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In the United States, secondary education students generally progress through pre-algebra courses, then algebra, Euclidean geometry, more algebra/trigonometry, then calculus or statistics.

I am particularly interested in the place that geometry holds in this sequence. When did this become the standard way to teach in the United States?

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I've read a few interesting articles over the past few months in the Notices of the AMS that offer a brief discussion of this. The most notable is a critique and comparison of American and Chinese mathematics curriculum including the beginnings and development of each. It's titled "A Critique of the Structure of U.S. Elementary School Mathematics" by Liping Ma. www.ams.org/notices/201310/

The jist I believe is that back in the 60's America (led by the NSF) wanted to revitalize its mathematics curriculum to compete with the Soviet style. California specifically followed suit and developed the basis of the curriculum we see today with the strands structure.

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    $\begingroup$ I don't know what exactly do you mean by "mathematics curriculum competing with the Soviet style", but I can tell you that at that time Soviet secondary education comprised 10 years, with the years 9 and 10 being either academic-heavy high school, or trade-oriented vocational school. Algebra, geometry as well as physics started in grade 6 and continued until the senior year, including trigonometry and differential calculus in algebra, while plane geometry in grades 6-8 was followed by stereometry in grades 9-10. I don't know how the American system, whether AGA or integrated, can compete. $\endgroup$
    – Rusty Core
    Dec 12, 2019 at 21:55
  • $\begingroup$ See Some aspects of Soviet education (1960) for a list of subjects. $\endgroup$
    – Rusty Core
    Dec 12, 2019 at 21:59
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Looking at my father's War Manual textbooks (published ~39, versions of older texts), it seems like the sequence was much like it is now:

*Algebra

*Geometry (very similar content to what I had in the 80s)

*College Algebra (almost exactly matches Algebra 2, even has a "refresher chapter" at the beginning to cover contents of "high school algebra")

*Planar trigonometry AND spherical trigonometry

*Analytic geometry (conic sections, rotations and translations)

*Calculus (very similar to the AP course I took in the 1980s, even to including almost identical chapters on sequences/series and on ODEs)

Note the placement of geometry is same as the current US stereotypical pattern, not mixed like Saxon or (some) Common Core.

Probably only the first two courses were expected to occur in high school, but smarter students might be accelerated and encounter some of the other materials.

The presence of spherical trig makes that a lot harder topic. The curriculum does seem to lack vectors, which seems unfortunate to me. Also there is no "pre-calc" in the sense of a course where you learn a little bit of differentiating and antiderivatives prior to the AP calculus to make that transition softer. (But then school systems seem to vary a lot now on how the treat the path after algebra 2 and before AP calc, even now. There is little clear definition of what should be in a "precalculus" course.)

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    $\begingroup$ One correction that I'd make is that Common Core does not take a stand on whether geometry should be taught in the middle of algebra or afterwards. The standards for algebra are all listed together, but the high school standards are consciously and deliberately written without grade levels like the K-8 standards are. I've taught at schools where both A1-G-A2 and A1-A2-G are the sequence and both were Common Core aligned. $\endgroup$
    – Matthew Daly
    Nov 23, 2019 at 11:53
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At least around here in Chile, school curricula are defined by law/decree of the Ministry for Education. So to answer the question would mean digging through the official documents. To find out why it came to be that way gets lost in some murkiness of (much off-the-record) discussions among "interested players" (who might, mostly not, have a clue). All seasoned with a healthy dose of whatever the current popular "feeling" is.

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