Having come this far it should be noted that although the quadrivium was officially part of the curriculum on medieval universities it was on the whole rather neglected. When taught the subjects were only taught at a very elementary level, arithmetic based on the primer of Boethius, itself an adaption of Nicomachus, geometry from Euclid but often only Book One and even that only partially, music again based on Boethius and astronomy on the very elementary Sphere of Sacrobosco. Often the mathematics courses were not taught during the normal classes but only on holidays, when there were no normal lectures. At most universities the quadrivium disciplines were not part of the final exams and often a student who had missed a course could get the qualification simple by paying the course fees. Mathematics only became a real part of the of the university curriculum in the sixteenth century through the efforts of Philip Melanchthon for the protestant universities and somewhat later Christoph Clavius for the Catholic ones. England had to wait until the seventeenth century before there were chairs for mathematics at Oxford and Cambridge.

From this, by Thony Christie. I didn’t know about this.

It reminds me of something else that I think about all the time, which is the article from 1920 announcing the creation of NCTM:

About ten years ago an organization known as the National Council of Teachers of English was formed. Today it has a membership of 5,000….

During the same period high school mathematics courses have been assailed on every hand. So-called educational reformers have tinkered with the courses, and they, not knowing the subject and its values, in many cases have thrown out mathematics altogether or made it entirely elective. The individual teachers and local organizations have made a fine defense to be sure, but there could be no concerted action. Finally, the American Mathematical Association of america came to the rescue and appointed a committee to study the situation and to make recommendations. Already two valuable reports have been issued and others are in preparation. The pity of it is that this work, wholly in the realm of the secondary schools, should have to be done by an organization of college teachers. True they have generously called in high school teachers to help, but the fact is that it remained for the college people to initiate the work. They could do it because they possessed a live, vigorous organization.

To help remedy the existing situation the National Council of Teachers of mathematics was organized last spring at the N.E.A meeting held in Cleveland.

Math has a far less secure foothold in the curriculum than you might think. Historically speaking, at least.