How does the average level of expected mathematical sophistication at high school level increase?

Question

I remember reading an old calculus book (years 1920-1930) and in the preface it was portrayed as revolutionary because it was for high school students. Nowadays, that is not revolutionary, because most countries have calculus in high school. So, this made me wonder: how did we go from having no calculus in high school to having calculus almost world-wide in high school? How exactly does such a significant shift in curriculum happen, with a new subject area added to high school?

Answer 1

Briefly, in the United States, Calculus was introduced to the high-school mathematics curriculum in the late 1950s by a movement called the New Math Movement. The New Math Movement itself started in the early 1950s and lasted until the early 1970s. The New Math was an approach to teaching mathematics to students by using a form of discovery learning (students were encouraged to use their own deductive powers to discover how to solve mathematics problems). According to R. Hayden (A History of the New Math Movement in the United States, PhD dissertation, Iowa State University, 1981):

the New Math Movement brought about change in the school mathematics curriculum on a scale and at a rate unknown before - or since.

In A brief history of American K-12 Mathematics Education (see here), D. Klein writes:

The U.S.S.R launched Sputnik, the first space satellite, in the fall of 1957. The American press treated Sputnik as a major humiliation, and called attention to the low quality of math and science instruction in the public schools. Congress responded by passing the 1958 National Defense Education Act to increase the number of science, math, and foreign language majors, and to contribute to school construction.

So, in response to your question: how did we go from having no calculus in high school to having calculus almost world-wide in high school? one can say that at least in the United States, the launch of Sputnik by the U.S.S.R. in the fall of 1957 played an important role in the introduction of Calculus (and other "New Mathematics") to the high-school mathematics curriculum.