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Written by Vince Vatter on 2024-12-13 at 23:16

unfortunately the price was determined using new math so I didn’t buy it

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Written by Matt McIrvin on 2024-12-14 at 22:39

@VinceVatter ah yes, all the kinds of New Math: sets, number systems, AND computers

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Written by Matt McIrvin on 2024-12-14 at 22:58

@VinceVatter also I think the abacus crashed, try turning it off and on again

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Written by llewelly on 2024-12-15 at 11:17

@mattmcirvin @VinceVatter

Although most of the math textbooks I had were published after the "new math" effort had flopped and been forgotten, I did have one from that era, and it covered arithmetic in different bases, from base 2 up to base 36, but focused on base 2 , base 8 , and base 16 . It also covered set theory and boolean algebra, which I didn't see in a lecture or class format until I took discrete structures in college.

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Written by Matt McIrvin on 2024-12-15 at 15:31

@llewelly @VinceVatter In another thread I was just discussing the extent to which New Math ideas persisted. I went through elementary school a few years after it was basically over, and I think there were some remnants hanging around--math textbooks would often have a little "fun facts" squib off to the side about alternative numeral systems and different bases, but it wasn't a primary topic. I think I encountered set theory in an old "New Math" book for kids, simpler than this one.

I knew about binary through pop-technology books on computers and because my dad was a systems programmer; he taught me how to convert numbers between decimal and binary. I remember the explanations of how computers represented bits in magnetic core memory.

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Written by Matt McIrvin on 2024-12-15 at 15:36

@llewelly @VinceVatter But I do think it's underappreciated that the "New Math" reform of arithmetic teaching basically persisted. The way they taught how to do multi-digit arithmetic operations pre-New Math avoided any discussion of theoretical concepts at all; you'd just memorize facts like "6 from 4 is 8 carry the 1". Afterward, they talked about "regrouping" and emphasized that it worked that way because the tens digit represented groups of ten. And that's the way I learned it.

Tom Lehrer was a math educator so he was very aware of all of this, and his wry song "New Math" went into amazing detail about it. I remember hearing this and realizing that the puzzling New Math version was what was familiar to me, and the "way we used to do that" seemed weird and alien.

https://www.youtube.com/watch?v=W6OaYPVueW4

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Written by llewelly on 2024-12-15 at 15:38

@mattmcirvin @VinceVatter

oh! Yeah, I had not realized some aspects of New Math persisted, despite being familiar with most of Lehrer's songs.

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Written by Matt McIrvin on 2024-12-15 at 15:42

@llewelly @VinceVatter My favorite bit of that is the patter aside at the beginning about how "if you're under 35 or went to a private school" you do it one way and "if you're over 35 and went to a public school" you do it another way... which is subtly acknowledging a previous round of confusing reforms!

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Written by Matt McIrvin on 2024-12-15 at 15:57

@llewelly @VinceVatter Of course the culture-war echoes of it persisted too--to this day, set theory is one of the topics that "Christian" homeschooling curricula proudly advertise that they DON'T cover.

I've seen people way overthink why that is, speculating about transfinite arithmetic being some kind of threat to traditional theology, etc.

I don't think that's it at all. I think it's just that set theory was a big part of Sixties New Math, which was liberal hippie junk, so it's still anathema to these people.

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Written by Matt McIrvin on 2024-12-15 at 16:08

@llewelly @VinceVatter (oh, yeah, and emphasizing that "addition is commutative"? We definitely got that, and that was New Math too--I don't think that the older elementary arithmetic curriculum particularly emphasized that this was a property with a name.)

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Written by llewelly on 2024-12-15 at 16:14

@mattmcirvin @VinceVatter

yeah, I recall getting "addition and multiplication are commutative, subtraction and division are not", but I didn't realize the emphasis came with "new math".

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Written by Matt McIrvin on 2024-12-15 at 16:35

@llewelly @VinceVatter I think, basically, what happened was that there was a certain selection process--the elements of the New Math reforms that were just confusing or that many teachers couldn't handle got dropped, and the stuff that fit well into the existing arithmetic sequence was retained aside from the occasional "did you know?" edutainment break.

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Written by Leon P Smith on 2024-12-20 at 14:17

@mattmcirvin @llewelly @VinceVatter

Venn Diagrams are also one of the long-lasting contributions of New Math, which is an echo of set theory that's pretty much unavoidable in modern culture.

Julie Moronuki mentions that in her presentation on the Unreasonable Effectiveness of Metaphor:

(Another fun fact: Wittgenstein's Tractatus Logico-Philosophicus may have introduced and at least popularlized truth tables. But I more typically appreciate the later Wittgenstein who was highly critical of the Tractatus.)

https://argumatronic.com/posts/2018-09-02-effective-metaphor.html

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Written by llewelly on 2024-12-20 at 14:26

@leon_p_smith @mattmcirvin @VinceVatter

true, but living in the western USA, I don't think I saw Venn Diagrams in a text book until I took Discrete Structures in college, so they're a part of New Math that didn't last, at least not that part of the world.

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Written by Leon P Smith on 2024-12-20 at 14:31

@llewelly @mattmcirvin @VinceVatter

I remember set theory from elementary school, but I'm sure it was past the point of spending any significant amount of time on it. But as a child who was already writing BASIC programs for a Commodore 64, I had mental models to relate set theory to, and I was a supremely example-efficient learner... so you had my full attention whenever you talked about set theory, and I didn't forget much till next time. In fact I'd probably spend quite a bit of time thinking about whatever that lesson was, and maybe even clarify certain things in my mind before next time.

Also, my Algebra II teacher in High School introduced the class to set-builder notation, which is very similar to list comprehensions in Haskell.

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