# Tag Info

28

In the first place, the impetus to "reform" math education was motivated by politics, not by any serious observed deficit. By coincidence, there was a "new" style in higher mathematics, reflecting the previous 50-60 years assimilation of set theory and rewriting of many things in terms of set theory. But until the "sputnik scare" no one had incentive to ...

16

You might want to read Kline (1973). I haven't read the book, but according to Wikipedia, In 1973, Morris Kline published his critical book Why Johnny Can't Add: the Failure of the New Math. It explains the desire to be relevant with mathematics representing something more modern than traditional topics. He says certain advocates of the new topics "...

12

The textbooks we used for Algebra 2 at Miramonte High School, Orinda, California, in 1967 - 1968 must have been SMSG Units 17 - 18, entitled Intermediate Mathematics, Part I and II. I recognize the content as being that of the PDF Documents (scan) available at ERIC corresponding to the same titles. Ref.: http://eric.ed.gov/?id=ED135625 http://eric.ed.gov/?q=%...

12

I think very roughly speaking: "new math" (also known in europe as a fearful period of time, especially for parents) followed a mathematical construction of mathematical knowledge rather than a psychological one. Mathematically, you would introduce an abstract concept like an equivalence relation first and then introduce concept like terms or fractions as ...

10

New math was introduced in the US in the 1960s. Before it was introduced, math was taught very algorithmically with little emphasis on understanding. Student were taught a method to do an arithmetic problem and drilled until they remembered the process with no understanding of what was being taught. New math introduced many new topics including boolean ...

10

The following three books are, I believe, the most significant of the earlier treatments of new math, and I suspect you can find much in them that will direct you towards literature for your questions #1 and #3. Also, since it is very likely that at least one of these 3 books will be cited by any reasonably researched publication, you can google their titles ...

9

Your question is twofold: (1) Did any school districts actual teach the curriculum as planned and (2) what were the results for the teachers and students? At the moment, I have an answer for (1): Yes. For (2), the results for teachers and students exist in various forms, but I have not combed through them carefully. And so your second question is certainly ...

9

My very incomplete understanding: I know from Henry Pollak (first-hand, but mentioned briefly here and in an article below) that one of the driving forces behind SMSG (with whom New Math is often associated) was Ed Begle. It should be noted that Begle's influence on mathematics education moving forward was also nontrivial: He served as advisor (along with ...

9

Whenever "the new math" comes up, I must point out that there was no one "new math" curriculum and much of that post WWII exploration into math curriculum and pedagogy had different aims and philosophies (Davis, 2003). (This doesn't directly pertain to your question, but the actual use of new instructional methods and curricular content during this period ...

9

Update: I had believed not, but see Paul Stanley's response above. A good source for information about twentieth-century textbooks on algebra and geometry is: Donoghue, Eileen F. "Algebra and geometry textbooks in twentieth-century America." A history of school mathematics 1 (2003): 329-398. In the section entitled "SMSG's First Course in Algebra" (...

8

It sounds like a variation of subtracting that I learned in high school (1968). My instructor called it European subtraction. \begin{array}{ccc} & 3 & 4 & 2 \\ - & 1 & 7 & 3 \\ \hline \end{array} You start by saying $9$ plus $3$ is $12$. You write the $9$ as shown and "carry" the $1$, of the $12$, as a subscript of the $7$ ...

7

As SMSG books are public domain, I have found some more PDFs. Thanks mweiss for checking it is the right document. http://babel.hathitrust.org/cgi/pt?id=mdp.39015017374235;view=1up;seq=7;skin=mobile Here is an index of a number of SMSG scans: http://onlinebooks.library.upenn.edu/webbin/book/lookupname?key=School%20Mathematics%20Study%20Group The original ...

7

Please refer to Whatever became of the New Math?, a series written by Professor Raimi of the Department of Mathematics of the University of Rochester, and also Whatever Happened To New Math?. Together with PSSC in physics education, SMSG (most popular of the New Math) actually was initiated from professional mathematicians, started to produce high school ...

4

There is an article by Phillips: Phillips, C. "In accordance with a `more majestic order': the new math and the nature of mathematics at midcentury." Isis 105 (2014), no. 3, 540--563 that presents a thoughtful analysis of this curious episode from the history of math education. The way I understand his argument, the sequence of events was as follows. ...

4

The original sequence of the high school SMSG texts was: First Course in Algebra; Geometry; Intermediate Mathematics; Elementary Functions; Matrix Algebra. The first three are year long courses, the last two were one semester courses. The sequence up to and including Elementary Functions would be what was needed for calculus when you got to college. Later ...

4

I know a research group in the School of Education at the University of Michigan that would be very happy to receive them. My email address is in my profile.

3

Just a short addition. Ed Begle published a valuable study through MAA/NCTM entitled "Critical Variables in Mthematics Education", which was an attempt (in part) to sort out some of the lessons of the SMSG.

3

I studied with SMSG materials in San Diego 1963-1968 grades 7-11 under an "advanced math" program. Grade 7 was an introduction to math. Grade 8 was half geometry and half algebra. Grade 9 was algebra. Grade 10 was geometry. Grade 11 was trigonometry and pre-calculus. If I had taken grade 12, it would have been calculus and computing science.

2

They failed to deliver the punchline: the uniqueness of the reals, as a [complete] ordered field. Once numbers were under­stood as forming an ordered field, and the positive integers among them as a certain inductive subset, and once the language of sets became standard, so that statements with quantifiers made sense, then and only then would ...

2

I would characterize the "New Math" as a "top down" approach to math. The idea was to have young students see the "big picture." The danger is that they fail to "see the trees for the forest" (the reverse of the usual malady). I was a grade/junior high school student during the "new math" debate of the late 1960s.

2

There was an Algebra II course using SMSG, as I remember taking it in 1964-1965 at College Park High School, Concord, CA. I do not know what the text was named, but it followed the SMSG format.

2

In 1963-64, I took (or was taken by) a class called Algebra II, in which we used an SMSG book. Like SMSG Algebra I (or just plain Algebra) I found it utterly wretched and resolved to leave anything science-related, and to become chief poet in my high-school. Well, funny how things turn out-- I went on to do a doctorate in Biochemistry, and recently ...

2

The SMSG textbook for algebra II and trig was entitled "Modern Algebra and Trigonometry, Book 2" by Dolciani, Berman, and Wooton, published by Houghton-Mifflin. We used this during my junior year in high school (1965-66). I wish I'd kept the book instead of returning it to our bookstore for credit, because I recently had to purchase a used (...

1

Dan Ghica has a blog post on discovering category theory for primary school children by way of knot theory. Quite charming, I think, albeit not really an answer to your question. Still, I thought it might be worth noting here. (I came across it when reading Paweł Sobociński’s Graphical Linear Algebra blog.)

1

Great question! Yes, this was Piaget's project after initially working with more classic structuralism (e.g. his text titled Structuralism). He explicitly mentions Mac Lane's work in his book on understanding functions, Epistemology and Psychology of Functions I discuss this a bit in my dissertation, but am not familiar with other work that compares ...

1

Dolciani eventually went on to write an explicit 'Algebra 2' book, used in the 1970's and 1980's commonly. That Algebra 2 book has an exact replica of the material in the SMSG Intermediate Mathematics. So I think that should resolve it. 'Algebra 2' is the SMSG 'Intermediate Mathematics.'

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