This question has been kicking around in the back of my head for a couple of years, but the impetus to post it now came from reading the related question at When did the American school system's progression of math classes take its current form?.

I have been trying for some time now to locate digital copies of the School Mathematics Study Group (SMSG) textbooks, colloquially known as the "New Math", and have accumulated quite a good-sized collection, available here. (My understanding is that all of these texts are in the public domain, and may be freely distributed.) I should acknowledge that I found most of these texts in an archive formerly hosted by Tom Giambrone at Buffalo State College that seems to no longer be available online.

One of the curious things about this archive is that it contains more than one text with the words "First Course in Algebra" in the title (including Parts I and II of both a Student's Text and Teacher's Commentary, plus a "Programmed First Course in Algebra") but there does not seem to be a follow-up "Second Course in Algebra" or "Algebra 2" or something similarly named. The description of the SMSG archive at the UT-Austin also seems to lack anything that is obviously recognizable as "Algebra 2".

I'm not sure whether there was a "Second Course in Algebra" text that I simply can't find any trace of, either because it is no longer extant or because my Google-Fu isn't strong enough, or whether such a book never existed in the first place.

Does anybody know:

  1. Was there an SMSG "Algebra 2" textbook or the equivalent, and if so, what was it called?
  2. If so, is it available anywhere, either in print or digital form?
  3. If not, what was the SMSG course sequence for students after Algebra and Geometry?
  • I just made a comment here that you might be interested in. Actually, I thought I was commenting on a question of yours, but after I made the comment I realized it was someone else, but I left it there anyway. – Dave L Renfro Jan 15 '15 at 14:55
  • I studied SMSG Plain and Solid Geometry in a metal spiral binder. As a sophomore the solid and advanced solid (I take now as Hyperbolic) was a bit above my head, but I caught up with aid from my Dad who thought the manual was tops! He was an N-dimensional grade math user at the time. This was in El Paso, Texas. I was moved overseas and schooling was advanced but not SMSG, they used college texts as references. Martin – user5299 Jun 14 '15 at 18:30
  • @mweiss: I'm interested in the legal status of these books, as well as other Sputnik-era books of this type. I've asked a question about that here: law.stackexchange.com/questions/5131/… – Ben Crowell Nov 9 '15 at 23:48
  • @BenCrowell I appreciate that you raised the question. I have been under the impression that SMSG is in the public domain, and have freely distributed them under that assumption. It would be good to have confirmation on that. – mweiss Nov 10 '15 at 0:12
up vote 11 down vote accepted

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=%22Allen+Frank+B.%22&id=ED135626

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    I have this at home, having collected SMSG volumes (actual print copies) for nearly 30 years, and when I read mweiss's question just now (for the first time), it occurred to me that the Intermediate volumes might qualify if anything does. – Dave L Renfro Jan 14 '15 at 22:07
  • Paul and Dave, thank you! I had no idea that ERIC had scans of some of the SMSG texts. In addition to Intermediate Mathematics I see they also have a number of other volumes that I was missing from my collection. This is enormously helpful. – mweiss Jan 15 '15 at 15:18

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" (beginning on p. 366) Donoghue writes:

Among the members of the [ninth-grade SMSG writing] group were Eugene Northrop of the University of Chicago, Mary Dolciani of Hunter College in New York City, and Henry Pollak, a research mathematician at Bell Laboratories. The group decided that algebra ought to form the core content of ninth-grade mathematics. In their view, all citizens could benefit from studying algebra; for the college-bound student, it was essential.

The key names above are Northrop, Dolciani, and Pollak.

Northrop went on to write a textbook, Fundamental Mathematics, which dedicated about one third of the corresponding class time to Algebra; you can read more about it in my earlier MO answer here.

Pollak has now been a ("visiting") professor at Teachers College Columbia University, where Donoghue earned her doctorate, for the past 25 years. He has not written any textbooks, but he has personally remarked to me about the great skill possessed by Dolciani.

Dolciani did go on to write another textbook on Algebra. It is the subject of the subsequent section in Donoghue's article, entitled: "Dolciani's Modern Algebra: Structure and Method, Book One." She later wrote other books (which you can search out online) so that you may wish to look into work by Mary Dolciani.

(See also this wonderful link provided by James S. Cook.)

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    Benjamin Dickman, I hate to un-accept an answer, especially almost nine months after accepting it, but it appears that there was in fact a second SMSG Algebra text -- it just didn't have the words "Algebra" or "Second" or "Two" in the title. See Paul Stanley's answer for details and link. – mweiss Jan 15 '15 at 15:26
  • @mweiss Happy to be corrected! An existence proof is tough to dispute. – Benjamin Dickman Jan 15 '15 at 15:43
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    Fun fact, Mary Dolcani's contribution to the math community lives on through dolcianihalloran.squarespace.com in addition to her work on popular math texts. – James S. Cook Apr 13 '15 at 13:18
  • @JamesS.Cook Excellent; I have put the link into the body of my response! – Benjamin Dickman Apr 13 '15 at 21:05

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 ERIC link is freely downloadable for everyone, while I've just noticed that Hathitrust only allows subscribers to do full downloads. However, the Hathitrust scans are done by Google and the quality seems to be better than the ERIC scan.

  • This appears to be the same text as the one in the accepted answer. Thanks for finding another source! – mweiss Mar 16 '15 at 0:20

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 on, two other semester long courses were offered which could replace the Matrix Algebra course: Analytic Geometry and a course on Algorithms. Later still, a year long calculus course called Calculus of Elementary Functions was added as an option. This course mixed Elementary Functions with Calculus and was the advanced placement AB course of the time. There was also a year long Calculus course which had Intermediate Mathematics as a prerequisite. This class had most of the Elementary Functions material in appendices and was the Advanced Placement BC course. Finally, they added a Geometry with Coordinates course that was a mixture of the Geometry course with some Analytic Geometry. I got this information by studying the material on ERIC about the vision, actions, and execution of the SMSG plan. Also, a very helpful item is a price list for their materials also located on ERIC. Note also that I took the original sequence in high school.

Pretty much all of these course materials (student texts and teacher's commentaries) are availiable on ERIC along with the Elementary and Junior High courses and lots of supplementary materials.

  • Richard, thank you for this detail about the SMSG sequences and how they changed over time. Could you edit this answer to include something about your source for this information? – mweiss Apr 13 '15 at 17:06

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.

  • Julia, do you think that perhaps the textbook you used in Grade 11 was the 2-volume "Intermediate Math" text Paul Stanley referred to in his answer? He provided a link there to a PDF version of the text. Does it look familiar? – mweiss Mar 15 '15 at 23:15

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.

  • I have heard similar anecdotal reports from others who remember using an SMSG text for Algebra II in the 1960s, but have not found any independent confirmation that such a book ever existed. I suspect that it may have been not actually an SMSG book but rather was producing by one of the other "New Math" consortia -- but would be very happy to have some evidence that I am wrong. – mweiss Jan 1 '15 at 1:27

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 published a theoretical article (all quantum mechanics) in Journal of Chemical Physics.

No thanks to SMSG though. The geometry text wasn't so bad -- how could you screw up Euclid, after all? but the the algebra was godawful.

A particular hang-up of mine was irrational numbers -- the simple proofs of irrationality, say of the square root of two, seemed like sleight of hand to me (still do, in fact) but in a larger sense, I couldn't get my mind around irrationality. When in college, a friend gave me Boyer's book on the "History of the Calculus" and I came to understand that the question of irrational numbers had perplexed the greatest minds of our civilization from Pythagoras to Cantor.

If someone had put it to me in these terms in high school -- that these are difficult ideas that men have wrestled with for millennia-- I might have done better earlier.

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    This doesn't really answer the question in the spirit it's asked -- which was about the sequence of textbooks and topics. It's interesting information, but it doesn't really address the issue. – DavidButlerUofA Mar 30 '15 at 10:39

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