Tom Lehrer - New Math (Animated)
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- เผยแพร่เมื่อ 14 ต.ค. 2024
- The full 'New Math' song by Tom Lehrer animated by myself for a school project.
I created it in Flash CS4 and ran it through After Effects to convert it. I'm sorry it's not HD.
Thanks very much for watching, I hope you enjoy it and please do subscribe for more videos like this. - ภาพยนตร์และแอนิเมชัน
My favorite part is that this still works, because it's less about "new math is bad," and more that "explaining anything in depth makes it sound complicated."
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
it's funny how I'm super confused about the original ways to do it because I grew up when new math had been around for a long time.
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
I spent the first half of this video wondering what the heck he was doing until he started making fun of new math, and I was like, "Oh, there's the math I know." I guess now it's not new math anymore, it's just math.
it's math that's about as new as your Mets
LETS GO METS!!!!
Me too---my way is the "new" way.
I just broke out my translation of the Treviso Arithmetic published in 1478 (An Italian textbook from 544 yeas ago!!!) and that math is like the first one! It's very cool old tech! It uses overflow or modular arithmetic like in a computer. This make it so you carry, just like on addition, but on the *bottom* number instead. Neither seems faster or less error-prone that the other unless there are zeros in the top number. The old method doesn't get the clumsy borrowing chain problem since you're carrying the 10 left as you go.
"New math" lost a huge number of kids. The math my kids learned was distinctly different; it seemed clearer. There still was a problem that made my son cry despite him being pretty good at elementary school math.
@@megalocerus1573 Lost parents and their support too.
I love how all of these arguments are over Tom Lehrer's original song, and barely any of them mention how your animation caught the flow of Lehrer's singing perfectly...especially the sarcasm. Excellent animation set to this truly unique musical satire!
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
All of Lehrer's songs were written 50+ years ago and the vast majority of them are somehow just as relevant today as they were then
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. 🤷🏼♀️
One of my favorite songs from junior high, and the animation is absolutely brilliant.
Note to commenters: This recording is from 1965. When he says "over 35", he's talking about people born before 1930. This has absolutely nothing to do with the Common Core.
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?
"I hear you cry" lol. That's my favorite.
*_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've always been amazed with his incredible memory and his perfect control of his tongue, speaking fast and difficult words without stumbling, and while playing piano at the same time. I can't even talk while playing the piano.
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
When I arrived at MSU as a freshman in 1977 I was informed that I needed to take a remedial math class because my SAT score in math wasn't the best. For the final we had to do a problem in base 8. I went back to the dorm and that night pulled out my Tom Lehrer abum that had this song on it and the problem written out on the back cover. I listened to the album over and over again until I understood the principle. When I took the test the next class I got the right answer...I just did the problem wrong! I barely passed.
Then you screwed up twice... you didn't understand what you were doing, and you got the right answer 🤣
maybe don't study math from a song
Well, but it's more important to know what you're doing rather than get the right answer, didn't you listen to the song?
I suspect many people for whom math is not their strong suit relied on Tom Lehrer and lots of smoke and mirrors to get through math classes.
Fun fact: Lehrer means teacher in German.
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)
50 people don't know why 4 plus minus 1 plus 10 is 14 minus 1 because addition is commutative.
... right!
And so you got 13 thirteen tens and you take away 7 and that leaves 5.
Well, 6 actually but..
(hahaha)
The idea's the important thing.
@@asheep7797 i like how the argument is just wrong
a thousand more don't give a shit
4 plus minus 1? Or 4 plus negative 1?
In light of common core debates it is amazing how the debate has remained the same but what was new is now old.
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!
Huh...I didn't recognize the old way whatsoever, but the New Math made sense to me. That's how I remember being taught.
Until he got to 'Base 8'...what the hell?!
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.
I didn't realize, until this animation, that I knew new math.
Which is still irrelevant, as calculators and Excel are thing that exist.
It could be worse we could know Really New Maths as is taught to my brother which is unexplainable bullshit (and that is before I start on the wonderment of "Phonemes" which just mean you can't spell anything as kids don't understand what letters are but they know sounds)
yeah, and how dumb will you look reaching for one when your kid can do it on paper?
I prefer to see what I'm doing.
As a programmer, I do a lot of base conversions between base 10, 16, 8 (sometimes) and 2. Enough that needing a calculator for it all the time is too time consuming. But yes in general computers will just do this stuff for you.
No, it's not irrelevant. A calculator -- hardware or software -- can do the
mechanics of subtraction for you, but the "new math" attempts to teach you
the principle behind base 10 (or base 8, or whatever) notation.
Except that when you do lighting calculations for a spot light and you want to give it a smooth edge, calculators and Excel can't tell you that you should apply a cosine interpolation to the area you want to smooth out, let alone how to do it. That's why maths is hard sometimes. It gives you tools, but most of the time it is your job to figure out which tools you can use to solve a problem.
First you need to get that down, *then* you can tell Excel to crunch the numbers for you.
The "New Math" method of moving tens is what I learned in school. Your video actually helped me understand base 8 better.
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😂😂
This song was performed in 1960's. Most American kids learned this so-called NEW MATH in the 1960's in public schools. It has NOTHING to do with NCLB and Common Core, etc. New Math was abandoned for other methods for better or worse. Leher would have a ball with Common Core! Too bad he's no longer performing.
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.
I love how instead of hating on new math he just makes both sound needlessly complex. Tom Lehrer is truly a genius
“ Well, you ask a silly question, you get a silly answer.” That’s a classic line.
Not what I teach MY kids:... "A stupid question CERTAINLY needs a sensible answer!"
Parallels with computer jargon: "Garbage in - garbage out"...
Whenever I hear some complain about "Common Core" and how they don't understand how kids are being taught maths, I just point them to this song and remind them that's exactly what previous generations said about how we were taught.
+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.
Well...the "new math" in this old song actually makes perfect sense, just like teaching kids to understand what they are doing makes sense. But what this song demonstrates perfectly, is that:
1. people will generally be sceptical of new things and new ways,
and
2. it is easy to make fun of things that you (or in this case your audience) don't understand.
I think you do Mr Lehrer a disservice. I got the impression that he's making fun of the people who don't understand why this method is being taught when it's "so much more complicated". He was a Maths teacher after all.
@@Musikur Well, it's a satirist's privilege to satirise any way he wants to, but as you say, he was a maths teacher, so he probably knew the value of the "new math" as well as anybody, but he could also understand confusion among (mainly) older people who'd learned a different method.
It's worth noting that in 1965, he'd be 37, so probably learned the old way himself originally.
I was in primary school (In England) in the 1950s, and definitely learned it the old fashioned way. Interestingly, when I was in the top class of the primary school (aged 10 or 11), one day we had a visitor come into the class who taught us something he called "gypsy arithmetic". I can't remember the details (wish I could), but I have a feeling it used the elements of "new math" without calling it that. It was not a written method, although you may have been allowed to use your fingers.
I think that, other than people who are going to become mathematicians, scientists, or engineers, it's actually not all that important to know why it works, and probably less so in those days, when the majority of people went into manual or clerical jobs. All they needed was a way to get the right answer every time. Understanding could come later, for those of a questioning mind, or who had a natural gift. Of course, there were no personal calculators at that time.
BTW, googling seems to reveal that "New Math" was being dropped in the USA by the end of the 1960s, although it may have survived in some districts.
In the UK we had various attempts to modernise maths teaching. The following is quite a long story, and in some ways, quite a depressing one:
emaths.co.uk/index.php/blog/item/a-brief-history-of-mathematics-education-in-england
@@mikewellwood1412 For what its work the "new Math" method for subtaction is what I learned in the early 2000's it was a private school though so who knows.
Edit:
Did some googling, I think most of the werider parts of new math got toss out liketrying to teach preteens what base 8 was. But the idea of taking someting from the tens place stuck around to my time.
you arrogant prat. tom lehrer forgot more math than any of us ever learned. people are skeptical of bullshit emperors wearing new clothes.
@@Platinum_Squid I think the teaching in different bases was what made up the core of new math, because taking from the tens place is basically the same thing done in the old math, just written down.
Wow, your animation is really well done and gets Lehrer's (somewhat misguided point) across clearly. I'm a math ed PhD student studying the history of school mathematics, so I'm grateful for this video. We'll probably end up using it tonight in class :) Thanks!
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.
I memorized this song and dance back in 6th grade (1972) and did it in Math class...
Naturally I got an A++! While doing the base 8 bit, I noticed the teacher rolling on the floor in laughter at the back of the classroom.
Apparently he was well aware of Tom Lehrer and the song! Later, I attempted to memorize The Elements for Science class, but unfortunately, I couldn't get the whole song down in my head...
You should do one for "Lobachevsky", with a map of Russia! That would be fun!
O that would be amazing.
The pre-1965 method said:
3-2 = 1 & 10-1 = 9
Then either:
4-1 = 3 & 7-3 = 4 & 10-4 = 6
or
7+1 = 8 & 8-4 =4 & 10-4 = 6
Then either
3-1 = 2 & 2-1 = 1
or
1+1 = 2 & 3-2 = 1
The "New Math" 1965 to sometime recent is what most of us learned in school and is described in the song.
The "common core" number line method would say:
Start with 173 and add little bits at a time, whatever you're comfortable with, until you reach 342, so 173 + 7 = 180 + 20 = 200 + 100 = 300 + 40 = 340 + 2 = 342.
Then add up all the little bits you plugged in so 7 + 20 + 100 + 40 + 2 = 169
The "common core" chunking method would say:
Split the each number into 3 separate numbers, each with only one non-zero digit. This method is not recommended when you need to regroup/borrow because apparently teachers think this is too hard. But here it is:
300 - 100 = 200
40 - 70 = -30
2 - 3 = -1
Then you add up the differences from each chunk (in this case subtracting because some of the values are negative) so: 200-30-1 = 169
I love his old-school, nasally, American accent.
East coast Harvard jew
It was recorded in 1965
@@shatterdpixel the year that was
he sounds like those old hosts you here on the telly
@@raspberrycrowns9494 he still sounds the same no joke
I ljust love the way he says "fractions" at the end. Cracks me up every time.
As a mathematician I have a very great appreciation for New Math, though I’m young enough to be baffled by the previous way, because the algorithm he describes is also applicable to doing the same in polynomials (1234=1*10^3+2*10^2+3*10+4) or in base ANYTHING (my favorite is base 13). In fact, every arithmetic algorithm you learn with New Math applies this way, just with a couple extra steps. I think that’s pretty cool.
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.
I showed this to my parents (born in the early 50s) and they were stunned to find out that they'd learned New Math. I had to literally 1) suss out how the frick old math was supposed to work and 2) explain it to them.
The funny thing about the base-8 example is that it shows the value in prioritizing understanding what you're doing above getting the right answer. Old Math was just memorization; 'New Math' is applicable to any base.
I don't know about the "new math story", but I totally agree with the sentence at 1:11: the important thing is to understand what you're doing rather than to get the right answer.
Firstly, if you really understand what you're doing, you can do things more reliably. Because you don't have to rely on sheer memorization, you can see if you're making an error in a formula, or if you get an inconsistant result at the end. But by applying a method blindly, you can write complete nonsense without even realizing it.
Secondly, it allows to do more thing. If you learn a method by hearth, you can only apply it. But if you understand it, you can adapt it to other situations, make a similar method for another case, or making it into a computer program.
Thirdly, memorizing things is boring whereas understanding is interesting. And people are way better at things they're interested in, so making a subject interesting is very important. Many people think that math is just memorizing and applying premade methods, and don't understand why some people like it. But the core of mathemetics is completely different, it's understanding how things work. And this is the reason why math can be so interesting. Unfortunately, education too often focus on blindly applying methods, which is not very useful: children will pretty quickly forget them because it seems arbitrary and many of them will hate the word "math" for the rest of their lives.
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..
When your mockery of a teaching approach ends up being the best explanation for that approach. Someone is in trouble
*trouble
The best animation to the song I've seen on TH-cam.
You could've pasted a bunch of crappy pictures like the rest, but instead you put work into it to allow us to think through the comedy ourselves.
3,840 people (plus) appreciate your effort.
This video is the inspiration for my own animated version of this song.
Did you do it?
@@gustavoabreu3097 th-cam.com/video/gP80KAQ0Og0/w-d-xo.html
"Ask a silly question, you get a silly answer." is still one of my favourite lines in the entirety of comedy.
More tragedy than comedy. If you really think about it.
Gotta love those Greeks!
I got this record in 1967 and have certainly enjoyed "New Math."
Two years later I got a book by magician and memory expert Harry Lorayne, who included a chapter on simple arithmetic and, as far as I am concerned, turned the matter upside down and made no allusion to Lehrer. I had not had the best of skill in arithmetic in grade school; by this time I was out of school and picked up Lorayne's tips, which allow the learner to do arithmetic problems left to right.
When I was in school, every problem in my math book said "How do you know?" after it. I was tempted to, just one time, write "BECAUSE I AM BATMAN."
+C.J. Stanbridge One time, in about 5th grade, I wrote "did it in my head" when asked to show my work, because that's how I did the problem.
+almostfm good comment
I knew one kid who just drew a brain.
👏👏👏👏👏👍 that is so funny if I did want to be a teacher then I would hope one of my student would want to do that. I could never be a teacher
I remember in elementary, every book I had, inside the front cover, said, "THIS BOOK IS THE PROPERTY OF:" and in fourth grade, I had a book that said Tyson in it. I told someone about that in tenth grade. I think he dropped out, but at my high school reunion this year, someone asked why Tony Carter wasn't there. When I heard Tony Carter, it made me laugh and I said I was thinking the same thing about Cole Duren, who only went to my charter high school in ninth grade. Ricky Carter was Tony Carter's twin brother. I think Ricky Carter punched the PE teacher, Mister Walsh. Mister Parker got fired when I was in ninth grade, and Mister Carver and Mister Walsh got fired when I was in tenth grade. The school opened when I was in 8th grade and my older sister was in tenth grade there. That was the year that I thought only smart people went to school there. After my first week of ninth grade, I realized that I was wrong. I had seven classes with two people, who had eight classes with each other. I don't know what they had sixth period, but I had a homework class. I had the same teacher second and sixth period, and the same classroom with different teachers fourth and eight period.
I was born in the 80's so I came up on new math. It was easy. I looked at the old way 3x. I had no idea that existed. I don't get it. So, yes. HOO-RAY FOR NEW MATH.
They didn't use "new math" by the 80s. It gets a lot more confusing.
what's funny is I'm one of the kids who had learned "the new math" and it's what I still use to this day...
Then my kids had "Common Core" math... and I was absolutely stunned by how dorked it was... lol.
Then again... my kids didn't need to do "Octal" manipulation (Base 8).
Parents of the first few classes to be taught “new math” also thought “new math” was a dumb idea.
Mostly because it wasn’t being taught the same way they remembered being taught.
This song was recorded in 1965 and it’s still relevant today.
I'm only 20, so I don't even know a different method than the "new" math. Its just math. What was the old way like??
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.
This was made way back in the 1960s, given the reason why it sounds like a song you might here from a barber in the olden days. This method was considered as new math since it was thought as clever back then but now we use it every day.
Jared Khan, you did a Bang-Up Job with the Visuals, which really added to the performance!
Excellent animation, Jared. Most people scoff at "New Math", but it's true --
understanding the principle is more important than learning the mechanics by rote.
Tom Lehrer's explanation is actually quite good. BTW, this is from circa 1965, as I recall.
That Was The Year That Was, 1965
I was taught the "new" method of subtraction in schools. Made perfect sense and I understood every bit of it. I've never used it. _Ever._
Instead, I used a method I'd figured out on my own: If you can subtract the digits normally (e.g. 8-5), do that and move left. If not (5-8), subtract the smaller number from the bigger one anyway (8-5=3), then subtract the result from 10 (3 becomes 7). Then subtract 1 from the top number in the next place over before you start on it.
Today I learned that this is the normal "old math" method for people "under 35 or went to a private school". I invented it on my own, I've always used it, and it's never made a lick of sense to me.
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.
I remember both New Math in 7th grade...1961-2.....
Also,I remember this song.I was surprised to find it here on TH-cam
1960’s: computers starting to be used in business. Elementary school math teachers felt we should understand very early that not all number systems used 10 digits. They tried to teach us base 2 and octal arithmetic. I remember doing this in 2nd and 3rd grade. Not a fond memory.
I'm gonna cry in a corner thanks tommy
that growl at 2:13 though
Thanks, Jared. My neighbors just banged on my door, to get me to stop laughing. Old favorite...
I love this bit by Lehrer and I think your animation adds a lot--especially showing the "work"!
That was just wonderful. Thank you for the animation, it truly brought the song to life.
Doe anyone else do math with "approximations"? For example, with 342-173, I'd subtract 170 from 340, getting 170. Then I 'd subtract 2 from 3 to get -1, add the answers and get 169.
Oh, absolutely, I did that all the time in school.
@@TheWanderingLPer Me too!
That's... Common core.
But...I understand it...
***** I thought the song was from the 50s, or was this one of Tom's newer ones?
TrekkerLLAP
1965 actually. The album was called "That Was the Year That Was"
yeah this isn't hard
Tom Lehrer made this back in '65. So, unless you were already an adult back then, you likely grew up with the New Math.
And being an adult already back in '65 means that nowadays you'd be at least 53 years old.
I WAS born in 1965, to the young wife of a PhD math candidate. Neither is dead. Still married. Still in their 70s
At first I had I was extremely confused when he did it in base 8 'cause I'm young and never heard of base 8, so I googled it and now I understand the full meaning of this song. I love Tom Lehrer.
My dad showed this to me when I was very little. When I got to learning "the subtraction algorithm" in third grade, I was very glad I had memorized this song, even though I understood none of the jokes.
A brilliant visual to accompany a brilliant song. Thank you, Jared Khan!
I have no idea what he was doing before "new math", but I grew up with this math and now there is a new new math. I am not sure how it works aside from it is completely different.
pure musical genius. incredible talent.
And now there’s new new math. New math actually made a lot of sense. Because you’re going through the steps, there’s less room for error, especially for children. As an adult, I can subtract in my head just fine without going through the whole borrowing stuff, but it helped when I was 6
Loved the animation ... especially the "You're" over the "your" :)
I loved this when he first came out with this because I was learning "New Math" in school at the time!
Absolutely brilliant animation! Thank you for sharing your school project!
And Jared, I'm a guy who learned his computer languages from Kemeny himself, fighting the DTSS! Such an admirer of Tom Lehrer. Driest stand-up comedian (immaculate timing!), most versatile pianist, most relaxed tenor, ever, and a consumnate mathematician, and teacher, as well. Still prowling the library at UCSC, last I heard. Thanks!
O. M. G. ... It's the COMMON CORE of the 60's!
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"
I love this. It's simple, so very simple, that all but a child will even understand the base-8 subtraction part.
Apparently, they taught octal to children back then because they thought it was important for computers
Lehrer actually makes some conceptual errors in this. He treats a one in the hundreds place as a one in the tens place, rather than as ten tens or a hundred
I figure that was to keep the patter going.
My dad was the director the new math program, and was asked to review the math in this piece before it was released. He found the song very funny.
The animation makes it even more funnier (and I have to admit more understandable for not native speaker like me). Well done!
tee hee hee
I was raised with the new math in this video. Now there's another new math- so I can't help my little one either. Just crazy. Lol
It seems like in the new math, you have to understand how people in the far east do it.
wow! Old maths is new and New Maths is old to me now!
The part on base 8 is actually helpful in computer science.
I've heard this song before, but because of the animation this is the first time I ever followed the words carefully, and I was surprised to realize that Lehrer was actually saying something that made sense (unlike, say, The Vatican Rag, which is funny but doesn't really tell you anything useful about the Catholic faith). In particular, I realized that the "New Math" is how I was taught math in elementary school back in the 1960s, and that "the way we used to do it" was unfamiliar and rather baffling. Three from two is nine? Eight from four is six? _Huh???_ I had to think about it for a while to figure out why it worked. Is that really the way they used to do it? The "New Math" makes a lot more sense to me! But then I was always good at math (ended up with a degree in physics), so maybe it's just that the "New Math" was targeted at children like me.
My dad used to play all of Tom Lehrer's songs - you did a great job with the animation!
I was taught that you borrow from the tens place where you cross out the four and put three. Then you put a little one in front of the 2 to make it 12. 12-3=9. Then in the tens you now have 3-8, which also does not work so you carry over from the hundreds place, crossing out the 3 to put 2 and putting a little one to make 13 in the tens place. 13-8=6. Then in the hundreds you have 2-1=1. I don't get the old math. The base 8 was something I never learned either. I'm 17.
Learning any base but 10 is not useful unless you are going into a field where it will be. And if you are, then you can always learn it once you decided to go into that field. A young adult will grasp this much faster than a frustrated child. Teaching any of this to someone who is just learning column subtraction in base 10 is criminal and just produced a generation of math haters.I understand the basics of base 8 but I'd have no idea how base 16 would work. In base 8, 8= 10 so 9= 11. Okay cool. So base 16 is 16= 10, right? But what about 6 to 1? Technically 6 would be 0 then and going down the line, 1 would be -5? Or I'm just getting this all wrong because I just can't wrap my head around it?? Obviously, I'm NOT in a field where any of this is useful.
Mc Hobbit In Base 16 you use the digits 0-F. 0-9 work like normal, A = 10, B = 11 and do on to F = 15. From there it works identical to your understanding of other bases.
@@mchobbit2951 Not that you'd probably use duodecimal (base-12) either, but like hexadecimal you also use placeholders for single digits; 1 through 9, dec (either a stylized D or a cursive x), and el (a lowercase epsilon) for what would be ten and eleven. Do (pronounced like do-re-mi &c), written 10 in base-12, is where you start again.
@@aqacefan You might if the dozenalists get their way!
I love that people seem to think that this is validation of their hate of Common Core era "New Math" and their belief that would should stick to "Old Math" when what Lehrer is jabbing at is their "Old Math."
Sophia Goodwin Only if they're 40 - 60. My mom (born in the 60s) learned New Math as a little kid, I (born in the 00s) learned "Old" Math. New Math was a failed experiment
Still waiting for fractions
he was kidding, dude, he's not going to do fractions...
Oh, that wasn't too bad.Short division, and set theory.Try it!
Superb, subtle nuances, timing and form all excellent. I loved this song the first time I heard it (50 years ago) and you have improved it - very well done.
I subtract from left to right. Such a rebel.
You commie! :P
"New Math" had its U.S. national television premiere on That Was The Week That Was (NBC, April 6, 1965). Lehrer wrote numerous songs for TW3, but didn't perform any of them. The "New Math" segment featured Buck Henry as a mathematics teacher and Nancy Ames as an exasperated parent.
May you send a link?
I am 23, working with mathematics, and I honestly cannot understand this new math method. It seems to take twice as much time. The children seem confused as well, honestly...
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.
The kicker: if you pay attention to the old and new methods, they are doing the same thing in the same way. The "new" method just spells out the implicit borrowing the "old method" is doing anyway. 2-3=9 carry 1 (the first step of the old method) is just 12-3=9 borrow 1, since the carry digit is (as said) either subtracted from the top or added to the bottom of the next column anyway. It just doesn't take the time to note or explain the borrowing until we get to that column.
1:01
and that's, ironically, what KILLED the New Math.
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.
It's funny cause the 'new math' is our basic math now. common core is now our 'new math' math.
"Understand what you're doing rather than get the right answer"
GCSE sciences in a sentence
Something like that.
Tom Lehrer was something special. His songs were both educational and made me laugh.😊
1) Take two ways of doing things, one that audience already knows, one that they don't.
2) Say "You all already know how to do one of them because you spent time learning it"
3) Go though old method quickly because everyone already understands it.
4) Go through the new method way too quickly for anyone to pick up for the first time.
5) Let morons wallow in their preconceived notions that "everything was better back in my day".
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.
Amazingly, Tom Lehrer is still around in 2024. He's 96 now and hasn't performed in public since 1972. Don't ask me to explain that in Base 8.
I guess I have a math brain, because to me there's nothing absurd about the new math. Both ways are essentially the same and equally easy/difficult, and then the base 8 is a tad harder, but just the same process in base 8, so what's the big deal? Actually it's kind of nice.
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.
How talented was this Tom Lehrer fellow? Complicated , humorous lyrics while playing fault-free music.
He was a Math teacher
Patty Jeddy more explicitly, Tom was a Professor of Mathematics at Harvard Universityand a darn good piano player too ;)
Currently working in has 2, 8, and 16. I think of this song every time 8 comes up
At 1:05, you said "your" when the correct word was "you're"
Yes, and primitive was spelt wrong - but the video is fantastic
As a second grade teacher who teaches three-digit subtraction, I find this very amusing... The 1960s "new math" in this video is now the "old math" that parents complain we don't teach anymore. (We actually do teach it, and it still becomes the default method for most of my students. But we also teach other strategies for students who can't grasp crossing out and changing a bunch of numbers.)
Apparently new math and old math are exactly the same thing.
+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!
I got to work with those colored sticks of different lengths when I was a kid. Because of that, I automatically 'know' that 12-3 is 9 and 14 - 7 is 7.
... I never learned about Base 8... Never even heard of it O.O
PrideInIndividuality I was told how to use positional notation when i was 11 years old.
PrideInIndividuality Base 8 just means, that instead of adding 10 to the your number when you "borrow", you add 8 :)
PrideInIndividuality Base 8 (octal) s not much used. Base 16 (hexagesimal) is more common, the numerals running from 0 to G. The Babylonians used base-60 (sexagesimal), which has many advantages, division not being one of them.
+Jim Roberts almost right ... hex is 0 to F. Octal is used most of the time when setting UNIX permissions (chmod 755 myfile.html)
I love it when mathematicians come together.
I went to school in Ontario in the 70s and 80s. From Peanuts cartoons, I had heard of the terrors of "New Math" in the US. From every encounter with the question since, I still have no idea whether I learned old math, new math, a hybrid of the two, or something else, nor did anything ever explain to me really what differed or why one was better.
This is what I learned, although my Math teacher described it a lot simpler than this.
Sorry but CC math in america is fucking comedy central to me.... no wonder people are so dumb... besides i consider anyone who cant calculate 3digit numbers in their head not very intelligent ...
***** Assuming you mean subtraction and addition not including division and multiplication or your expectations are insane :P
***** ok how did your subtraction method work
***** cuz I learned subtraction the way the song does it and I was lost the method in the beginning totally lost me. So I wondered how to do it the old old way
+tyrannisis lucifaeris well me from the past it was easy to learn.
and the even MORE modern approach is to say the answer is zero, because it's all just a social construct.
3 from 2 is 9? WTF is that? And that apparently made more sense? I literally cannot make that work in my brain. I showed it to my college roommates and they were all "WTFing" too.
If people thought the world was collapsing with the introduction of this when to kids, like me, who grew up with it it's much more logical I wonder if this uproar over common core is largely exaggerated.
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.
I was hoping for that fractions lecture...
Shame it never happened.
I would have loved that. :(