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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?

#141

Post by thaumasiotes »

OskarS wrote: post #120
kloop wrote: post #113

Earlier quoted context omitted.

> I think the song is very funny and charming, but I do think this is a rare case where Lehrer is just wrong, the "borrowing" style is a much better and clearer way to explain subtraction. How much of that is that you're familiar with this method (the same way Tom was familiar with the old method)?

It's a good question, I'm not sure. I do think it's clearer what's going on, and the steps are more obvious. Like, there's a joke in the song about what to do with the carry, if you add it to subtrahend digit or remove it from the minuend digit ("if you're over 35 and went to public school...") which to me indicates that it's rather arbitrary and "learn algorithm by rote". Like, the "borrowing" thing just much better…

The other system, as described in 19th-century textbooks, says this:

----

[What if the digit in the subtrahend is bigger than the one in the minuend?]

Imagine adding 10 to both numbers. Obviously, the difference between them will not be changed.

But adding 10 to the digit in the subtrahend is the same as adding 1 to the digit immediately to its left.

So, add 10 to the [current] digit in the minuend, add 1 to the [next] digit in the subtrahend, and then perform the subtraction.

Re: Why did Tom Lehrer swap fame for obscurity?

#142

Post by aidenn0 »

coryrc wrote: post #69
bitwize wrote: post #25

Earlier quoted context omitted.

New Math was a response to the Soviet lead in the space race. It was thought that introducing more abstract concepts, like different bases and set theory, would help kids grok math more. It was a fool's game. Just like every other "innovation" in mathematics education since, up to and including Common Core (one of which you probably encountered). At the elementary school level, the only way to increase math proficien…

> Just like every other "innovation" in mathematics education since, up to and including Common Core Have you actually looked into it? I was skeptical too, but then I saw they were trying to teach kids the way I do math. For example, what's 4001 - 3989. The old way would be to borrow and carry three times. But change question to 1+4000-3990+1 and the answer is perfectly simple. Kids I went to school with would litera…

Implementation is terrible though. The only explanation I have for the terrible tests given at my kids' schools is that they are to test the teachers not the students.

For example, the curriculum indicates a teacher must teach 4 strategies for multiplication. Totally reasonable. But then the test will have questions like "Perform this multiplication using strategy foo" which seems like putting the cart before the horse. Isn't the whole point of teaching multiple strategies is so that at least one sticks?

[edit]

And no, they aren't doing times (nor even addition) memorization in school. We did them at home and the benefits were absurd.

Re: Why did Tom Lehrer swap fame for obscurity?

#143

Post by vundercind »

thaumasiotes wrote: post #115
contrast wrote: post #73

Earlier quoted context omitted.

I’m fascinated - I’ve never thought of reading the time as a maths skill. How does it depend on learning multiplication? (non-American here, I may be lacking context that makes it obvious)

It doesn't; multiplication isn't involved at all. The only skill required is remembering that the shorter hand is hours and the longer hand is minutes. https://images.thdstatic.com/productImages/f220d887-1a05-418...

Of course it’s involved!

Hour 6 is also minute 30. There’s some arithmetic for you! Six times five, if you like, or six times ten divided by two if you prefer.

Many don’t have numbers at all, so you’ll need to build a good intuition for fractions and converting those to hours and minutes if you want to read them fast. Most of us do it so automatically we don’t notice, but some of that’s plausibly fraction multiplication.

Re: Why did Tom Lehrer swap fame for obscurity?

#144

Post by 123894893 »

thaumasiotes wrote: post #138
123894893 wrote: post #124

Earlier quoted context omitted.

> 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.

Borrowing isn't even a New Math idea. Here's an American Old Math mathematics textbook from 1931: https://archive.org/details/in.ernet.dli.2015.509299/page/n2... Beyond the intriguing assumption that an adult man might purchase this book, a manual of basic arithmetic, for the purpose of self-improvement, it's pretty much indistinguishable from what we have today. This is the treatment of subtraction: > If any figure…

> Borrowing isn't even a New Math idea.

Borrowing and base 8 weren't created by New Math. Teaching them to students, at least according to the song, was part of New Math. Lehrer specifically says this. In the intro he gives the way it was taught ("Now, remember how we used to do that…Three from two is nine, carry the one"), then he says "But in the new approach, as you know, the important thing is to understand what you’re doing rather than to get the right answer. Here’s how they do it now…", then he immediately shows the borrowing approach, which is followed by the chorus "Hooray for New Math!" After showing "how they do it now", he then goes on to show the same problem in base 8 for the second verse (followed by a repetition of the chorus, and then the song ends).

I get that you don't think the approaches are different, or that they're tied to New Math. Lehrer and his audience did, which is the entire point of the song.

Re: Why did Tom Lehrer swap fame for obscurity?

#145

Post by sophacles »

noneeeed wrote: post #132

I can't imagine many things worse than being famous. I guess if you are the kind of super-rich where you can completely avoid interacting with the rest of society that it would be fine, but not being able to just walk down the street or go to the pub without someone stopping you must get tedious. The kind of quiet fame that Lehrer managed, known to a smallish segment of the population, for being really good at someth…

Mr Lehrer's treatment of Oedipus is one of my recent favorites. For the last few centuries it's usally approached in either and overly-serious or ham-fistedly humorous way - very tiresome.

Re: Why did Tom Lehrer swap fame for obscurity?

#146

Post by vundercind »

coryrc wrote: post #69
bitwize wrote: post #25

Earlier quoted context omitted.

New Math was a response to the Soviet lead in the space race. It was thought that introducing more abstract concepts, like different bases and set theory, would help kids grok math more. It was a fool's game. Just like every other "innovation" in mathematics education since, up to and including Common Core (one of which you probably encountered). At the elementary school level, the only way to increase math proficien…

> Just like every other "innovation" in mathematics education since, up to and including Common Core Have you actually looked into it? I was skeptical too, but then I saw they were trying to teach kids the way I do math. For example, what's 4001 - 3989. The old way would be to borrow and carry three times. But change question to 1+4000-3990+1 and the answer is perfectly simple. Kids I went to school with would litera…

> Have you actually looked into it?

I’ve had three kids go through the early grades with it. I was on the fence at first. It turned out to be awful. The kids hate it. We hate it. There’s weird unhelpful bullshit vocabulary everywhere (“let’s use ‘number sentence’ in kindergarten before we’ve taught kids what a regular sentence is, that’ll surely help!”). Solving the same problem five ways which is infuriating to a kid who “gets it” already and has been very harmful to their opinion of school in general. Their deeper mathematical understanding doesn’t seem to be any more advanced than mine was in elementary school, which was supposed to be the point, and we’re having to supplement the “bad” stuff like multiplication tables so they’re not lacking the very most important math skills in every day life and needed to make actual progress on wrapping one’s head around even simple stuff like, say, algebra involving fractions.

Terrible, way worse than even my more-pessimistic guesses would have been.

Re: Why did Tom Lehrer swap fame for obscurity?

#147

Post by chmod775 »

t-3 wrote: post #116
123894893 wrote: post #64

Earlier quoted context omitted.

The song "New Math" is actually funny to listen to, I think most people don't pay attention to what's happening in it. In the first verse, he's mocking the idea of teaching kids the concept of borrowing, as if it's a bizarre and confusing concept that almost no one would understand. He was completely wrong, of course, and it's the way almost everyone - at least in the U.S. - does subtraction now. The "right" way that…

The only thing I found strange about it was that he started from the least significant digits rather than the most. It's basically the way I've always done subtraction, just backwards.

If you do it the other way around you may have to backtrack if subtracting a less significant digit from another worked out to <0. You will also have to be careful about alignment, since in one number you start from the first digit, but in the other you may start from the middle. It's slightly more complicated than just starting from the least significant digit.

Re: Why did Tom Lehrer swap fame for obscurity?

#148

Post by fragmede »

BizarroLand wrote: post #139
noneeeed wrote: post #132

I can't imagine many things worse than being famous. I guess if you are the kind of super-rich where you can completely avoid interacting with the rest of society that it would be fine, but not being able to just walk down the street or go to the pub without someone stopping you must get tedious. The kind of quiet fame that Lehrer managed, known to a smallish segment of the population, for being really good at someth…

My favorite will always be poisoning pigeons in the park, introduced to me courtesy of Dr. Demento. https://www.youtube.com/watch?v=yhuMLpdnOjY

The sun is a misama of incandescent plasma, by They Might be Giants for me.

https://www.youtube.com/watch?v=sLkGSV9WDMA

A 2009 follow-up to their original song from 1993, the sun song, in which they erroneously claimed the sun is a mass of incandescent gas, to weigh the follow-up song is a correction.

Re: Why did Tom Lehrer swap fame for obscurity?

#149

Post by thaumasiotes »

vundercind wrote: post #143
thaumasiotes wrote: post #115

Earlier quoted context omitted.

It doesn't; multiplication isn't involved at all. The only skill required is remembering that the shorter hand is hours and the longer hand is minutes. https://images.thdstatic.com/productImages/f220d887-1a05-418...

Of course it’s involved! Hour 6 is also minute 30. There’s some arithmetic for you! Six times five, if you like, or six times ten divided by two if you prefer. Many don’t have numbers at all, so you’ll need to build a good intuition for fractions and converting those to hours and minutes if you want to read them fast. Most of us do it so automatically we don’t notice, but some of that’s plausibly fraction multiplicat…

No, the usual case, where the minutes aren't printed on the clock itself, is that you've memorized the positions of :00, :15, :30, and :45, and you report the time by reference to that.

Re: Why did Tom Lehrer swap fame for obscurity?

#150

Post by vundercind »

andrepd wrote: post #93
bitwize wrote: post #25

Earlier quoted context omitted.

New Math was a response to the Soviet lead in the space race. It was thought that introducing more abstract concepts, like different bases and set theory, would help kids grok math more. It was a fool's game. Just like every other "innovation" in mathematics education since, up to and including Common Core (one of which you probably encountered). At the elementary school level, the only way to increase math proficien…

Amazing how this comment is diametrically opposed to the truth :) It's in fact the very contrary! "Drilling maths" into kids is how you get everyone except the most pre-disposed to "hate maths" with a passion. Because they grow up thinking mathematics is deathly boring busy work of repeating the same busy-work ad nauseum. Teaching rote memorization is useless and wastes time that could better be used exploring ideas…

I am deeply suspicious of this POV because in my actual experience it was precisely when we shifted from “apply this thing” to something more like real math that classmates started to give up on math entirely. They may not have liked it before, but that didn’t mean they were bad at it. The anger and resentment and resistance to math came later, when we were past arithmetic and drilling (which were also by far the most useful parts of our primary and secondary school math education, in actual life, for most people)

[edit] my suspicion is because it’s both entirely contrary to my experience, and always seems to come from people who like math so much that they majored in it and started to really love it right around the time the folks I’m thinking of above—a far larger set—have decided not just that they dislike math, but that they can’t do it and also that hardly matters because it seems to be pointless.

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