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From reviews on Amazon of the various high school math texts by Mary Dolciani et al of the SMSG, I assume that there might be a successor to the approach (referred to as “the new math”) taken by the SMSG. Does anyone have any insight into this, and whether there really were “math wars” when the SMSG series was introduced in the 1960s in response to the Soviets’ launching of Sputnick?

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    $\begingroup$ Regarding new math, see my answers to Where can I find primary sources from the New Math movement in the 60s? and Different Kinds of Variables, the latter of which I sometime need to revise to more specifically answer the question asked and also to move the more detailed book information to the former answer, but of course this is not relevant for what you're interested in. In the U.S., after new math there was "return to basics", (continued) $\endgroup$ – Dave L Renfro Mar 6 at 20:27
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    $\begingroup$ and then the more problematic calculator concerns began arising in the late 1980s and early 1990s (especially graphing calculators and beginning calculus instruction), which led to calls for less emphasis on algebraic manipulation, which led to "wars" (and the term "new new math"), especially in California. Right now I don't have time to write anything worth putting as an answer, however. $\endgroup$ – Dave L Renfro Mar 6 at 20:28
  • $\begingroup$ Heh, I just found out I spelled "Sputnik" incorrectly. $\endgroup$ – nowradioguy Mar 9 at 4:43
  • $\begingroup$ You might find this post relevant: matheducators.stackexchange.com/a/7231/267 $\endgroup$ – Andrew Sanfratello Mar 9 at 5:11
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There was indeed a great deal of pushback to the New Math. You can find a brief summary of this on pp. 12-16 of my textbook, from which I will quote liberally:

To say that these curricula were ambitious would be a dramatic understatement. Inspired by the mathematicians of the Bourbaki movement, New Math curricula stressed mathematical structures as a key topic. The language and notation of sets was introduced as early as 1st grade; students were told to distinguish the word number (referring to a quantity) from numeral (referring to the representation of a number in written form), and to focus on properties such as order and equivalence. In upper elementary grades, students wrote numbers in different base systems (i.e. base 6 and base 2 in addition to the familiar base 10). At the middle-grades level, students were taught to distinguish between an "open sentence" (like $3x + 5 = 17$) and an "equation" (such as $2 (3 + 5) = 6 + 10$). So strong was the emphasis on set theory and precise language that some felt the New Math went too far. Richard Feynman, who served on the California State Curriculum Commission in 1964, objected to what he saw as the excesses of the New Math's emphasis on language:

In regard to this question of words, there is also in the new mathematics books a great deal of talk about the value of precise language — such things as that one must be very careful to distinguish a number from a numeral and, in general, a symbol from the object that it represents... For example, one of the books pedantically insists on pointing out that a picture of a ball and a ball are not the same thing. I doubt that any child would make an error in this particular direction. It is therefore unnecessary to be precise in the language and to say in each case, "Color the picture of the ball red," whereas the ordinary book would say, "Color the ball red."... Although this sounds like a trivial example, this disease of increased precision rises in many of the textbooks to such a pitch that there are almost incomprehensibly complex sentences to say the very simplest thing. In a first-grade book (a primer, in fact) I find a sentence of the type: "Find out if the set of the lollypops is equal in number to the set of girls" — whereas what is meant is: "Find out if there are just enough lollypops for the girls."...

If we would like to, we can and do say, "The answer is a whole number less than 9 and bigger than 6," but we do not have to say, "The answer is a member of the set which is the intersection of the set of those numbers which is larger than 6 and the set of numbers which are smaller than 9."

It will perhaps surprise most people who have studied these textbooks to discover that the symbol $\cup$ or $\cap$ representing union and intersection of sets, and the special use of the brackets $\{\}$ and so forth, all the elaborate notation for sets that is given in these books, almost never appear in any writings in theoretical physics, in engineering, in business arithmetic, computer design, or other places where mathematics is being used. I see no need or reason for this all to be explained or to be taught in school. It is not a useful way to express one’s self. It is not a cogent and simple way. It is claimed to be precise, but precise for what purpose?...

It will come as little surprise to anyone who has lived through the more recent waves of mathematics (and other curriculum) reforms over the past several years, and the sometimes intense political controversies that have accompanied them, to learn that the New Math met with an intense and prolonged backlash from parents, teachers, politicians and other stakeholders. Critiques ran the gamut, from the gentle mockery of comedian Tom Lehrer’s song New Math and whimsical references in Charles Schulz’s Peanuts cartoon, to the no-holds-barred attack of the best-selling 1973 book Why Johnny Can’t Add: The Failure of the New Math, written by New York University mathematics professor Morris Kline...

It would probably be giving Kline's book too much credit to claim that it single-handedly ended the New Math, but it is certainly correct that it served as a punctuation mark at the end of the era. By the late 1970s the New Math had virtually disappeared from classroom use. The era of the New Math had given way to what came to be known as the Back to Basics movement.

That last sentence contains the answer to the question in the title: Yes, there was a successor to the New Math movement, and it was generally known as the Back to Basics movement.

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  • $\begingroup$ In high school back in 1963-77, we used all four of the Dociani series from Houghton-Mifflin (two algebra texts, one geometry, and one on "modern introductory analysis"). I notice that there is an emphasis therein on "structure", which is to be interpreted as "set". And, yes, a "numeral" was not the same thing as a "number", but I really don't believe that we were thrown off-course to the point where we failed to see the forest for the trees. I'm using this set of texts as my reference for the pre-calculus course I'm currently teaching for a local CC. But thank you for answering my question. $\endgroup$ – nowradioguy Mar 16 at 5:03

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