Tom Lehrer: New Math (concert live) (1965)
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- Опубликовано: 23 ноя 2024
- SMALL NOTE: When Tom talks about "subtracting" or "taking away [A] from [B]", he really means "B - A".
For example, subtracting 2 from 5 is the same as 5 - 2, which is 3.
The first part of the video (my signature slide) is overlaid by the final bars of "La Borinqueña", which I played on my keyboard.
The main part of the song is one of Tom Lehrer's live performed songs, "New Math". It is part of Tom's third published live performance album, "That Was The Year That Was". But I obtained the actual music from the box set, "The Remains of Tom Lehrer", which was released in 2000. Enjoy.
And the last part is the main theme of "The Phantom of the Opera", by Andrew Lloyd Webber. Simply the 'cherry on top', and my personal song.
Here's the description Tom Lehrer himself made about the song: "Third, for the benefit anyone who wants to follow the subtraction problems worked out in 'New Math', they are:
342₁₀ - 173₁₀ = 169₁₀ and 342₈ - 173₈ = 147₈.
(If this doesn't make any sense to you, ask the nearest eight-year-old you meet to explain it.)
[This attempt to revise the teaching of mathematics in schools was something of a threat in 1965, but it subsequently passed through the curriculum, not like a breath of fresh air but more like a kidney stone.]"
Sorry I gave so much information about the music earlier. I don't want to get screwed by stupid WMG again. They are a bunch of arse-holes. And to make sure I am not screwed, have them read the following credits:
Recorded at the hungry i, San Francisco, CA (7/26/65-7/31/65)
Produced by JIMMY HILLIARD
Engineered by DON GEIS
From the album "That Was The Year That Was," Reprise #RS-6179 (1965)
"The Remains of Tom Lehrer" Compilation ℗ 2000 Warner Bros. Records Inc. & Rhino Entertainment Company.
It has just occurred to me that The Incredibles is set in the sixties and Bob has trouble with Dash’s math homework so bravo to Pixar on that one
Great observation! That makes the movie a lot cooler :)
The movie review really jumped out at me. "Daaaaad," he says. "That's not the way they want you to do it." His Dad complains, "But I don't know that way! Why did they have to change Math? Math is Math! MATH IS MATH !!!"
The first one might be, but in the second one they clearly have cellphones, it's an important part of the plot.
Parents struggling over their children's homework is a time invariant.
@@inigo8740
Yeah I mean look at today with common core
@@inigo8740 we don't talk about 2nd one
He makes the new math sound complicated as hell, but since this is the way I learned it, to me it makes actually perfect sense xD.
Judith, it's not weather you get the right answer or not. It's if you understand what you've done!
How's the weather where you are? . . . Whether or not you understand what you've done, imho, it is important to get the right answer.
He's a mathematician. Give him some space to joke about his own job or something.
Its the same method, but done idiotically by breaking it down in a pointless way.
Ex: 111-89
"Old" Method:
11 - 9 = 2
10 - 8 = 2
Answer: 22
New Method:
(10 * 1 + 1) - 9 = 2
(10 * 1 + 0) - 8 = 2
Answer: 22
I've included the tens place in the "old" method, for visual clarity, since it is still basically there. As a student, I primarily use the "old" method, and the new method just gives me headaches, and causes me to mess up by overly complicating things. I fucking hate this, since this pointless crap seeps into my thought process, and wastes my time by causing me to repeatedly check my work. Thanks elementary school!
They dumbed it back down to the old math for me, and it still hurt.
This new stuff nearly killed me!
This song is so old the new math has become the old math, that new math has become old and now we have a new new NEW math.
Really? I'm in school currently and we still learn math like this.
My parents had to teach me the old math because I didn't understand the new math and neither did they, and I was like this so much easier and makes sense
It's just a bunch of useless eggheads, trying to re-invent the wheel.
I thought the new math was just the old math taught to a generation that has completely forgotten that math was different?
new new new math is just new math though. new new math was a failure, so they switched back to new math.
Hadn't heard this in a long time. What a clever and funny guy. He's 92. May he live to 120.
Why stop there? I’d be glad to see him live to 180(get the ref? 😜)
@@jmwoods190 Just a matter of ... degree.
OMG he's still alive
Proof that tom was the bo burnham of the 20th century
*Bo Burnham is the Tom Lehrer of this century.
Also I discovered that Tom is actually still alive, the other month.
@@captainjirk9564 ...barely.
@@davidlafleche1142 Aren't we all?
@@davidlafleche1142andddd he’s still alive! So much for “barely”
@@Orincaby Yes, but have you heard him? His voice is very shaky.
I genuinely can't comprehend how they did math the old way.
They memorized math facts I think
IDK about neurotypical people, but some people with ASD and/or ADHD (myself included) can just kinda do mental math like that. Like, the regrouping is just kinda intuitive.
Super simple and easy the old way.
Yeah, more or less! They taught "why" for initial math ( think single integer addition/subtraction/multiplication/division) and alongside did a lot of drills for memorizing them after you got the general idea. I remember getting homework pages of columns consisting of
0+1 0+2 0+3
1+1. 1+2 1+3
2+1 2+2 2+3...etc
They'd do this and then randomize the grids for testing. Once you know how the single digit integers behave, they taught shorthand formulas that work for all larger numbers. It works well and is intuitive for those of us it clicks with, though if you got shakey foundations in the initital arithmetic for one reason or another, or if you think in really spatial terms as opposed to more abstract ones, you'd start falling behind fast and people would have a harder and harder time trying to catch you up.
I remember tutoring people who were perfectly capable of doing long division, but couldn't do a simple sum in New Math. And yes eight squared is 64.
As someone with a mathematical disorder this is basically what any modern math problem harder than 10x10 sounds like to me
What is “mathematical disorder”? How is it different from not being good at math?
@@jeffburns4219 it’s a little hard to explain but basically no matter my age or the effort I put in, anything math related just goes… poof in my mind. Like dyslexia but for numbers. I’ll be adding up the simplest equation and I’ll just suddenly forget the numbers or what I was even trying to accomplish with them. Anything above fourth grade level feels and sounds like gibberish to me (like in the song). I actually find math really cool! I’d get good at it if I could
I believe "dyscalculia" is the word you're looking for
I am very dyslectic, and have a tough time with numbers aswell.
I've always found it difficult to describe, but I feel it comes down to the task of processing letters into words, or juggling numbers in ones brain, these don't fit well with the way our brains operate.
I think that's why many (including myself) describe this "error" type of feeling.
90s kid here... in my 30s im beginning to realize the amount of ways to be "objective" and/or "efficient" render both concepts as self defeating.
was taught math like this, and due to my adhd, it was incredibly difficult as my short term memory isn't good enough to remember all the steps i have to take AND the numbers i'm using at the same time...funnily enough, the things we were just told to memorize, like timestables, actually stuck. And i know how to count by eights purely because of minecraft, LOL.
really?
Minecraft has base 2, base 8, base 16, and base 64. Plus coordinates, which are base 10, and have chunk coords (base 16) and region coords (base 32). So a lot of fun number systems, with only base 10 having a prime factor other than 2.
I don’t think that people realize that this “new math” was new in 1965
@@stardust86x it is still relevant though because there is a new math strategy that elementary school teachers must teach. It hasn't made it to my high school classroom yet but it will and then I will be stuck trying to learn "new math"
Tom Lehrer was such a genius.
A HARVARD professor who might have treated students to some of the greatest songs since that time.
“We’ll all fry together when we fry.
We’ll be French fried potatoes by and by.”
Friends and I obsessed with memorizing the best lyrics.
NEW MATH comes around every so often. Nobody writes songs about the ‘newest new Math’.
But it’s all asinine. It was then, it is now.
Thing is because I was actually taught "new maths" as a child in the sixties I found it was actually fairly straightforward to follow his base 8 arithmetic.
Still not as easy as the bar of just receiving one and adding it to the other lol
@@marineopferman Base eight is at least as easy as base ten (easier really, because eight is a power of two). You’re just used to base ten. A tabula rasa student will not be used to any base.
As a kid, I listened to this song over and over again, just so that I could eventually sing along.
Then I actually _listened_ to the words.
And that's how I learned the concept of bases.
[And yes, Base 8 would make *perfect* sense for a four-fingered species! Base 10 for them would be like hexadecimal for us.]
Number of fingers does not indicate what base number would make sense to a species. While decimal may have been inspired by our ten fingers, that does not mean that it is innately intuitive to humans. It's just one of the many, many systems that could have become predominant.
Seximal made *perfect* sense to the Proto-Uralic people. Duodecimal made *perfect* sense to many ancient peoples from Nigeria to Egypt (And is used in our current method of time keeping). Vigesimal made *perfect* sense to the ancient Celts and Basques, and still makes perfect sense to Inuits who use the Iñupiaq numbering system today.
None of them are any more or less innately intuitive to our species than the others.
Why would our base 10 be decided by fingers when we have 20 fingers and toes combined?
@@Penquinn14 Maybe because toes are busy keeping us walking, standing and/or are stuffed into some sort of footwear and thus otherwise occupied. The fingers are at the ends of our hands, practically begging to be put to use manipulating our environment.
Now if we had TEN-fingered hands, then Base 20 might feel natural to us. Donning gloves would be a royal bitch, though...
Base eight is base 10 if you’re missing two fingers, that was a brilliant analogy. Even though they denied him tenure, Harvard didn’t hire no dummies lol.
Pianist, singer, comic, teacher and above all mathematician. Pure respect.
And worked for the NSA
Not to mention a brilliant lyricist!
It's crazy that New Math was the 'convoluted' way of doing math in the 60's (even though that's what every adult uses today), whereas Common Core is today's convulated way of doing math.
To be honest I didn't even know that the way I did subtraction/addition had a name until this video!
As a student I understand it, as a human watching it I lost track after you started singing
yeah, the song was kinda made to make fun of how "complex" new math seemed at its inception
He's from the 60's but he sounds like he could be present day. Like a 60's bo burnham.
i think the same thing all the time !!
They both have a song called New Math
@@lanceroan7561 Because they both got math changed on them after they graduated.
I think what you mean is that Bo Burnham is a 2010s Tom Lehrer. 😁 Tom Lehrer’s music was censored and even considered “too controversial” to be released on a record label. He had to sell his first 400 records himself on campus. A local record store helped sell as well, with a minimal markup. Pretty soon, the record became viral through word of mouth, although, as Lehrer himself said: “Lacking exposure in the media, my songs spread slowly. Like herpes, rather than ebola.” People were writing him from the other side of the US, asking him to mail them copies of the album. My parents were in college when he started writing the music for the American version of TW3 and became well known. I grew up listening to his music, since my folks were socially liberal boomers, and also because he wrote songs for The Electric Company kids’ television show.
This man was ahead of his time.
No, Lehrer was right with his time. One guy who was 30+ years ahead was Stan Freberg. Look up "Elderly Man River." Freberg nailed "Political Correctness" long before anyone even knew what it was.
My grandad showed me his O level papers (the exams taken in the UK at 16 which were replaced with GCSEs in the 1980s) and what surprised me was the lack of working out space. This explains why.
this guy belongs in the modern age . oh wait hes still alive,
Grew up in the 60's as something approaching which in those days was called a 'beatnik'...... my red book waving Maoist mates and I used to listen to this chap on a regular basis .....'An evening wasted with TL' was my particular favorite, but they were / are all still good. At 70, his drole witticisms and subtle remarks still bring a smile to my face and time warp me back to intellectually unstimulating, pot smoking, baked beans eating, cheapest wine you can get (guaranteed to get your eyesight back in a week) , everyone dressed in black, wonderful evenings. Nowadays we say 'emo', I suppose. Many thanks for uploading.
+Stewart Liebenstrudl - Aw, thanks! I'm glad you enjoy it. Songs will be uploaded once a week, every Saturday. Feel free to check out the full playlist by clicking the card in the top-right corner.
"The important thing is to understand what you're doing rather than to get the right answer." Truer words have never been said about math class.
Also I was taught this way of doing math in elementary and middle school... We had to review base 10 at the start of every year for 6 years! And DON'T even get me STARTED on multiplication and division! I couldn't get past 8s and didn't get Oreos on my ice cream sundae at the end of the year!
BTW, at the time my mother confirmed what Lehrer Tom said about borrowing in subtraction ("if you're over 35 or went to a private school ... "). I learned subtraction by 1960 and we always borrowed from the next higher column by reducing its top digit by 1, but she, being over 35, had learned it by adding one to the lower digit.
Ok, I posted a reply, but it disappeared for some reason. My question is, Why did your mother learn to add one to the subtrahend instead of subtracting one from the minuend, like we used to do it?
@@AlexSh789 Because when my mother was learning it in school, that is the way that they taught it. I have a 1914 arithmetic text book (The Walsh-Suzzallo Arithmetics, covers the first six years of school math from counting to filling out the basic paperwork needed to run a small business (that last within 10 pages)) and that is the way that the book teaches it: 90-74, so when you borrow, you "Carry 1 to 7 which makes 8" (quoting from the text book). My mother was born in 1918, so she would have learned this same method around 1926. Judging from Tom Lehrer's remark of "if you're over 35" made in 1965, it would have been in the late 1930's that they changed from the old method of borrowing in subtraction (which is referred to in the text book as "carrying") to our current method (at least as of the 1960's -- no idea what might have happened since then).
We do things the way that we were taught. And the way that we're taught changes at times. She was taught one way and we were taught another. Frankly I think the way we were taught makes more sense, but I'm sure she felt the same about the way she was taught.
I see. It's still a mystery, who came up with that method in the first place? I'm just like you, even though my education came 30~40 years later. (I'm sorry if I made you feel old.) To me, it makes much more sense to subtract one from the minuend (to take a ten and change it to ten ones) because I grew up with that method.
I also remember learning it with physical blocks, similar to Legos. Ten blocks would form a stick, a hundred blocks would form a square, and a thousand blocks would make a cube. For this example, changing a ten to ten ones is the same as taking a stick and breaking it into ten blocks.
I am sure, someone who grew up with the old system (adding one to the subtrahend) would have an equally valid reason for using it. I would love to talk to someone who actually used this method when they were growing up.
@@AlexSh789 There are many older methods of calculation, many quite ingenious and which appear totally arcane since they make use of number properties that are no longer taught since they are no longer needed. But anybody raised on this particular older method would have to be well into their nineties or older, none of whom you'd be allowed to visit. There are undoubtedly mathematicians who have studied older methods and have written on it. Inquiring with the math department of a local university might yield some leads.
I just now look at the Wikipedia Subtraction article Section "The Teaching of Subtraction in Schools" (en.wikipedia.org/wiki/Subtraction#The_teaching_of_subtraction_in_schools). Different methods exist and have existed at different times in different countries. From the comparison of two major methods, it appears that our old method was called the Austrian method which was then replaced by one William A. Brownell who appears to have been active around 1940. Those should give you some leads to follow.
If you're interested in mathematical oddities, I found a German RUclips video by Lehrer Schmidt about what he called the old multiplication method which he says was taught in Germany in the late 1800's. You successively double one number and halve the other until the halved number is 1, then you add up all the doubled numbers whose halved number is odd, giving you the product. It's also known as Russian Peasant Multiplication because you don't need to know the multiplication tables, but rather only how to multiply and divide by 2, how to add, and how to tell whether a number is odd. It turns out to be binary multiplication in disguise, something that most programmers with assembly experience know about. I wrote a page on it at dwise1.net/trivia/binary_mult.html ; I apologize for it being rather pedantic.
Wait, Common Core is a bad old idea that we can prove nwver worked?!
I took advanced calc 13 years ago and this song JUST actually explained bases to me. Dang.
Well the idea that understanding what you're doing is more important than getting the right answer is 100% true in all seriousness. If you want the right answer, you could just use a calculator, but that's not the point of learning math.
It's interesting to realize from this video that every generation always seems to think that there's some imaginary "new math", I had no idea this idea went back to the 60's.
I love this guy's music 😂
As a computer programmer, I have to say, "YES!" If you get a right answer without an understanding of the process, you're hosed as soon as the problem changes due to being in a different situation. Plus, if someone else screwed up, understanding what you are doing makes it much easier to find the bug.
Solve a man's math problem and he has a single solution. Teach him the underlining principles and processes, and he can solve a vast number more.
Besides, solving a math problem quickly isn't that important. Being able to tell a computer how to solve a problem will solve people's thousands of problems in microseconds.
It boggles the mind that some people seem to disagree with this. It's like them praising fish-having over fish-getting.
Why would I care that some kid has the right answer to a trivial and irrelevant arithmetic problem? I don't need the answer, and if I did, I could get one myself. I don't know where he got the answer. All that matters is if he can reliably reach the answer in the future. If he's got the answer now but has no clue how he got it, he's useless. If he got the wrong answer through some trivial slip but understands the principles necessary to obtain the right answer, then it's just a matter of future diligence and luck.
But if you can get the right answer no matter the question does it matter if you understand? People get paid to do the math correctly not understand it (I still see your point though).
@@Iisthebest You know that gag where a previously uninvolved character stabs a guy with an oak stake, but when they say "You've saved us! But how did _you_ know he was a vampire?" he responds with "He was a vampire?"? That's how I feel about people who get something right but don't understand the problem :P.
@@bretsheeley4034 my friend is a computer scientist and I remember him doing a few interviews back in college for internships and the way they tested applicants was usually with abstract problems. They were easy enough to brute force and solve usually, but thats not what the companies were looking for. They were trying to see how you implemented solutions, and considered long term potential for those problems. Things like solving problems with variables that you can easily change. Things like comments and code organization to make it easy to understand even as someone who didnt write the code. Things like scalability, they may ask you to make a program to sort a list of size 10, but what if they gave you a list of 20,000, could your program still handle it, etc.
These many caviots made even simple programming problems a very deep facited problem to help determine the most talented coders and the people with the best grasp on the concepts they were given.
I really wish more fields would do a similar technique.
By the time I was in school they stopped officially teaching this version of 'new math' but it was still in our old textbooks. The teacher said not to read that chapter but I read it anyway because I wanted to find out what this 'secret math they don't want us to know about' was all about.
New Math got its revenge in the end!
In my Catholic school, " New Math", was cancelled after 1974- 1975.
Thanks... Now I have to rethink every decision I've ever made to understand whether I'm high or not
His rapid-fire delivery is amazing! NEVER ceases to amaze me! What a genius!
Thank you, Alexander. Always have trouble figuring out which Tom Lehrer song is my favorite, but this 52 year-old song (did my new math on the recording dates at the Hungry I) is definitely up there. His fast-talk expertise (maybe an auctioneer or a barker could rival his speed, but not his enunciation!), impeccable comedic timing, hilarious asides, poking fun at himself, the audience, and the educational confusion of those days, make it a great piece. Then his nimble fingers, the musical asides, and the glorious major-minor-major-minor progressions of the chorus make it superlative!
that’s actually... the exact way i was taught/learned math and it makes.... perfect sense
What's going on in this comment section?
Doesn't anybody have a sense of humour? This man is a genius!
Maybe so, but what's the point of doing it that way? Why not just do straight, old-fashioned arithmetic? If it's good enough for Newton, it's good enough for me.
@David Lafleche That’s the whole point.
@@davidlafleche1142 I love your answere David.
This is an example of perfect comedic timing and setup. These things are not easy to pull off.
I came out of primary school as a calculating machine... not understanding one bit about how numbers actually work... but I could mechanically calculate all sorts of things... and subtracted by "borrowing" from one line and "paying back" to the other... Duh? That was 1958;
I later became a Primary Teacher and had to teach "The New Maths" and lo and behold I actually began to understand how numbers work...... I also learned that there is no one "correct" algorithm when it comes to calculations....
I had one pupil who was having trouble with subtraction..... one day he came to me and said, "Sir I can do it." He proceeded to do a really quite complex subtraction calculation.... he started on the LEFT hand side of the sum... that's right... the LEFT hand side....This lad demonstrated that he understood the number system.... he was 8 years old BTW.
Lehrer being a mathematician, I have to admire his gently mickey taking.... The new Maths wasn't.... it was the old Maths approached in a different way perhaps..
I wish I had a better understanding of numbers like that, there are so many reasons to learn math conceptually like that and many people don't seem to get that.
The old system sounds really unintuitive. I'd much rather get the right answer and understand why it's right so I can apply it to other situations
It really doesn’t matter if you get the right answer if it’s only an exercise anyway. Shouldn’t that be obvious?. I don’t why everyone’s laughing.
@@jeffburns4219 Laugh track
@@jeffburns4219because they’re a bunch of confused parents and/or math nerds. Being exposed to a wacky novelty song that addresses both groups while then-still being relevant and elevating thrilled the audience
@@Orincaby are you using wacky in a positive or negative or even neutral way
usually the new concept is useless in this age with calculators.
The retired math/physics professor is STILL scaring students to death in the UC Santa Cruz Library!
Stolen from Wikipedia:
Lehrer has commented that he doubts his songs had any real effect on those not already critical of the establishment: "I don't think this kind of thing has an impact on the unconverted, frankly. It's not even preaching to the converted; it's titillating the converted ... I'm fond of quoting Peter Cook, who talked about the satirical Berlin kabaretts of the 1930s, which did so much to stop the rise of Hitler and prevent the Second World War."[37]
He was a live wire
It’s so odd watching this, because I was raised on “New Math” so it’s just math. Watching him do it the older “simple way” was baffling, like I figured it out but I just kept listening over and over thinking “why would you do it like that?”
It's still relevant, bc I played it for my 15 yr old, who sees no point in showing his work 😅 He said "that is so true, and they even tried it with reading"
I remember my dad doing math like from when I was a wee lad that and having no idea what he was doing.
I remember when i was 5 i didn't really understand my homework and yes this was when the "New Math" was a thing and I hated it and my sister taught me this song that was 1968 and so now i listen to this for hours. My Sister is a really nice girl and I wish i could meet her up but i can't right now
I remember one of my math teachers in high school bringing this in and playing it for us.
This likely inspired Animaniacs to write a multiplication song for Rob Paulsen (Yakko) to sing and it goes like this
7 x 3 is 21,
Which, as you know,
Is just two 10s plus 1, and so,
We put the 1 right here,
And we carry the 2, one left
To the top of the tens place, right next door
And we put it on top of the number 4,
Which is really four 10s that we multiply
Times 3 in the ones place and that's why
We now have 12, which we add to the 2
That we carry to get 14.
See how easy that was?
Oho, it's multiplication
It's math education
Hey, Albert Einstein said that it's so easy to do
It's simple it's breezy it's fun and it's easy just buy a calculator,
You can multiply, too!
And now, the second digit.
7 x 8 is 56,
Which, as you know,
Is just five 10s plus 6, and so,
We put the 6 right here
In the tens place, left of the 1
And we carry the 5 like we did before
To the top of the tens place next to the 4,
Then multiply that 4 x 8
To get 32. See, isn't this great?
Then, we add the 5 that we carried before
To get 37, then add once more
Straight down to get 3,901!
Isn't this swell?
Oh let's give multiplication
A standing ovation!
Issac Newton multiplied a couple times two
Times two! Times two! Times two!
It's simple it's breezy it's fun and it's easy
So buy a calculator
And study this stuff later
Maybe someday, you can multiply numbers
Too, three, four five....
Recess!
I just watched that episode and came here because of it!
The "New Math" makes sense, the first version is basically "do negatives, then just minus 1 from the next number", which is kinda correct? But, again, try and explain negative numbers to a child. They aren't gonna get it day one. Most kids understand "take 3 away from 5, you have two left", but when you say "take 5 away from 3, you have 8", you're gonna get a lot of kids who say "you can't take 5 apples from the box of 3, that doesn't make sense!"
Don't you mean "Take 5 away from 3, you have -2"?
Edit
Took me a moment to realize you were doing in small part of a bigger thing like the song. 5 away from 13 rather to get 8 due to borrowing.
Homestuck
I had to learn The New Math when I was 10 years old. I am still undergoing therapy
It's ridiculous to overcomplicate the imparting of basic addition, subtraction, multiplication, division, percentages, etc by using the rhetoric of algebra. But thaaaat's what they did.
Oh James, I would still like to get the name of the moron who proposed the theory. It seemed to take logic out of math.
2nd and 3rd grade were the speed tests with addition and subtraction. Anyone remember how you folded your paper like an accordion and worked line by line from your workbook?
Then I’m 4th grade, NEW MATH! We already knew how to add, subtract, multiply and divide two digit numbers! But now, it’s in the tens place and the ones place. Indoctrination!
Brilliant man. Lightened up my childhood and taught me about dark humor.
This is the way I learned math as a kid, and I can’t do addition or subtraction in my head anymore
just use old ways
Love this! This is EXACTLY how I was taught, after I already knew how to subtract the regular way. To this day I feel guilty about saying that I'm "carrying" anything. We had to say we were "exchanging"!
When you realize their new math is your old math 😅
I think that arithmetic has not changed for some time. The 'new' part he's referring to is arbitrary number bases other than the classic 10's (decimal). Probably not the whole story, but a good start.
Please explain base 8
@@xenonguard No, it changes. Alexandra is correct. I was in 5th grade in the 70s (division had just been taught in 4th grade) and my mom stopped being able to help me with math because they did it so differently.
I started teacher training a few years into this change. It was the first time I passed a math exam!
it's hilarious seeing parodies of things that are now common place. the idea of doing math like at the beginning sounds like a nightmare lol
I agree, that seemed weird
And it wasn't how it was done. About the only new math ideas in the video is the use of the term "regrouping" in the first (base ten) pass, and of course doing math in bases other than base ten. The pre New Math way most often used thew idea of "borrowing", and as all the elementary/middle school teachers cringe in horror, (they even get a little jittery at "carrying", I present some history (they probably cringe at that word too, delicate creatures!).
pballew.blogspot.com/2023/01/subtraction-borrowing-carrying-and.html
Borrowing is used for subtraction. Carrying is used for addition - at least how I learned it.
The way this song explains it, is how I learned to do subtraction. What he says at the beginning is the old way I never heard of before listening to this song.
I was taught math in the beginning way im in my early 20s
Remember this isn’t the current 2020 new maths this is much older new maths cause we get better at teaching.
You *REALLY* think "Common Core" is "better"? Really?
I remember fifth grade and “new math” in 1965…didn’t understand it then nor do I understand it now.
Life goes full circle. My grandfather was a banker, and I remember him staring at my math homework, and saying, “I know this answer is wrong, but I have no idea why!“ When my girlfriends teenager was in fourth or fifth grade, I had the exact same response to a double digit multiplication problem. I knew her answer was wrong, but bless me if I knew why
'Now let's not always see the same hands'. This is like so true I swear every single lesson I've ever had the teacher has said that 😂😂😂
I love you, Tom Lehrer, through my entire life (> 60 years)! You've cheered me up so many times and helped me sleep peacefully.
I'm reminded there are only 10 kinds of people. Those who understand binary and those who don't.
There are 10 kinds of people in the world: those who understand binary, those who don't, and those who didn't expect this joke to be in base-3.
@@AlexSh789 Only deaf people used to understand hexadecimal, now all but two of them are dead.
there are 10 kinds of people: those who understand binary, those who dont, those who didnt expect a ternary joke, those who didnt expect a quaternary joke, those who didnt expect a quinary joke, those who didnt expext a senary joke, those who didnt expect a septenary joke, those who didnt expect an octal joke, those who didnt expect a nonary joke, those who didnt expect a decimal joke, those who didnt expect an undecimal joke, those who didnt expect a dozenal joke, ...
"Math is math!"
-Mr. Incredible
You win a internet point. Congrations, you done it.
MATH IS MATH! - Mr. Incredible circa early 1960s.
Warren Lehmkuhle II The Incredibles movies are meant to be set in the 70’s apparently
😎
I think of this song whenever I'm doing calculus homework.
I actually remembered this whole song so proud.
I found this song on Pandora while listening to a comedy station, I thought this current....didn't know it was from the 60s....and also didn't know he was describing HOW I DO SUBTRACTION! I'm 31 lmao hearing it sang out loud sounds ridiculous and hard but I did it on paper to the song and it's fine lol....now.....I wanna know where tf the 1 came from in his 'old math'and why the 3 in the hundreds place seems totally forgotten dang it. I tried to follow along but....couldn't.
Studying math in the university I have to say I love this song
Understanding what you're doing is the most important thing imo. Once you get to more advanced math, doing things by rote doesn't work anymore.
This is such awful truism that caught on these days, but it's bulshit. Half the kids in elementary school don't need to understand math, they need to understand their future profession and do the counting right when the occassion comes.
The other half should have figured it out on their own by the time they are applying in collage if they have any bussiness being in there.
@@frankydostal4758 That wasn't my point at all. I was saying that IF you're going to do advanced math, you can't do it by rote. I never claimed people HAD to do advanced math...And i'm not saying it as a truism, I'm speaking from personal experience.
@@zecchinoroni First off you can in terms of academic success. Results may vary obviously.
Second off the song is taking a piss of the idea that school children should learn this shit and perhaps more smartly of the idea that you can learn how to count without having to count properly.
It's truism because people just say that a lot, hands on experience or not. Sorry.
@@frankydostal4758 Properly taught math encourages thinking and understanding what you're doing, it's not just about counting numbers.
@@tomaszadamowski But that's exactly the truism I'm moderately objecting to. Most people don't need to know the underlying principles. It wastes their time and attention and unlike simple properly trained algorithm they won't ever use it.
When he first started out with the numbers and he started to get into a rythym I was like omg this man can rap, cant he?
And now THIS is the old math. How in the hell did people show work under Old Algebra?
1.75 speed is how teachers explains work and assignments. Also examples. 0.25 is how primary teachers greet.
So damn true. I was in junior high school in'67 and couldn't get this to save my life. I got an F at midterm and brought it up to a D for the final grade, but that's ok, cuz in those days, a D stood for Done. When I got into algebra in the 10th grade, I got the right answer, but I didn't understand what I was doing and couldn't show the steps, so I always got partial credit. No wonder I had to be a history major and become a lawyer. Love Tom Lehrer and this is a wonderfully illustrated posting. Mahalo
I had the same problem. I had a lot of difficulty grasping Math concepts; but words always came easily. As for New Math and Common Core, I can't think of a single legitimate reason to teach it that way.
It's very helpful to learn this way for then learning binary and hexadecimal which are staples of computing, although the latter is more useful day to day.
funny that my mother taught me the old math back in 2000`s and all my teachers were perplexed as to why do i do it that way and how can i get correct results... now, 20 years later i see that she didnt just pull a magic trick outta her ass but followed the doctrine that i do today, and that is to avoid any change and stick to the old ways... Amazing that she was actually taught the new math as both of us are from the ``new math`` era, so who taught her the old math? probably my grandfather on her side, whose name i carry, so i guess i truly lived by my doctrine way before i noticed that any change was for worse and brought naught but complication and engineered obsolescence... What a gem the Tom Lehrer is, to not just shower us in wit and humour but to still impart and reveal the joys of the old ways... Along with how to hunt and have good time giving and receiving the gifts of love among many other things such as but not limited to proper feeding of pigeons...
I had people cheat on my paper engineer high in high school so I always did math problems in base 25 then reconverted
I'd love to hear Tom's take on "Common Core".
That's what you just heard.
@@effiebug4278 "Common Core" is the same old garbage in a shiny new can.
I like how the last digit of every number are meme numbers today. 42, 69, and 73 (sheldons Number)
73 is also known as the "B0aty" number in runescape :P
When I took a computer science class in college we had a test that had a long division problem in hexadecimal.
Lehrer's math-related songs are surprisingly relevant to computer science studies. I took calculus, linear algebra, mathematical logic, statistics, as well as chemistry and physics electives, and there was always at least one relevant Tom Lehrer song for each class.
I sometimes do division in computer bases like binary. But it's a pain to do it all in the base without a lot of practice, because I am so used to working in base 10. So I tend to convert to and from base 10 as needed, heh. Thankfully if you are doing math using computer-cetric bases, it's probably because you are working with a computer, and you can use the computer to assist you :)
Be glad you learned New Math, then!
Good man.
Now I will readmit myself to the loony bin just as I was on my way getting better.
This is like yakko warner as a teacher
pfp checks out
_note self, send this to the new Animaniacs writers_
Me: Can't wait for school!
Friend: Why?
Me: United States Canada Mexico Panama-
Lyrics: (because someone has to) (I skip some of the talking parts)
Well,
You can't take 3 from 2,
2 is less than 3,
So you look at the 4
In the tens place.
Now, that's really 4 tens,
So you make it 3 tens,
Regroup,
And you change a ten to 10 ones
Then you add to the
2 and get 12,
Then you take away 3;
That's 9.
_Is that clear?_
Now, instead of 4
In the tens place,
You've got 3
'cuz you added 1
That is to say,
10, to the 2,
But you can't take 7 from 3
So you look at the hundreds place.
From the 3,
You then use 1,
To make ten 1s
And you know why
4 plus minus 1
Plus 10 is
Fourteen minus one?
Cuz addition it commutative, right?
And so,
You've got 13 tens,
So you take away 7
And that leaves 5.
_...well, 6, actually, but..._
_The idea is the important thing!_
Now, go back to the
Hundreds place,
You're left with 2
And you take away 1 from 2
And that leaves..
_Everybody get 1?_
_Not bad,_
_For the first day.._
Hooray for, New Math!
New-hoo-hoo Math!
It won't do you a bit of good to,
Review math,
It's so simple,
So very simple,
That only a child
Can do it!
(Talking interlude)
You can't take 3 from 2,
2 is less than 3,
So you look at the 4
In the eights place.
Now, that's really 4 eights,
So you make it 3 eights,
Regroup,
And you change an eight to 8 ones,
Now you add to the 2,
You get 12 base 8,
Which is 10 base ten,
And you take away 3 that's 7.
_Ok?_
Now, instead of 4
In the eights place,
You've got 3
cuz you added 1,
That is to say,
8, to the 2,
But you can't take
7 from 3
So you look at the sixty-fours.
(Talking interlude)
From the 3,
You then use 1,
To make 8 ones,
You add those ones to the 3,
You get 13 base 8,
Or in other words,
In base 10 you have 11
And you take away 7,
And 7 from 11 is
4!
Now go back to the sixty-fours,
You're left with 2,
And you take away 1 from 2
And that leaves-
_Now, let's not always see the same hands.._
1, that's right.
_Whoever got 1 can stay after the show and clean the erasers._
Hooray for, New Math!
New-hoo-hoo Math!
It won't do you a bit of good to,
Review math,
It's so simple,
So very simple,
That only a child
Can do it!
The lyrics are literally on the screen.
@@AlexSh789 I was bored okay?
@@huhneat1076 - Fair enough
Hearing people laugh at their own ignorance, insouciance and arrogance all in once place is golden.
So this is where _Animaniacs_ got their Multiplication skit from
I still don’t understand what I’m doing with math. They didn’t let me just move on with the right answer.
The four operations are: addiction, distraction, mystification and derision.
I've went from 2003 to 2013 to a middle school in Germany so I never learned 'New Math' but it sounds very...complicated :D But I still write cursive in my daily life and I'm now 24
As someone who learned it this way, I will say that the new way of doing subtraction is, though wordier, actually a fair bit more intuitive. All that about bases is bunk, though. You'll only ever need to know a different base if you're a computer scientist, and even then only bases two, eight, and sixteen.
When I started reading my 'new math' book in the fifth grade back in '65, I said to myself, "This book ought to be titled _One Plus Equals Two, And Why_ ." Years later I read that the teaching methods therein worked excellently well for the math teacher who devised them but that few other teachers could duplicate his success.
pretty sure you did just the other way around, when you do written substraction in german schools you do exactly what he describes as the "new math", you write 342-173 on top of each other, then you go and look what you need from 3 to go to 2, since 2 is smaller it's actually 12 so 3+9=12. since it's a double digit now you carry 1 to the tenth. 7 is bigger than 4 and you add the 1 from before so 8 to 14 and you get 6 and carry 1 to the next so it's 2 to 3 and you get 169. in the song he describes just that but instead of going from the 173 to 342 he goes from 342 to 173 (so 12-3, 13-7 and 2-1) but technically that's exactly the same. greetings from another german
this is so attractive for some reason
Interestingly, the "new math" style matches how I do math in my head (and how I was taught in school in the early aughts) so at least some of the methods must've stuck around.
@glyn hodges As it's been pointed out *MANY* times here and would just a brief look at your surroundings to figure out.... The song is *OVER 50 YEARS OLD!* So if you're that old or younger, and didn't learn "Common Core" you *DID* learn the "New Math" he's talking about.
@@dementare Well, in a way, but they toned it down a lot. For instance they cut the "translating the basic algorithms to different bases in early elementary school" part.
@@Mnnvint
That was wise.
Base 10 is just the old math system explained in greater detail. But base 8... that is something else.
It’s really not too bad once you get used to it, just keep in mind that everything is grouped in groups of eight instead of ten and you’re fine.
Also, we have octal and hexadecimal calculators, so doing these calculations in other bases isn’t much of a sticking point. Also really, most of the time we just convert to base 10, do the calculation, then convert back.
Stephen Donovan unless the exsersise (remember this is supposed to pbetaken from a texsbook specifies that the problem has to be done in base 8, and this is the issue with a lot osfschool problemd, they force you to do things a certain way ( yes I know it’s to drill the method ) instead of focusing on an efucuent route to get to the correct solution . I suspect this is why auite a few people feel that math is hard, a nither thing us the pace it is tougt at, actually more the mindset thst the ckass has to be kept together at all times at all cost, people lern at different rates so splitting the class up and allowing people to learn at rheir optimsl rate us not a refleftion of oeople in the slow class beeing stupid( for the most part). I think splitting into groups based on speed of kearning avoids a few problems, 1: the fast learners hating the subject because they are bored, 2: tne slow learners( slow as in requering mor time to learn for whatever reason) not feeling stupid and/or confused and consequently viewing math ( ot other subject) as something they will just have to suffer trough and hopefulli never have to deal with ( sadly not a big chance with math) Disclamer: I’m not an educator or in any way involved in the “ed-biz”, so this comment might be utter rubish, any corrections areappreciated, at the time of writing these are my opinions on the subject they may change in the future
Me looking at a subtraction problem getting flashbacks from this man and starting to sing the song while solving it
You can't take three from two,
Two is less than three,
So you look at the four in the tens place.
Now that's really four tens,
So you make it three tens,
Regroup, and you change a ten to ten ones,
And you add them to the two and get twelve,
And you take away three, that's nine.
Is that clear?
Now instead of four in the tens place
You've got three,
'Cause you added one,
That is to say, ten, to the two,
But you can't take seven from three,
So you look in the hundreds place.
From the three you then use one
To make ten ones...
(And you know why four plus minus one
Plus ten is fourteen minus one?
'Cause addition is commutative, right.)
And so you have thirteen tens,
And you take away seven,
And that leaves five...
Well, six actually.
But the idea is the important thing.
Now go back to the hundreds place,
And you're left with two.
And you take away one from two,
And that leaves...?
Everybody get one?
Not bad for the first day!
Hooray for new math,
New-hoo-hoo-math,
It won't do you a bit of good to review math.
It's so simple,
So very simple,
That only a child can do it!
Now that actually is not the answer that I had in mind, because the book that I
got this problem out of wants you to do it in base eight. But don't panic. Base
eight is just like base ten really - if you're missing two fingers. Shall we
have a go at it? Hang on.
You can't take three from two,
Two is less than three,
So you look at the four in the eights place.
Now that's really four eights,
So you make it three eights,
Regroup, and you change an eight to eight ones,
And you add them to the two,
and you get one-two base eight,
Which is ten base ten,
And you take away three, that's seven.
Now instead of four in the eights place
You've got three,
'Cause you added one,
That is to say, eight, to the two,
But you can't take seven from three,
So you look at the sixty-fours.
"Sixty-four? How did sixty-four get into it?" I hear you cry.
Well, sixty-four is eight squared, don't you see?
(Well, you ask a silly question, and you get a silly answer.)
From the three you then use one
To make eight ones,
And you add those ones to the three,
And you get one-three base eight,
Or, in other words,
In base ten you have eleven,
And you take away seven,
And seven from eleven is four.
Now go back to the sixty-fours,
And you're left with two,
And you take away one from two,
And that leaves...?
Now, let's not always see the same hands.
One, that's right!
Whoever got one can stay after the show and clean the erasers.
Hooray for new math,
New-hoo-hoo-math,
It won't do you a bit of good to review math.
It's so simple,
So very simple,
That only a child can do it!
Come back tomorrow night. We're gonna do fractions.
Aaaaaahhh! Flashbacks!
I've been trying to figure out how he's doing 'Old Math' but it's so simple only someone from the 60's can do it.
I believe it works as follows: when subtracting, if the first digit is greater, get the absolute difference, call it x and then do 10-x = number to write down.
Then you carry the one, which is to say that you used a ten so when you repeat te process for the tens place you have to carry the "less one" because you used one ten already.
It's the same way basically, I think. Just less explicit.
That's the exact way I was taught in the early 2000's.
I have always remembered the basic subtraction facts, and the memory expert Harry Lorayne showed a better way to do subtraction in multiple-place problems.
I also love the musical reference to The Music Man ("We've got trouble, right here in River City!")
I had no idea I learned new math. I've heard people joke about it but figured I missed the wave...
depends on your age as there's now another wave of "New Math" going through the american schools at least.
@@dementare Ah, I'm 22 and American, so I might have missed this other wave of new math.
@@notgate2624 the second wave is connected to standard testing and is kinda bad.
Where are my base 12'ers at?
Why base 12 when you could base 6?
@@a_commenter Base 12 has more factors and will increase in digits half the time.
ArrZarr I don’t have time right now to explain why base 6 is better, but I can direct you to this video by Jan misali ruclips.net/video/qID2B4MK7Y0/видео.html
@@a_commenter Having watched both videos and commenting on the follow-up, I still disagree based upon a technical point. Let's both agree that base 10 sucks and leave it at that?
Base 16 gang
In 50s-60's my school taught both. My brother and I weren't particularly good students in any other subject, but we aced math right through college. It was in high school LIT class where 2+2=5. LOL
a zinger
Ooh, y'all were taught _1984_ in the 50s/60s?
Subtraction under the Common Core is no longer 'take away'; rather, you find the difference between the larger and smaller number. 342 - 173? Well, add 7 to 173 to make 180, then add 20 to make 200, then add 100 to make 300, then add 40 more, and 2 more. 7 + 20 + 100 + 40 + 2 = 169. With practice (and elementary arithmetic provides lots of that), this can be done in one's head rather easily, and no table memorization (remember doing that) is necessary. But of course, people who learned to subtract in some other manner are offended by those meddling Common Core nabobs.
Well admittedly it’s far more complicated and utterly inefficient, it’s also not any better for understanding the math behind the arithmetic. In other words, it’s worse in every important way for no important reason.
@@feartheghus hardly, i was taught arithmetic and ended up defaulting to the new style all on my own, it's much better for mentak maths where the traditional arithmetics and such are ideal for paper, they're both useful for different situations. You alsi forget that this is at the primary school level, so simplicity ought be forgiven.
solanceDarkMOW I said it was extremely over complicated, so simplicity isn’t something that needs forgiveness, the fact that it isn’t simple when it should be at the elementary level is one of the major issues I have with it.
solanceDarkMOW and it probably isn’t better for mental arithmetic because you have to remember more specific numbers to do the same job and have to do more operations for the same result.
I’ve been doing this on my own since second grade and I thought I was the only one! It’s way, way faster than carrying numbers backwards and trying to remember all of them.
Him still being alive in 2023 is so crazy to me
He outlived Henry Kissinger, that's what matters.
Still alive in 2024!
A couple of years ago, I actually sent him a letter, but it was returned to me. :(
@dawnp8868 - Did it say why it was returned?
@@dawnp8868 I sent him a letter too but he hasn't gotten back to me in months. I assume he's either too old to really care for mail correspondance or might be senile. I really hope he's enjoying the rest of his life!
Germany still used old math in the nineties. We're doing fine anyway. But don't ask anyone growing up in the nineties to check your spelling the new German introduced back then confused a whole generation. 😂
He is right, doesn't matter if your right anymore.
As a kid who grew up with the "new math"...at least we're not using lines and dots and taking 10 minutes and five sheets of paper to do it like the new new math
God the new new math sucks
Screw Common Core.
doing quick maths before it was a thing
There is nothing "quick" about this convoluted mess!
@@davidlafleche1142
i dont see anyone else with a faster convoluted mess than this
It actually did come from Russian peasants..
When doing fast mental math on the board (chem professor), I use mod 10 (you just loop around the tens, e.g. 4+8=2, 4-5=9, etc. It is a fancy remainder).
So if I'm looking at 342 - 173, I just do a naive ansatz, if you will, where I subtract each digit mod 10. So (3-2), (4-7), and (2-3) = 279. This is obviously wrong, but to correct my guess, I just go back and subtract 1 from the digit to the left of any that would have been a negative subtraction, pre-mod 10. So 169.
So you can kind of do this on the fly too, if you just do each digit starting at the 100s and work your way from left to right, just glancing to the right of the digit to see if you would have needed to borrow. So
(3-1) but a glance tells me (4 < 7), so (2-1) instead.
(4-7) but a glance tells me (2 < 3), so (3-7) instead.
Then (2-3).
All mod 10, never actually "borrowing" explicitly, but knowing the "original" borrowing method informs this one. Teach it to your kids multiple ways and teach them the physical meaning with physical objects too. It is hard to abstract without context.
Thank you for this!!! I was just thinking I needed to learn some of the tricks, and here you are. Thanks.
Good lord. Nothing like a friendly reminder how my brain doesn’t work.
Wtf! THAT'S what people call "new math"? That's what I learned, and I find it actually has mathematical sense, meanwhile the old way seems more like a nonsensical trick.
The old math has negative numbers mod 10, which really seems much less intuitive than addition being associative. And the old method relies on the implicit fact that you have to count "how much modulo" you apply.
Smh
This song is at least 55 years old.
@@AlexSh789 oh really? Well that explains it
See now, if you put this comment in song form, I might have a clue of what you're talking about.
@@AlexSh789 Tom Lehrer is still alive. He's 92 and lives in Manhattan. Should get him to update this song and his song on the periodic table while theres still time.
@@hardcorehunter7162 - He lives in Manhattan? I thought he lived in Boston? If this is true, you can tell me his address and I'll get in touch with him right away! (That's a half-joke.)
And on top of that, if you get it wrong they don't tell you why, ans later wonder why you don't understand it...
Professor La Flamme circa 1974 played this in class. Great stuff!