Maths is ... one domain.

Concepts of science, both natural and social, philosophy, logic, and history are others.

There's an (IMO) fascinating division in the teacing of skills versus "liberal arts" (ultimately: critical thinking, concepts of power and control) in education. What are now considered "technologies" had their beginning as "practical", "technical", or "servile" arts, contrasted with the Seven Liberal Arts:

- Grammer, Logic, and Rhetoric: the Trivium, from whence, "trivia". Think "input, processing, and output."

- Mathematics, Geometry, Music, and Astronomy: the Quadrivium. Think "quantity/measurement, quantity in space, quantity in time, and quantity in space and time."

This divide remains apparent in both lower ("tracking") and higher education. For the latter, top-tier "prestige" schools, followed roughly by major research universities (science), technical schools and polytechnics, what used to be called "teacher" or "normal" schools in the US (now mostly state college / university systems), two-year and vocational schools.

A huge problem of the pedagogical rigidity is the (usually) unstated goals of educational systems:

- Produce a technically-skilled, but politically pliable, working class.

- Produce a managerially competent, but not revolutionary, mangement and professional class.

- Persist existing power structures.

Observed by many over the years, including numerous 20th and a few 21st century commentators. I find John Stuart Mill's 19th century take interesting for its remove from immediate political machinations and for being possibly unexpected given the popular perception of his writings. See Hans Jensen's description, with cites:

First, the universities were given the task of providing an unceasing supply of ideologically correct candidates for vital positions in government, church, and business. The state was able to make the faculties of the "venerable institutions" of higher education, or rather indoctrination, assume this duty because it controlled appointments and held the purse from which "emoluments" flowed into the coffers of academics. Hence the members of the university "hierarchy" made it their "business, the business for which they ... [were] paid," to "uphold certain political as well as religious opinions," namely those of the "ruling powers of the state" (J.S. Mill, Autobiography and Literary Essays, p. 429 (1981), J.S. Mill, Journals and Debating Speeches, p. 350. (1988) ). Thus the universities pursued with vigor their assignment to inculcate in their students those political and ideological views that were cherished by the power elite. The graduates of the ancient universities were, therefore, well prepared for employment in, and by, those institutions that were instrumental in perpetuating the existing maldistribution of income. All of this might come to naught, however, if the masses of the underclass should achieve anything approaching success in potential attempts at throwing off their fetters.

The state devised a second educational strategy in order to prevent such a calamity from occurring. According to Mill, the "elementary schools for children of the working classes" were given the task of ensuring that the poor would continue to accept docilely their dismal station in life. It was very easy for the state to force the public schools to assume this role. It did so simply by failing malignantly to allocate sufficient funds for the operations of what Mill identified contemptuously as "places called schools" (J.S. Mill, Essays on England, Ireland, and the Empire, p.200; emphasis in original). These places were therefor understaffed. Moreover, the few teachers who were actually employed were completely "unfit for their work." The pupils therefore were so "wretchedly ill-taught" that they "did not ... even learn to read." And, said Mill with disgust, no attempt was "made to communicate ideas, or to call forth the mental faculties" of the children". (J.S. Mill, Public and Parliamentary Speeches, November 1850 - November 1868, p. 322 (1988). J.S. Mill, Essays on England Ireland, and the Empire, p. 200 (1982)).

Hans E. Jensen, "John Stuart Mill's Theories of Wealth and Income Distribution". Review of Social Economy. Pages 491-507. Published online: 05 Nov 2010.

http://www.tandfonline.com/doi/abs/10.1080/00346760110081599

Previously noted by me in:

https://old.reddit.com/r/dredmorbius/comments/6x7u6a/on_the_...