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Why did Tom Lehrer swap fame for obscurity?

theguardian.com

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Re: Why did Tom Lehrer swap fame for obscurity?

#121

Post by bluGill »

082349872349872 wrote: post #103
InfiniteRand wrote: post #100

Earlier quoted context omitted.

I have a theory that the enthusiasm of teachers teaching the material is a far bigger factor in the effectiveness of learning than the methods. So much so that any advantage from better methods gets quickly nullified without teacher buy in

I have an anecdotal theory that most people who came prepared to a STEM programme in the States last century did so despite, not due to, the modal 7-12 teaching. (if true, I hope it no longer is?)

Most teachers in the states did poorly in math, and never loved it. They in turn can't pass a love of math on. They are good enough at math to pass the tests, but that isn't why they are teaching.

Re: Why did Tom Lehrer swap fame for obscurity?

#122

Post by 123894893 »

thaumasiotes wrote: post #111
123894893 wrote: post #108

Earlier quoted context omitted.

The whole point of the song is that Lehrer thinks that teaching it as borrowing is so different that it makes it incomprehensible to people. > But I already pointed out that the steps aren't different. They are, with borrowing you make the change to the tens place first, "getting" the extra ten ones, then explicitly add it to the ones place, then do the subtraction. With the old way (Lehrer's preferred method), you d…

> I'm still not sure what they were actually doing with "3 from 2 is 9, carry the one." You could mentally change the 2 to a 12 and subtract three > you could also take the tens complement of the number being subtracted and add it to the number you're subtracting from > Or simply memorize a subtraction table, the same way people memorize a multiplication table Well, you can't take the ten's complement of the number b…

> Well, you can't take the ten's complement of the number being subtracted, because it's infinitely large. One obvious difference between subtracting 3 and adding ...99999999999999999999999999999997 is that it's possible to write "3".

The ten's compliment of 3 is 7.

> Including the new math approach; indexing your table entry under "12" and "3" is not a different approach from indexing the same entry under "2" and "3".

12 - 3 = 9 is quite different from 2 - 3 = 9 carry the one. The latter requires a separate explanation for what's actually happening.

> But they got better marks than the new math students, because they weren't graded on whether they understood.

People seem to do subtraction just fine with borrowing, and I've never heard anyone claim that the old method is superior outside of Lehrers song.

> As I just said, Lehrer knew that people couldn't understand it either way.

This is clearly false, though. Most people today understand borrowing just fine, while (at least according to Lehrer's song) people who studied the old approach had so little understanding of what was happening that they couldn't even grasp the concept of borrowing. If you look at what's actually being said, all of the stuff in the first verse that Lehrer is presenting as mindlessly complex for adults is completely intuitive to anyone with a decent grasp of modern elementary school math:

"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 'em to the two and get twelve And you take away three, that's nine Is that clear?"

The sarcastic "is that clear?" is there to show how confusing this is. But it's actually quite clear for people with a modern education. The problem is 342 - 173. You don't do 2 - 3 ("You can't take three from two, Two is less than three"), so you borrow a ten from the 40, changing it to a 30 and the 2 to a 12 ("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 'em to the two and get twelve").

Re: Why did Tom Lehrer swap fame for obscurity?

#123

Post by thaumasiotes »

zoky wrote: post #112
thaumasiotes wrote: post #96

Earlier quoted context omitted.

Is that what we're appreciating when we call the song a "banger"? Most people who like the song don't know the words.

Yeah, well, I do know the words, and I can confirm that it’s a banger. Antimony, arsenic, aluminum, selenium… Of course, I only know the lyrics due to the fact that I am the very model of a modern major-general…

Getting 80% of the first line of the song isn't the strongest possible evidence that you know the words.

But regardless, how much do you think you'd enjoy listening to the words absent the music?

Tom Lehrer has plenty of clever wordplay going on, of various types in different songs. When You Are Old And Gray has a fun example of wording for the sake of wording.

But I don't think wording is a strength of The Elements.

Re: Why did Tom Lehrer swap fame for obscurity?

#124

Post by 123894893 »

thaumasiotes wrote: post #119
OskarS wrote: post #104

Earlier quoted context omitted.

> But I already pointed out that the steps aren't different. They're the same style. Whether you use the term "carry" or "borrow" makes no difference to anyone. Obviously, it does. Like, that's what the song is about. You're not just disagreeing with the other commenters, you're disagreeing with the concept of the song itself. It's a different way of doing it, even if the underlying principle is the same. This stuff…

It's not that there's no difference in the underlying mathematics. That would be true, by necessity, of any subtraction strategy that worked. There's no difference in the steps being performed. If you go through each approach, you'll notice that you do the same things in the same order, with the possible exception that carries might appear before or after the actual subtraction with which they are associated. All of…

> The "new math" part of the problem isn't that you do the base-10 subtraction differently. It's that you're expected to be able to do the same subtraction in base 8 too.

That's the second verse. The entire first verse is mocking the "New Math" idea of borrowing, showing New Math subtraction in base 10.

Re: Why did Tom Lehrer swap fame for obscurity?

#125

Post by garaetjjte »

thaumasiotes wrote: post #111
123894893 wrote: post #108

Earlier quoted context omitted.

The whole point of the song is that Lehrer thinks that teaching it as borrowing is so different that it makes it incomprehensible to people. > But I already pointed out that the steps aren't different. They are, with borrowing you make the change to the tens place first, "getting" the extra ten ones, then explicitly add it to the ones place, then do the subtraction. With the old way (Lehrer's preferred method), you d…

> I'm still not sure what they were actually doing with "3 from 2 is 9, carry the one." You could mentally change the 2 to a 12 and subtract three > you could also take the tens complement of the number being subtracted and add it to the number you're subtracting from > Or simply memorize a subtraction table, the same way people memorize a multiplication table Well, you can't take the ten's complement of the number b…

Maybe they used "borrow" in the "new" method to avoid having both 2-3=9 and 2-3=-1, compared to explicit radix+2-3. But if you actually wanted to memorize subtraction table then "old" way is maybe easier, because your table is nice square grid instead of wider triangle (and if you actually need negative result you can do second lookup for 10-x).

Also try doing something like 2000-1111 in "new" method and you go on huge side quest to propagate the borrows and go back to the beginning. Compared to "old" method where you progress one digit at a time without backtracking.

Re: Why did Tom Lehrer swap fame for obscurity?

#126

Post by thaumasiotes »

123894893 wrote: post #122
thaumasiotes wrote: post #111

Earlier quoted context omitted.

> I'm still not sure what they were actually doing with "3 from 2 is 9, carry the one." You could mentally change the 2 to a 12 and subtract three > you could also take the tens complement of the number being subtracted and add it to the number you're subtracting from > Or simply memorize a subtraction table, the same way people memorize a multiplication table Well, you can't take the ten's complement of the number b…

> Well, you can't take the ten's complement of the number being subtracted, because it's infinitely large. One obvious difference between subtracting 3 and adding ...99999999999999999999999999999997 is that it's possible to write "3". The ten's compliment of 3 is 7. > Including the new math approach; indexing your table entry under "12" and "3" is not a different approach from indexing the same entry under "2" and "3…

> The ten's compliment of 3 is 7.

Not a good look for someone extolling the benefits of understanding the theory behind an algorithm. This is only true if you're working modulo 10.

I'm suddenly very curious what you think the ten's complement of 12 is.

Re: Why did Tom Lehrer swap fame for obscurity?

#127

Post by BeFlatXIII »

InfiniteRand wrote: post #100
CuriousCosmic wrote: post #54

Earlier quoted context omitted.

New math was actually pretty successful at the lower grades. The issue was that when it came to rolling it out to middle and high schools, they just kind of said "here's the textbook, figure it out" instead of going through a coordinated process of teaching the teachers while helping them develop their new curricula (which they did for elementary school). So you had this really ugly failure of teachers not really nec…

I have a theory that the enthusiasm of teachers teaching the material is a far bigger factor in the effectiveness of learning than the methods. So much so that any advantage from better methods gets quickly nullified without teacher buy in

That's why the US can get stuck in such educational ruts. There are too many teachers who don't have the in-depth understanding to alter their teaching methods to approaches other than the one they memorized in education college.

Re: Why did Tom Lehrer swap fame for obscurity?

#129

Post by pdonis »

andrepd wrote: post #97
pdonis wrote: post #51

Earlier quoted context omitted.

> Is that a bad thing? It's a bad thing if you never learn how to actually get the right answer. Which unfortunately seemed to be a common consequence of the New Math as a teaching method.

Why? The objective is understanding, not getting the rightsl answer, because you will never do a long multiplication in your life since a 3$ chip does it in a tenth of a microsecond

> The objective is understanding, not getting the rightsl answer

I would argue that if your "understanding" doesn't actually enable you to get the right answer, you don't really understand.

> you will never do a long multiplication in your life since a 3$ chip does it in a tenth of a microsecond

And how do you know the chip's answers are accurate?

Or what if you want to design the chip?

Or what if there's an EMP and all of the chips are fried?

More generally, if you're satisfied with just some conceptual-level "understanding" of anything that doesn't actually enable you to tell right answers from wrong, you are setting yourself up to be manipulated, misled, conned, etc. Critical thinking is a valuable life skill, and it requires you to be able to tell right from wrong answers.

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