True. And I was glad I knew set theory because the biggest issue I had in porting the Zurich Pascal compiler to Multics was the set data type. Jensen and Wirth assumed all machines had 60 bit word lengths.
I’ve seen a lot more papers using set theory than using calculus in my neck of the technical woods. I think my kids got it in 6th grade.
Now that the point of teaching set theory to kids has been made (or not), can I ask another question?
Is the division symbol ÷ still used in grade school? I hope not. If it is, all it does is set kids up to be unfamiliar with, or have less intuition for, fractions. In other words, instead of using the ÷ symbol, why not just use the ‘/’ from day one (or grade 3 or whenever).
What is the point of kids using the notation of, say, 7÷2 given that writing it instead as 7/2 not only demonstrates the fractional equivalent but also gives the correct answer! (I am not saying that kids should learn fractions before they learn division. I am just making a case for using ‘/’, the fraction symbol, rather than the ÷)
Since this GQ, I will ask: is the ÷ symbol still taught?
Did you watch the video I posted? It’s quite short.
My experience from talking to my friends elementary school kids is that they are learning different processes. Just like New Math was different than “Old” Math. Maybe the youtube video I found that matches what those kids showed me isn’t universal, but it’s definitely not the way I learned to do those arithmetic operations as a kid.
Also weighing against the ÷ symbol are that it’s not found on standard computer keyboards (when so much nowadays is done on computers), and that it can easily be mistaken for a +.
On the other hand, it has to be taught at some point, because it’s still the symbol used on calculator buttons (even if it displays onscreen as /).
But I don’t know whether it’s still used in grade school-- I only teach as low as 6th.
Ah, OK, I just watched that video. Not only is that not any different from New Math, it’s not different from Old Math. I was taught that method in the 80s, and so was my mother, in the 40s.
ISO 80000-2 says no, bad; but Common Core State Standards have it.
That said, it’s kind of pretty clear that the dividend goes in place of the upper dot, and the divisor goes in the bottom. ISO 80000-2 also says lots of stuff, like “log x shall not be used in place of ln x, lg x, lb x, or log[sub]e[/sub] x, log[sub]10[/sub] x, log[sub]2[/sub] x”, but, you know, sometimes I just want to write “log x” without specifying the base, and standards be damned.
ETA The ISO standard says its recommendations are “mainly for use in the natural sciences and technology”, so not primarily meant for teaching mathematics.
Note that there’s a lot of “behind the topic” stuff that goes on during education.
It is really important, to say the least, to teach kids how to think logically and clearly about stuff in general. Set Theory is one good way of introducing many concepts in logic.
This is true about a lot stuff in education. There’s what they are being taught on the surface and then there’s what’s being taught implicitly.
One other big problem is this resistance to learning that too many people have. So they think “This will never do me any good.” and don’t retain it.
One result is that they don’t realize later in life “Oh, I could figure this out using Set Theory!” when they encounter a real life problem. If you don’t retain and appreciate the material, you just won’t see it when it comes up. It really is handy … if you don’t have a negative attitude towards such things.
Making sure I understand correctly: There are three methods for long subtraction in the video that they call “Old Math” “New Math” and “Core Math”. Are you saying you and your mother both learned all three in elementary school?
The first two methods are similar enough as to be considered interchangeable. I don’t remember precisely which one I was taught.
But both I and my mother were taught both (one of the first two methods), and the third method.
More cynically… In Toronto there is OISE, the Ontario Institute for Studies in Education. There clever people get grants to study new ways to better teach kids the same old things. I’m sure every major center of learning has something similar. these guys get government grants to study and devise new curriculum and new methods of teaching. In this fusion of government, academia, and ego, nobody got kudos for showing “we’ve been doing it right all along”. They have to come up with bold new ideas that turn everything on its head. Bonus points if you can devise something like New Math in the 60’s and 70’s - “This is so radically different you parents won’t get it, so stay back and leave it to the paid experts like me…” So following on the same concept as “whole word” reading, academia took a serious wrong turn in order to prove that they were smarter than hundreds of years of trial and error experience.
Set theory is very nice. closed operations in the set, commutativity and all that. But what young children really need is numbers and how they work. Then they can delve into the mystery of why 2x3+3x3=(2+3)*3
I don’t know about anyone else, but I found New Math/set theory in 5th grade to be a refreshing change of pace from the arithmetic of previous years. I don’t know what they used to teach in 5th grade math, but I never had problems with any future math courses throughout grade or high school, so it must not have been anything important. Much like 8th grade math, which I could easily have skipped.
At any rate, I did need to know set theory in other math classes (I can’t remember which was the first, though) so learning it in 5th grade was not a waste of time.
An therein lies an entire lifetime of argument. You can find a remarkable number of arguments and differences of opinion just trying to work out what sentence means.
And the whole point of New Math was that kids weren’t getting how numbers work.
Right. “Old” Math was rote memorization oriented. If you encounter something outside what you’ve memorized you might not be able to generalize what you do know to the new problem.
It’s like with spelling: You can merely memorize how to spell a ton of words only or you can be taught fewer words plus the general rules of spelling (such as they are).
I agree the first two are very similar. But the second of them is “New” Math. For all the complaining about it… it was pretty darn similar. Probably the real complaining was about doing math in different bases.
I don’t recall ever seeing the third method as a kid. I don’t have any data on whether my experience not seeing it or yours seeing it is more typical. I can for sure say that there are plenty of people like me, even if we’re a minority, because I see them complaining that they never learned to do math that way and now they can’t figure out their kids’ homework 
Another relevant aspect is: even if you saw both methods, which one was the dominant one taught? For example, I remember briefly touching on Russian Peasant Multiplication, but it was not the general way I did multiplication. You mentioned that you teach math. I took plenty of math in school and majored and work in a math-adjacent field (Computer Science). We’re easily in the 95th percentile for remembering alternate mathematical processes.
The average parent is going to remember the one way that they did most subtraction problems and if the process their kid is learning is not that one way, is going to be confused, either momentarily (if they are comfortable with math) or dramatically (for most people who are not).
I don’t know that I have consciously applied set theory since math classes, but I unconsciously use it in my job and personal life on a regular basis. Boolean searching, logic puzzles, sql queries, etc
(With calculators ubiquitous, most people barely need arithmetic these days.)
One of the top objectives of elementary school math should be to awaken a possible interest in and admiration for math and logic. If teaching set theory is a good way to achieve that, I am in favor.
The whole point of New Math was that teachers and educators were in the process of dropping Math from the curriculum. After all, how much math do you actually need? If you’re a grade-school teacher, your learned experience was that you didn’t need very much math at all.
So that was happening, and then a couple of things happened: The Army. Sputnik. And mathematicians.
The Army wanted people with more math than you need to be a grade-school teacher. They weren’t happy with the entry standard they were getting. Sputnik galvanised a nation. And mathematicians didn’t think that math should be dropped from the school curriculum: so the mathematicians came up with some ideas about what they thought would be actually useful in a school math curriculum.
Regarding set theory, I can’t say that I think the mathematicians were wrong. I learned a notation for set mathematics in 5th grade, and that notation was used in my math classes for the next 25 years. I also learned some spelling, and I’ve found that equally useful: I skipped 6th grade, and never learned to spell the words on the 6th grade list: that’s given me an appreciation for the value of things you learn in grade school just because they are on somebodies list of things you should learn in grade school
You can be a better elementary school teacher by knowing at least algebra and geometry, because you can be a better everything by knowing algebra and geometry.
Calculus, I’ll admit is of use or interest only to a limited set of people, but we already correctly treat it as such: In the current system, nobody takes calculus unless they have some reason to be interested in it.
I think arithmetic needs to be burned in to the brain, to the point that one is told “John has 14 apples and gets 8 more” and then when asked to repeat it, says “John has 22 apples.” 8+14 is blurred with 22 in the brain. The addition facts should be as automatic as 2+2=4. The multiplication and division merely burn the addition and subtraction deeper in the brain. You can’t stop and pull out a calculator to do addition, but you’ll never get that good at addition and subtraction unless you use them to do multiplication and division. And fractions.