Tom Lehrer - New Math (Animated)

My favorite Tom Lehrer song is probably New Math. ▶ this video With its clever lyrics and rapid fire delivery it sounds like it could have come out last year and not fifty years ago.

Yes, he's mocking the idea of teaching borrowing. He gives the way he thinks subtraction should be taught in the intro. It's a way that, as far as I can tell, hasn't been taught in America in over half a century. After the intro, he goes on to mock the concept of borrowing, which was (apparently) part of New Math. Then in the final verse he mocks the idea of teaching bases. Here's a good animated version of the song that shows the different methods. You'll notice that the "silly" New Math method is the way that makes sense to Americans today, and the "simple" method preferred by Lehrer is very confusing for anyone who's not used to it: ▶ this video Here's more of the intro which makes it clear what's going on. My explanations in brackets: > Some of you who have small children may have perhaps been put in the embarrassing position of being unable to do your child’s arithmetic homework because of the current revolution in mathematics teaching known as the “New Math”. > So as a public service here tonight, I thought I would offer a brief lesson in the New Math. Tonight, we’re gonna cover subtraction. [ New Math is confusing, and he's going to go over how confusing it is in a humorous way.] > Consider the following subtraction problem, which I will put up here: 342 minus 173. Now, remember how we used to do that… > Three from two is nine, carry the one, and if you’re under 35 or went to a private school you say seven from three is six but if you’re over 35 and went to a public school

Yeah, ultimately it's the same algorithm, it's just a question of what are the details of the procedure, which makes it confusing if you've learned one way and not the other. The whole point of the song is that Lehrer thinks this is a new, less good way of doing subtraction. Look at this video if you haven't already: ▶ this video The first way he does it seems INCREDIBLY confusing to people who learned arithmetic in the last 30 or so years (the sentence "8 from 4 is 6" is nonsensical to most such people), but the "modern" way he's mocking is perfectly understandable. 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. It is just as fast, and it gives you a much better intuition about what's actually happening, instead of just learning the steps by rote.

It's inevitable to link to this now: ▶ this video It's Tom Lehrer, about 50 years ago, explaining subtraction in the context of the "new" math (the base-8 stuff starts at 2:40). Worth a listen.

Pounding the dust out of the erasers was something American students often found fun, especially as elementary school students; this is referenced in the Tom Lehrer song "New Math": ▶ this video

A whole lot of "I think", "I believe," "I feel". No reference to existing educational research on what works and what doesn't. >This isn’t a call to give up, though: instead, we should teach maths differently, in a way that doesn’t churn out mathophobes. When five-year-olds first encounter the subject, it’s as a creative, open-ended activity, involving play and exploration. They learn about numbers using colourful blocks that join up in different ways. They fit these shapes together and tell different stories with them. Just a year or two later, though, maths becomes a discipline with strict rules and a forbidding regime of right or wrong answers. Instead we should try to maintain that sense of exploration and open-endedness, of trying out different approaches to a problem and seeing what works. What’s important about times tables, for example, is not the answers, but the different possible relationships between numbers. What’s important about equations is not the solution, but the techniques we use to untangle a problem using logic. Some of these exercises could be presented more like a Sherlock Holmes mystery, where the focus is on how the clues are pieced together and not just on what the answer must be. Where's the evidence that this would actually be a superior teaching method? The point of drills is to counteract the natural tendency to forget things. Fluency is gained through practice and repetition. There's no way around it. Think of an actual Sherlock Holmes mystery

I think it depends on what curriculum your school's using; non-base-10 math is a punchline in Tom Lehrer's "New Math" [1]. Common Core might be getting rid of it? As a side note, comparing the complaints in "New Math" (from 1965) to those offered about Common Core is educational :) [1]: ▶ this video

Tom Lehrer complained about "New Math" some 60 years ago. ▶ this video (To be honest, "new math" makes sense to me. But whatever, for us oldies this is as obligatory as a XKCD) He had no idea about where the world would go with "woke", though.

It's not quite the same, but there've been several efforts in the US to shift math education away from "memorize this algorithm for addition, this one for multiplication, etc." and instead get kids to understand our number system. New Math was ridiculed for it[0], and now Common Core[1]. "Why are you teaching kids these inefficient ways of multiplying instead of memorizing the standard algorithm?" Despite it being the focus of Tom Leher's song, my go-to test for "Do you understand our number system?" is "Can you work out a multiplication problem in base 8?" If you understand the concept of digits, you can solve multiplication in other bases, and likely have solid grasp on how our number system work. From there, you'll understand both the standard arithmetic algorithms and will be able to figure out your own shortcuts. If you lack this understanding, you're likely stuck just mindlessly using the algorithm you were taught. (One other thing I'd also like for us to add is Fermi problems. Physics students learn to estimate everything from the mass of the earth to the number of dogs in their city. Seems like something everyone would benefit from practicing and that kids would really enjoy.) [0] Tom Leher has a famous and delightful song about it: ▶ this video [1] link (This is more a defense of Common Core, but in response to the common complaint.)

it’s so simple/so very simple/that only a child can do it! (and remember kids, base 8 is just like base 10, really — if you’re missing two fingers) ▶ this video

I find it funny that his "New Math" has now been replaced by an even newer math which parents can't understand. ▶ this video

doesn't have New Math ▶ this video growing up we had two Tom Lehrer albums (I guess my parents had their good points)