a way that was meant to help kids betten comprehend exactly what they were doing.

"Math is math"

Mathematics is mathematics!

God! Imagine all the times tables you'd have to memorise, one for each number base!