Talk:New Math

clearer general explanation needed

I just skimmed through this entire entry and I still have no idea what new math is. The most I can gather is it's a general set of teaching principles for how to teach math, but that's just a guess, I really have no idea what new math is from reading this. Someone needs to write a 2 or 3 sentence overview of what new math is as it needs to be described to someone from mars who's never heard of it before.

Also, if you want to be really helpful, you should have one simple example problem worked out and solved using new math steps.

I completely agree with this -- I have read this article and still don't know what "New Math" actually *is* -- can't someone put up some examples??? Danflave 08:16, 23 September 2007 (UTC)

This is still a problem in 2010. Can anybody give even an example of what the "new math" was? —Preceding unsigned comment added by 208.66.47.162 (talk) 18:57, 26 January 2010 (UTC)

For my History of Math class at Roger Williams University, we are required to improve a Wikipedia article about math. So I would like to add an example of new math, in particular, the example Tom Lehrer uses in his "New Math" song. — Preceding unsigned comment added by Ajohnson398 (talk • contribs) 16:03, 9 December 2010 (UTC)

Gee, when something falls out of favor, it sure gets difficult to find out many details about it. I was raised on New Math, and in sixth grade we were told we were 'learning New New Math from the guy who invented New Math'. After that we moved and I felt like I was being taught from McGuffey Readers. It was archaic. Too much emphasis on simple basics and none of that fun stuff that got me excited about math in the first place. And nobody would help me with the parts I was missing. I did miserably in math after that. I came over here hoping to find some of those elements that so delighted me before. All I found was criticism. — Preceding unsigned comment added by Leeeoooooo (talk • contribs) 05:04, 24 November 2012 (UTC)

Updating this to mention that in 2019 this page still does not explain what New Math is/was, nor any factual history of its development, implementation, or discontinuance. Is there an appropriate header notification that can be placed on the top of the page? The existence of the page itself doesn't seem warranted without such basic information.--Rosswagner1985 (talk) 20:23, 11 January 2019 (UTC)

I agree that a history of the development of the New Math would be very helpful. More details as to what the New Math contained would also be useful. As to the explanation of what New Math is/way, the first five sentences of the article read:

New Mathematics or New Math was a brief, dramatic change in the way mathematics was taught in American grade schools, and to a lesser extent in European countries, during the 1960s. The change involved new curriculum topics and teaching practices introduced in the U.S. shortly after the Sputnik crisis, in order to boost science education and mathematical skill in the population, so that the technological threat of Soviet engineers, reputedly highly skilled mathematicians, could be met. The phrase is often used now to describe any short-lived fad which quickly becomes highly discredited. Topics introduced in the New Math include modular arithmetic, algebraic inequalities, bases other than 10, matrices, symbolic logic, Boolean algebra, and abstract algebra. In elementary school, in addition to bases other than 10, students were taught basic set theory and made to distinguish "numerals" from "numbers."

Sometimes it is hard for those who are familiar with the topic to see what is missing. This seems like a basic, but accurate, description of the movement. Can you be more specific into what is lacking as to the explanation of "what New Math is/was"? --seberle (talk) 08:55, 14 January 2019 (UTC)

I had heard of "New Math" all my life (as a byword), but never knew what it was. It was perfectly clear to me after reading "Topics introduced in the New Math include modular arithmetic..." Perhaps those who still don't know what New Math is after reading the article are unfamiliar with those topics, in which case they ought to read the articles that those link to. The "new math" topics are centuries old, and are more relevant today than ever before. They are critical to understanding key parts of nearly all modern communication. (At the same time, the criticism that it was inappropriately introduced into the general math curriculum is quite valid.) I was absolutely delighted to finally learn what New Math is, or was ... the new math topics formed a large part of my career, and I am very grateful to the articles authors.SigProcEngineer (talk) 06:16, 1 March 2019 (UTC)

---

Ah yes, the New Math continues to be a persistent conundrum.

Thirteen years of talking about this article and still there has been no effort to explain what the New Math is/was. I guess the New Math is still too hard to understand. I repeat the first post: "I have read this article and still don't know what "New Math" actually is".

You might say, "Well, wiseguy, why don't you fix the article?". Well, I can't, I learned math the hard way starting with the multiplication tables up through Calculus and beyond without using the New Math. So I am unable to do so. I am optimistic that there is someone who might have the intuitive insight to point out what is "obvious" about the New Math. After all, it was taught to children.

I'll be back in thirteen more years to see if this issue might have been resolved, or not. Here's hoping.

Osomite (talk) 00:46, 15 April 2020 (UTC)

You are right. Since I wrote my comment above in January 2019, someone has muddled up the text with opinion and critiques. It is really no longer clear what New Math is. It needs editing or reverting. --seberle (talk) 17:30, 12 December 2020 (UTC)

The current (May 2024) lede is fairly decent, although my comprehension is within the scope of being a recipient of said "objectionable" training. Upside being, I actually had to understand *why* a formula worked, downside, it well equipped me to work in IT, where base 8, 16, 32 and currently 64 are old friends. Sets and subsets theory, preparing me for literally figuring in my head on the fly resultant sets of policy within a complex active directory environment. Things that confound those who did not receive such a more comprehensive education in math, despite my being actually dyscalculic and dyslexic.

Go figure. Frankly, just another Red Scare moral panic.Wzrd1 (talk) 23:38, 13 May 2024 (UTC)

discussion

I removed: "The U.S. experience does seem in retrospect to have the hallmarks of a moral panic.", as it is original opinion. If it is verifiably seen now as moral panic, it needs substantiating (that people believe it, not the belief itself!). Grayum 10:50, 12 September 2005 (UTC)

What in fact were the traditional concepts referred to in the following statement?

"New Math emphasized mathematical structure through abstract concepts like set theory and number bases other than 10, rather than strictly being concerned with mathematical concepts traditionally taught to grade schoolers." odea 00:21, 15 April 2006 (UTC)

Does "rather than strictly being concerned with mathematical concepts traditionally taught to grade schoolers" actually mean anything? It seems to me to be saying "rather than doing what was done before", which is tautological, so that entire phrase could easily be removed. If I understand correctly, what was replaced, or de-emphasised, was performing the calculations required for the four traditional arithmetic operations mechanically.

I'm also a bit baffled by the apparent claim that number bases other than 10 are an "abstract concept", while presumably a number base of 10 is not. Switching between different number bases would be an abstraction, but it would be the very useful abstraction of considering a number something separate from the string of decimal digits representing it - something that still seems to be done in grade school, for example when kids are asked to "count" money that is cunningly represented in different coins or bills.

RandomP 01:10, 16 April 2006 (UTC)

Lehrer's song

I am not convinced that the text is entirely mathematically correct. The third verse (which covers the tens place calculation of 342 - 173) starts with

From the three you then use one

To make ten ones...

Doesn't Lehrer here make ten tens? Sjakkalle (Check!) 08:31, 30 August 2006 (UTC)

I'm reminded of the old joke, there are 10 people that can understand binary, those that can, those that cannot and those that don't care.Wzrd1 (talk) 23:39, 13 May 2024 (UTC)

Where can we get pictures?

Back when I was teaching myself New Math with a "Cyclo-Teacher" in the '70s and '80s, I didn't know it had a name. Some of us only recognize New Math when we see those little set-theory diagrams. Does anyone have one that could be legitimately uploaded and used? --Lawikitejana 21:07, 3 October 2006 (UTC)

Something like ? Wikimedia Commons has a lot of them.--Prosfilaes (talk) 23:20, 2 June 2008 (UTC)

I'm not sure Venn diagrams would be the best illustration of New Math. Schools commonly teach Venn diagrams today, even in kindergarten, without much of a problem. But New Math put an extreme emphasis on sets and required students to learn set concepts, vocabulary and notation, which is generally not done any more. Venn diagrams would be an example of something introduced in the New Math that remained in current curricula. A better illustration might be a page from an old textbook teaching other bases, which is not done today at all. Then again the Venn diagram would not be wrong and might be better than nothing. seberle (talk) 14:32, 27 October 2008 (UTC)

Professor George F. Simmons

Does anyone know more about him? I have a both a calculus book and a differential equations book that he wrote. I liked his books for his heavy historical, biographical, and philosophical approach to mathematics. It is rare to find a "literate" mathematician; although, it appears that he is tainted by antisemitism? Comments anyone?--Lance ^talk 09:18, 14 November 2006 (UTC)

Repetition

In "The New New Math" section, the phrase "increase mathematical power for all students by creating frameworks which set world-class standards of what all students must know and be able to do" is repeated. I'd like to fix this up but I'm not quite sure how best to. Robert K S 13:00, 4 January 2007 (UTC)

New New Math

Unless there is serious objection, I will work up a separate New New Math article. There is, imo, no continuity between New Math and New New Math, aside from the similar names. Jd2718 23:17, 31 March 2007 (UTC)

Absolutely no objection here. There should not be a "New New Math" section in this article since, as you say, there is no relationship between the Math Wars of the 1990s and the New Math. I'm not sure you need a new article entitled "New New Math." The current article on the "Math Wars" is sufficient. There is also coverage of the Math Wars in other articles. What it is doing here in an article on an educational phenomenon of the 1960s is a mystery to me. If you do not move this section soon, I will probably just delete it.--seberle (talk) 02:03, 30 August 2009 (UTC)

well "new math" however was a commonly used term to distinguish those newer textbooks and curriculas from the conventional/pre 1990s ones.--Kmhkmh (talk) 17:09, 29 October 2019 (UTC)

Expansion request

The section "across other countries" lacks facts about how New Math influences Asian, African and Latin American countries. Please search for relevant sources and add these facts.--RekishiEJ (talk) 17:15, 27 September 2009 (UTC)

And while expanding, could someone explain what the sentence "In Japan, China and Asian countries generally, the emphasis on basic numeracy has traditionally been high" has to do with the New Math?

Absolutely nothing. I have deleted that sentence. --seberle (talk) 23:42, 21 November 2009 (UTC)

1970s?

I would like to say that I was taught the New Math in Arizona in the 1970s (1971-1976). I can't add this because it is anecdotal and subjective, but perhaps there are sources that show that the pedagogy had a long afterlife in US Elementary schools? Saudade7 03:30, 3 July 2010 (UTC)

Well, it was covered in Pennsylvania from the mid-late 1960's through to at least 1980, when I graduated. Removal disadvantaged kids graduating that wanted to go into IT, where non-base-10 math is the norm, not to mention sets and subsets concepts applying to silly minor things like Active Directory Resultant Sets of Policies.Wzrd1 (talk) 23:42, 13 May 2024 (UTC)

Axiomatic Set Theory

Reference 1 does not mention axiomatic set theory at all (words like “axiom”, “zf”, “logic” etc. are not mentioned) --Chricho ∀ (talk) 21:50, 14 October 2011 (UTC)

what???? — Preceding unsigned comment added by 41.107.83.210 (talk) 22:23, 21 August 2012 (UTC)

I haved removed the claim.[1] --Chricho ∀ (talk) 12:58, 27 December 2012 (UTC)

Parts of "New Math" are still used routinely

This page is definitely in need of work. One of the reforms in "New Math" -- which is actually even mentioned in the Tom Lehrer song! -- is the introduction of the concepts of "borrowing" and "carrying" to addition and subtraction problems.

 This is not so. I learned these methods well before New Math was taught anywhere. 

This *stuck* as a pedagogical technique. The way arithmetic was taught before appears genuinely bizarre to anyone who went to school from the 1960s onwards, to the point where I can't even describe it.

So some of the changes from the "new math" period were dropped, but others were permanent.

Needs a balanced treatment by someone who knows the pedagogical history. 24.59.161.166 (talk) 04:54, 27 December 2012 (UTC)

Gotta give, despite the dated entry, the valid point on the concept of "borrowing and carrying", which my WWII era educated parents fully understood and were able to teach. They got to then try to grasp sets and subsets, anything beyond base-10, etc. In hindsight, I emphasize with them, but do grasp novel concepts far better than they were educated to be able to do.Wzrd1 (talk) 23:47, 13 May 2024 (UTC)

Modern Exercises

This section doesn't seem to support itself with citations, and the claims of hat isn't taught seems contrary to what seems to be taught? There's no citation to what is taught today. 174.62.68.53 (talk) 21:54, 12 March 2014 (UTC)

elementary school only??

New Mathematics or New Math was a brief, dramatic change in the way mathematics was taught in American grade schools, and to a lesser extent in European countries, during the 1960s.. I had New Math in eighth grade c. 1963. Since this is mere anecdote, I guess it has no probative value herein, but the blanket statement should still be modified. — Preceding unsigned comment added by 108.249.146.8 (talk) 21:46, 5 April 2015 (UTC)

Excessive hyperlinking

This number of hyperlinks seems pointless to the article, and misleading in some points. Is it okay to remove the stupid ones?

90.174.167.118 (talk) 06:29, 26 November 2015 (UTC)

Common Core

Shouldn't there be some linkage to Common Core Math, given the similarity in traditionalist opposition to both New Math and CC? I'm not sure how it could be expressed, though. SpareSimian (talk) 20:53, 19 January 2017 (UTC)

The New Math was a historical international phenomenon, though particularly important in the U.S.. There was certainly opposition to the New Math's attack on traditional topics, but I'm not sure it all came from "traditionalists". Many who agreed the American curriculum needed changing (such as Feynman, who is quoted in the Wikipedia article) also felt the New Math was the wrong way to do it. Today, there is opposition from both traditionalists and reformers against the Common Core. So a claim that opposition in either case was/is particularly "traditionalist" would need some references. --seberle (talk) 14:31, 27 January 2017 (UTC)

I see that an anonymous editor has added "Common Core" to the "See Also" list. I don't doubt there might be some connection (other than "traditionalist opposition"), but I'm not sure what this person (and possibly others?) had in mind when this was added. Can someone explain a motivation for adding this? --seberle (talk) 08:11, 29 March 2021 (UTC)

As near as I've ascertained, it's an objection to any mathematical concept beyond "one, two and many" math. Traditionalist objections are basically objections from rote memorization, which is decidedly odd, given their rejection also of anything complex enough to make a nuclear weapon, while thoroughly embracing said weapons. Odd period, to put it mildly, but growing up during the trailing edge of it... It's just odd. Upside was, Nineteen Eighty-Four was required reading, which eventually was gifted reading four our children. Downside, parents ill equipped to help their kids out with math homework assignments.Wzrd1 (talk) 23:52, 13 May 2024 (UTC)

common misunderstanding

"The name is commonly given to a set of teaching practices introduced in the U.S. shortly after the Sputnik crisis, in order to boost science education and mathematical skill in the population, so that the technological threat of Soviet engineers, reputedly highly skilled mathematicians, could be met."

engineers \neq mathematicians. there are mathematicians who focus on applied mathematics/engineering problems and I am sure there are rare engineers who do 'mathematics' but by and large the two are very separate disciplines. engineers focus on applying previously known mathematics and science to 'real world' problems. key features of engineering involve building things in well posed, goal oriented contexts with clear motivation. mathematicians do math, sometimes just for math's sake, and sometimes in the context of applied problems. very few engineers go around proving theorems about an infinitely-differentiable hypergraph whose elements are Lebesgue-measurable varieties endowed with the atomic measure (I made that up it is arbitrary jargon) and few mathematicians design and build bridges.

this section should be say something like

"so that the technological threat of Soviet engineers could be met." (preferred). or "so that the technological threat of Soviet engineers, reputedly highly quantitatively skilled, could be met." even this is redundant. any good engineer worth his salt is quantitively skilled...

As it stands now, the section reads to a mathematician like saying "so that the legal threat of Soviet lawyers, reputedly highly skilled poets, could be met." both professions use the english language like both mathematicians and engineers use math, but they just ain't the same. — Preceding unsigned comment added by Lovelobster (talk • contribs) 03:51, 2 February 2017 (UTC)

You might be right. However, keep in mind that the article is not directly about Soviet engineers and mathematicians, but rather the public perception of them at that time. This article needs a bit more development of the historical forces behind the New Math, and more references to support the brief overview in the article. Some good references could guide us to make this sentence more accurate. seberle (talk) 08:23, 2 February 2017 (UTC)

"Mathematicians" should not be so narrowly defined as to suggest that Soviet engineers were not "reputedly highly skilled mathematicians." All forms of error communication coding (Reed-Solomon, BCH, Golay, Turbo, LDPC) make use of abstract algebraic techniques to solve an engineering problem. The code inventors are generally considered mathematicians, and are published in engineering journals. The namesakes of the Reed-Solomon code are Irving Reed and Gustave Solomon, each with a wikipedia article immediately stating that the person is a mathematician and engineer. Each received a Ph.D. in mathematics (CalTech and MIT, respectively), and awards from leading engineering societies. Similar things are true of Golay, Berlekamp, and other pioneers in the field. Note that this field (error correction coding) uses precisely the topics covered by "New Math." I realize the underlying math topics are centuries old and discovered by more pure mathematicians, but certainly the point that engineering can be advanced by highly skilled mathematician-engineers is valid.SigProcEngineer (talk) 06:45, 1 March 2019 (UTC)

Both fail to consider, public policy isn't decided entirely by the populace, but by the leadership and their perceptions. Also, what was considered a mathematician in that era vs more modern times is also a fair bit blurred. Show me a modern mathematician that wouldn't be called a programmer back in the mid to late 1960's to '70's, as an example, while engineers and physicists today would equally be considered mathematicians back then and now, defer to mathematicians in some portions of their own theories. Nothing can be "pure", as the universe operates upon mathematics and well, "God doesn't play dice with the universe" has been disproved by thoroughly loaded dice.  ;) Wzrd1 (talk) 23:59, 13 May 2024 (UTC)

Praises

This section should be relabled "influence" or "legacy" as it does not illustrate proponents for or potential benefits of new math. There should also be a proper praises/benefits/advantages section to balance against the criticisms/disadvantage section. There is a lot of criticism and negative bias toward this subject and it would be nice to counterbalance with some actual purported advantages for the sake of keeping the article free of bias. — Preceding unsigned comment added by 209.42.145.183 (talk) 14:09, 29 July 2017 (UTC)

Modern mathematics

I am removing the "Etymology" section:

Etymology

In 1973 Morris Kline wrote following in his book Why Johnny Can't Add: the Failure of the New Math:

For many generations the United States maintained a rather fixed mathematics curriculum at the elementary and high school levels. This curriculum, which we shall refer to as the traditional one, is still taught in fifty to sixty per cent of the American schools. During the past fifteen years a new curriculum for the elementary and high schools has been fashioned and has gained rather wide acceptance. It is called the modern mathematics or new mathematics curriculum."

Further it continues:

The origin of the term "modern mathematics" is relevant. Even before the members of the Commission on Mathematics had determined just what they were going to recommend, they gave addresses to large groups of teachers. Their main message was that mathematics education had failed because the traditional curriculum offered antiquated mathematics. ... The Commission contended that we must drop the traditional subject matter in favor of such newer fields as abstract algebra, topology, symbolic logic, set theory, and Boolean algebra. The slogan of reform became "modern mathematics".

Other publications used the terms "New Math" and "Modern Math" as well, for example 1975 Concepts of Modern Mathematics by Ian Steward says the following in the preface:

Some years ago, "new math" took the country's classrooms by storm. Based on the abstract, general style of mathematical exposition favored by research mathematicians, its goal was to teach students not just to manipulate numbers and formulas, but to grasp the underlying mathematical concepts.

It is good to see progress in the editing of this article. But I don't think it is helpful to dwell excessively on Kline's use of the term "modern mathematics". As others have pointed out, Kline sometimes refers to this movement as "Modern mathematics" instead of "New Math". However, this is not particularly important, except possibly as a passing comment, for these reasons:

1. "Modern math" is a very broad term which simply means the mathematics studied in modern times. This term is very often used by Kline and nearly everyone else to refer to the abstraction of mathematics which began in the late 1800s. "New Math" is specifically the movement in this article where American educators attempted to incorporate the abstractions of modern mathematics into the school curriculum. Kline seems to be using "modern mathematics" in the sense of "non-antiquated" mathematics in the first quote, rather than as his term for the movement.
2. The quotes in the deleted section do not really explain the "etymology" of the term "New Math", nor do they seem to explain much at all to me. (Maybe I'm simply missing the point?) Even if Kline is using "modern math" to refer to the American movement in the first quote, I don't see how this merits more than a passing mention.
3. In the second quote, Kline is again referring to the fact that the movement is claiming to incorporate modern mathematics (i.e. 20th century abstract mathematics) into the curriculum. I do not believe he is explicitly referring to the fact that the movement is called the "modern math" movement. He is just saying that books are promoting the new curriculum by claiming to be "modern mathematics".
4. Even if Kline is referring to the American movement as "modern math", we don't need a whole section about this fact. Again, this really does not merit more than a passing mention.
5. In the third example, I don't see the term "modern math" at all, so I'm not sure how this supports the statement "Other publications used the terms "New Math" and "Modern Math" as well". We know that nearly all publications refer to this movement as the "New Math". We don't need a random supporting statement of this fact.

There is no problem alluding to the fact that New Math is an attempt to incorporate modern mathematics into the school curriculum, or that Kline sometimes referred to the movement as "modern mathematics" instead of "New Math" (if, in fact, he really did). But we don't need a whole section about this, and it is best to keep the two terms clearly separated in the remainder of the article. seberle (talk) 12:23, 27 April 2018 (UTC)

As you might have noticed, I did not revert your changes reinstating my addition of "Modern Mathematics", I accepted your position that this is just "New Math". The Etymology section therefore was put there to justify later comments from Kline about "modern mathematics" being pure propaganda and such, and to link together New Math and Modern Mathematics that Kline talks about. For this reason I intend to put the quotations back in, if slightly abridged. Mikus (talk) 15:16, 27 April 2018 (UTC)

By all means, anything to help readers understand what Kline is referring to would be helpful. Maybe a sentence next to Kline's criticism in the Criticism section?

This article is a disgrace.

You would never know from reading this article that the creators of the New Math curricula had any reason for doing what they did. To understand the reasons, it would be instructive for any interested party to try the "airplane test": Tell the person sitting next to you on the airplane that you're a math teacher. Almost certainly, you'll get one of two responses: the more honest "I hated math in school!" or the more polite "You must be a genius!" Just imagine if the result of 12 or more years of schooling were that the overwhelming majority of people considered themselves unable to read or write, or to understand why anyone might want to read or write. That would be a national catastrophe. It is a catastrope, an ongoing one, with respect to mathematics.

Most of the damage is done in elementary school, precisely in the teaching of arithmetic. It takes the form of drill and practice in algorithms that are to be memorized without understanding. Consider multi-digit multiplication: "Six times seven is 42, write down the two, carry the four..." Carry the four? What does that mean? Why does it work? For the majority of children in an "old math" classroom, this is just an arbitrary sequence of steps. They'd be just as happy (or unhappy, more to the point) if the rule were "write down the four, carry the two." To understand why the algorithm works, you must first understand place value—and many children, and adults, don't.

How do you teach someone to understand place value? It turns out that talking about powers of ten doesn't work very well, especially because the spoken names of numbers already have the powers of ten built in, e.g., "thousand" means "times ten to the third power," but that's not how people think of it; they think in terms of "add three zeros." So it's not absurd to think that it might help to spend a little time practicing arithmetic in base seven, or base twelve, to force kids to think about the algorithm instead of applying it mindlessly. And it does help, if the teacher understands the mathematics and the pedagogic reasons for teaching it in this way.

The downfall of the New Math came not because its ideas were wrong but because teachers had it thrust on them without adequate preparation or buy-in. It was one of a long, ongoing sequence of educational innovations that failed for the same reason: Some academic had a good idea, influential education administrators bought into it, and come September the teachers found themselves with new textbooks.

That the New Math started from foundational, and therefore abstract, ideas rather than from applications is a valid criticism. Within the community of mathematicians, it did get such criticism. But the politicians and the general public didn't get the message that there were specific intellectual problems with what was, after all, the first generation of a new way of thinking; the message instead was that teaching should forever be done in the way it was done 100 years ago, that any attempt at improvement was inherently absurd. And that same message pervades this article.

Another thing: 100 years ago they didn't have calculators. Today kids have calculators (as cell phone apps) in their pockets. The article mentions, mockingly, trying to teach college students to understand the ideas of the calculus instead of developing skill at integration by parts and so on. But is it completely irrelevant that today we have Wolfram Alpha in our phones? Maybe skill at integration, like skill at arithmetic, isn't as important as it once was.

Yes, it will improve kids' quality of life, a little bit, if they know that six times seven is 42. But in the modern world it would be serious malpractice for any human being to try to multiply two three-digit numbers by hand in a real context (rather than a school context). Kids should do a little of that in school, only for the purpose of helping them to understand place value, and that's why today's math curricula invent unfamiliar multiplication algorithms, typically involving the explicit writing down of partial products and the explicit writing down of zeros to line them up correctly, rather than just magically writing them to the left of other partial products. Parents don't like that, either, because it's not the familiar "carry the four" algorithm. But, unlike the latter, the new algorithms make sense and so they're more learnable.

I recommend starting this article over from scratch, with a less snarky attitude. Briankharvey (talk) 01:33, 16 March 2020 (UTC)

That seems excessive, and the tone of this article doesn't seem "snarky" - but the article does need a section before "Criticism" explaining why the changes were made - as you point out, this article doesn't explain any motivation for the change. You're welcome to take a stab at it! - DavidWBrooks (talk) 11:55, 16 March 2020 (UTC)

I agree with Briankharvey's understanding of best practices in modern mathematics education. However, I also agree with DavidWBrooks. I fail to see the "snarky" tone in this article, and I don't see the point of rewriting this article.

It might help to keep in mind that, in the opinion of many, the New Math was a mixture of good and bad ideas. Algebraic inequalities and matrices, which were derided by Morris Kline as useless for high schoolers, have been retained in the American curriculum. However, telling first grade teachers that they must pedantically insist that children use the words "numeral" and "number" correctly, or that young children must learn abstract set theory, was probably excessive. I grew up in the 60s and delighted at learning how to calculate in Base 4 in elementary school. However, looking back, I see that there was little attempt to connect these new abstract procedures to our understanding of Base 10 arithmetic, so I imagine there was little or no impact on students' arithmetic skills or comprehension.

In any case, this is a Wikipedia article reporting on a historical phenomenon. It needs to remain neutral. As DavidWBrooks suggested, a section that more fully develops the motivation for the change would be welcome. It should be told from a historical point of view, but could include insights from a more modern understanding of good pedagogical practices. --seberle (talk) 09:20, 23 March 2020 (UTC)

Well i think there are 2 things overlapping in that criticism. The issue with new algorithms for long multiplication and alike is afaik at least partially an issue with the new math of the 1990s, which is different from the new math of 1960s of this article. And one criticism is, that not every "didadictly devised" algorithm really does what it claims to do, that is significantly improving understanding among students. Another problem associated with that is that memorization often gets devalued in parallel, however it turns out a lack of sufficient memorisation tends to impair understanding as well.

As far as the current article is concerned, it certainly could amended by paragraph explaining the motivations behind new math and a lot of other things could be improved as well. But that doesn't make the article is a disgrace, it is just one of many wikipedia articles that have a lot of room for improvement.--Kmhkmh (talk) 12:58, 24 March 2020 (UTC)´

I've started working on improving the article. I took everyone's advice and didn't start over. But I'd like to justify my characterization of the article as disgraceful. The main thing was the way it jumps right into criticism. The "Overview" section, before I worked on it, used prejudicial language, e.g., "students were ... made to distinguish 'number' from 'numeral'" in which I've changed the word "made" to "taught." And the authorities it cites are only enemies of New Math, especially Kline. This is like writing an article about, I don't know, No Child Left Behind and citing only Alfie Kohn, much as I love him. Such an article should cite him, but not to the exclusion of the authors of NCLB. And not as the authority on what NCLB was trying to accomplish.

Because the New Math predates the Internet, there isn't a lot of primary-source material online, but there is some, thanks to Google Books and to university archives. There's better source material physically preserved at universities, but I can't use physical libraries right now because of COVID-19. I'll be adding citations to what is online shortly, when I get out from under the work I get paid for. And I promise to finish the job if I'm still alive when libraries open again. Briankharvey (talk) 06:35, 16 April 2020 (UTC)

It's always good to see edits that improve an article. I myself would be interested in seeing the viewpoints of some supporters of the New Math. I strongly suspect there were not many at the end. The movement died for a reason. If the article seems one-sided, it is because the consensus opinion eventually became that the New Math had some very serious flaws. You might find that most of the support will be from the 1950s and early 1960s when the movement was new.

As people edit, I would seriously consider taking Kmhkmh's input into consideration: Most of Briankharvey's criticism sounds like support for the reforms of the 1990s, most of which were in fact eventually accepted in moderation and incorporated into modern standards. Remember to keep a distinction between those reforms and the New Math movement of the 1960s. There may be a bit of overlap, but for the most part they were very different. We can't use reformers' ideas from the 1980s and 1990s to show support of the New Math of the 1960s. --seberle (talk) 15:36, 20 April 2020 (UTC)

I agree with the commenter who said that the article is way too one-sided. I began first grade in September of 1961 and was definitely a child of the New Math. Sets, functions, bases - it all made sense to me, and it became second nature early. And I learned my multiplication tables, though that was quite tedious. I am still engaged with math (although I not a mathematician) and that early material still makes sense to me and is still foundational for me. Admittedly I was not the average kid, and maybe I had well-prepared teachers. I went to public school in a school where there was one class per grade - no stratification between classrooms. I can't speak for others, but I benefited greatly from the New Math. This article needs to be more balanced. — Preceding unsigned comment added by 71.191.145.7 (talk) 00:45, 1 June 2020 (UTC)

Enduring Legacy section

I am a bit outside my domain of expertise, but I have some doubts about the section on Enduring_Legacy, which currently reads as follows:

The New Math is often described as a short-lived movement with no lasting influence on current teaching practice. For better and for worse, that's not the case. One example concerns the introduction of the field axioms. Understanding the ways in which an arithmetic formula can be reordered helps students solve mental arithmetic problems such as 3+18+7 by recognizing that the problem can be reordered as 18+(3+7) and recognizing numbers whose sum is ten. (If the problem were 3−18+7, the grouping of operations would have to be considered more carefully before reordering, because subtraction isn't commutative.) On the other hand, the words "commutative" and "associative" are hard to remember, hard to spell, and therefore intimidating. But they are still sometimes taught, in part because the use of New Math textbooks was much more common than the provision of New Math teacher preparation workshops. Traditional teachers can add "commutative" to the weekly spelling list without actually giving students challenges in which the Commutative Law is helpful.

The style of work in modern elementary mathematics lessons is very heavily influenced by the New Math. Organizing the classroom space into table groups of (generally) four to six students facing each other rather than facing front was a New Math innovation. The use of manipulatives (physical blocks of wood or plastic that can be combined to illustrate ideas about quantity and shape, such as Cuisenaire rods) didn't start with the New Math, but it wasn't until the New Math popularized their use that they became universal. Publishers of current curricula provide manipulatives in table kits.[3] [4]

Another enduring result of the New Math has been the willingness of teachers and curriculum developers to use arithmetic algorithms other than the ones used in the 19th Century. Those algorithms were designed to minimize the number of steps needed for an experienced adult to carry out a calculation. But in the 21st Century all but the simplest computations are done by machine. Educators still have children do arithmetic, because some practical experience is necessary to understand the mathematical ideas. But they invent algorithms that are easier to understand, rather than faster to carry out.

Citations from secondary sources are needed discussing this enduring legacy and the many claims made in this section. --seberle (talk) 22:07, 24 April 2020 (UTC)

Electrical and Digital Engineering

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.

To me, that statement comprises my early 70's memories of New Math. I have no recollection of discovery learning methods.

I was frustrated as a 12 year old wondering about the justification for having to learn some of that, especially the "bases other than 10", likewise gradians and radians.

Then I got a math degree.

But, when I studied electrical engineering and then an embedded systems developer, applicability of set theory, modular arithmetic, algebraic inequalities, bases other than 10, matrices, symbolic logic, Boolean algebra, and abstract algebra, all became abundantly clear; especially in the context of the development of digital systems, then, integrated circuits, then computers and the software that controls them; all being the foundation of military and economic advancements from the 50s on.

I was rather surprised to see that this was not particularly covered in the article, but my perspective may not be relevant or accurate.

IveGoneAway (talk) 19:09, 10 February 2021 (UTC)

This article could definitely use some more work. I agree that the topics you listed seem to be those most commonly associated with the New Math, and that I have never come across a reference to discovery learning being associated with New Math. Your personal experience sounds like the experience of many. What in particular were you surprised not to see covered in the article? --seberle (talk) 07:56, 11 February 2021 (UTC)

New Math wasn't just a reaction to Sputnik: it was also a rejection of current pedagogic developments. Specifically, educators felt that Math had no relevance, and should be de-emphasized or removed from the primary curriculum. After all, your 3rd Grade teacher had never, in her entire life, used any mathematics more complex than addition and subtraction: why should she be wasting her student's time with long division? In reaction to the well-established push to make schooling more relevant by removing Math, mathematicians, engineers and scientists examined the math they were actually doing, and recommended moving that into the primary curriculum (replacing or extending what had been originally clerical/business/spreadsheet math). In retrospect, it's interesting to see that statistics wasn't nearly as important then as it is now. — Preceding unsigned comment added by 124.187.243.156 (talk) 00:48, 12 February 2022 (UTC)

Well, was educated in New Math, prepared me for IT work later in life and well, earlier and much later, helped me with those whole rads and grads in guiding indirect fire to rather unpleasant people, who were about to hurt a lot of really pleasant people. As for the IP editor claiming statistics aren't as important then as now, crypto required statistical precision - always, as has nuclear physics and well, health care in general and especially public health, it's always been important, you conflate perception of importance with actual importance. Which equates a witch doctor with a medical doctor as full peers.Wzrd1 (talk) 00:06, 14 May 2024 (UTC)

New Math inspired by east-west rivalry?

This article makes prominent claims that New Math was inspired by the Sputnik crisis and concern that Soviet engineers were, by reputation, better at math than their US counterparts. These claims appear to be unsupported by any reliable published source. I see no in-line citation to allow independent verification of these claims. No other explanation is offered as to the origin of New Math - just Sputnik and concerns about the mathematical skills of Soviet engineers!

When people dislike something, and dislike it with a passion, many are easily recruited to any simple ideology that discredits that something by linking it to something else that is undeniably objectionable. I can well imagine that parents and teachers who objected to the New Math would be attracted to the notion that it had been invented by silly politicians and misguided educators who were motivated by a desire to recruit school children to the task of helping the US overhaul the Soviets in the space race, or worse still the arms race.

Whether or not the New Math was in any significant way spawned by east-west rivalries or the Sputnik crisis, and whether or not Wikipedia should report it in this way, should be determined solely by the quality of the sources provided to allow us to independently verify what is stated in the article. Even if evidence can be found of a minority view that New Math might be related to Sputnik, Wikipedia avoids giving undue weight to minor points of view. If no reliable published source can be provided, this aspect of the article should be regarded as someone's original research, and erased. Dolphin (t) 05:21, 9 September 2023 (UTC)

A week has passed with no User responding to my comments above. I will amend the article to remove the unsourced claim that New Math was inspired solely by the Sputnik crisis and concern that it showed US engineers and scientists were inferior to their Soviet counterparts, especially in fields including math. If a User subsequently finds a reliable published source to support this claim they are welcome to add the claim, and an in-line citation, to the article. Dolphin (t) 10:18, 17 September 2023 (UTC)

As one that grew up in the era after Sputnik, it spurred the effort enough to gain momentum that was slowly building, as both digital computers were gaining momentum and the non-base-10 math, sets and subsets also gaining due to ill preparation of students for modern college educations and to add an odd number to the coupling of both, statistical analysis was and remains critical in modern life, from anything from general physics, such as electronics, through figuring out how a thermonuclear device operates and balancing electrical loads on a modern power grid during a geomagnetic storm (to add in a quite recent non-event, due to the successfully managed otherwise hot mess).Wzrd1 (talk) 00:10, 14 May 2024 (UTC)

I also grew up in the era right after Sputnik and it was always "common knowledge," that the space race had spurred on the New Math. It is possible that this was a false assumption, but I would find it suprising that there are not any references refuting, confirming, or at least mentioning this idea. Before simply deleting this information, try attaching a "citation needed" tag first. --seberle (talk) 16:39, 28 May 2024 (UTC)