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The image attached is a comic strip from "Peanuts," dating back to 1965. It portrays Sally, the younger sister of Charlie Brown, throwing a tantrum over learning set theory in elementary school math. While it appears to satirize the 'New Math' movement, the set theory terminology that Sally uses seems rather advanced for elementary school level. Did American elementary schools actually teach such complex set theory concepts during that era?

Relatedly, a Japanese mathematician who was active in America during that time once wrote an essay recounting an incident where his daughter asked for help with her math homework. Upon reviewing it, he found the material incomprehensible. Interestingly, this mathematician was so accomplished that he was awarded the Fields Medal.enter image description here

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  • $\begingroup$ I can only claim to have erased all the New Math I supposedly learned back then. Doing so never hurt my career at all. $\endgroup$
    – Jon Custer
    Commented May 19 at 11:26
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    $\begingroup$ New Math:"New Mathematics or New Math was a dramatic but temporary change in the way mathematics was taught in American grade schools, and to a lesser extent in European countries and elsewhere, during the 1950s–1970s... Topics introduced in the New Math include set theory, modular arithmetic, algebraic inequalities, bases other than 10, matrices, symbolic logic, Boolean algebra, and abstract algebra." This happened when many educators took the early 20th century obsession with "foundations" too seriously and decided to bring it to the masses. $\endgroup$
    – Conifold
    Commented May 19 at 11:47
  • $\begingroup$ I never saw material on "sets" until SMSG. Also, the topics enumerated by @Conifold . That would have been around 1965. But for me that was junior high school, not elementary school. $\endgroup$ Commented May 19 at 12:26
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    $\begingroup$ Historical remark: "New Math" really originated in France, under the influence of Nicholas Bourbaki, who systematically introduced set theoretic approach. They had a strong influence on how mathematics is written nowadays, both in mathematics itself and in education. But math education somewhat overreacted. This was a world-wide phenomenon. $\endgroup$ Commented May 19 at 13:48

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Yes. I was there.

I was at an American school in São Paulo, Brazil. Apparently, it was easier to introduce the new ideas in such foreign settings (a private school, no school boards to satisfy, teachers adventurous enough to spend a few years in foreign parts). I remember learning about one-to-one correspondences, unions, and even Cartesian products, all in the first few grades. As Tom Lehrer has it, we “regrouped” instead of “carrying.” Of course, not all of the terminology was in place, but I recognize most of what Sally quotes.

My students today are flabbergasted to hear that I was doing modular arithmetic in 7th grade, knew what a field was in 8th, and spent pleasant hours doing row-reduction in 9th. We learned propositional logic (either in 7th or 8th grade). The discussion of trigonometry distinguished functions of an angle from functions of the measure of an angle. It was wild.

But we learned the usual stuff too, with less drill and repetition, but we did it.

I loved it all. It may not have worked for everyone, but it certainly worked for me. Maybe I had special teachers. I still remember them and I am grateful.

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  • $\begingroup$ Haha. thx for sharing your memories. $\endgroup$
    – enjin2000
    Commented May 24 at 8:08
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If it helps, I was in the fifth grade at an American elementary school in the 1969–1970 school year and I recall plainly Mr. Moore’s teaching us about sets, subsets, supersets, unions, and intersections, along with the symbols $\subset$ and $\supset$ for the relations and $\cup$ and $\cap$ for the operations.

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  • $\begingroup$ I don’t think he covered the Axiom of Choice, though :-) $\endgroup$ Commented May 26 at 19:14
  • $\begingroup$ FYI, I was also in 5th grade during the 1969-1970 school year. Our teacher was absent quite a bit throughout the day, for reasons I don't know, so my memory was mostly of reading several dozen juvenile U.S. history books located on the window shelf at the back of the classroom (some that I've since purchased at used book stores are Wild Bill Hickok Tames the West and Bill Williams: Mountain Man (continued) $\endgroup$ Commented May 26 at 23:53
  • $\begingroup$ and The Winter at Valley Forge and Daniel Boone. The Opening of the Wilderness and The Pony Express) and doing some lengthy multiplications for fun (e.g. $2 \times 2 = 4$ then $4 \times 4 = 16$ then $16 \times 16 = 256$ then to $65536$ and two more past this -- I still have my scrap paper work from this) and imaginations about how big a trillion is (about $32,000$ years of seconds; (continued) $\endgroup$ Commented May 26 at 23:54
  • $\begingroup$ also number of cubic millimeters in a $10$ meter cube, which astounded me by its seeming comprehensibility in comparison to the number of seconds description). Very little academic work took place, in fact for me this was pretty much true throughout elementary school until 7th grade, and most everything I knew in math and science were things I learned from public library books (especially by Isaac Asimov and the World Book encyclopedia, the latter of which I had at home). Incidentally, some comments about my 1st grade math book are here. $\endgroup$ Commented May 26 at 23:54
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A useful resource here is a 2014 article and a follow-up 2015 book by Phillips:

Phillips, Christopher J. In accordance with a "more majestic order'': the new math and the nature of mathematics at midcentury. Isis 105 (2014), no. 3, 540–563.

and

Phillips, Christopher J. The new math. A political history. University of Chicago Press, Chicago, IL, 2015.

I personally found the article more useful than the book, but in this case the book actually contains a mention of "equivalent sets" on page 82 and elsewhere. I haven't found any mention of "placeholders" though; that seems a bit far-fetched.

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