Blog Response #11: The Arithmetic of Medieval Universities

 These are the three quotes from the article (Shrader, 1967, pp. 264-278) that made me stop and think, or surprised me:  

- “The Greeks were concerned with the education of free men as future citizens. Plato, whose plan was a theoretical one probably never put into actual practice but nevertheless reflecting the spirit and ideal of his period, conceived of such education as the sole occupation of the first thirty-five years of a man's life. He would have the first twenty years spent on gymnastics, music, and grammar, the next ten on arithmetic, geometry, astronomy, and harmony, and the next five on philosophy. Only then would a man be equipped to take his rightful place as a useful member of society” (Shrader, 1967, pg. 264).  

- “In the first ages of the Church, when Christianity was struggling for its existence in a pagan world, the seven liberal arts were denounced by such Christian writers as Origen, Tertullian, and St. Jerome, not because the arts were evil in themselves, but because they were the basis of the pagan educational system which was a threat to the infant Christian Church” (Shrader, 1967, pg. 265). 

- “In the twelfth century and the first half of the thirteenth, the arithmetic taught at Oxford was largely derived from Boethius) Cassiodorus, and Isidore; it consisted of the study of the properties of numbers: ratio, proportion, fractions, and polygonal numbers. No practical calculations were done so no abacus was necessary” (Shrader, 1967, pp. 269-270), and “It is interesting to conjecture whether or not we are today facing a similar upheaval in theoretical mathematics. Is it not possible that someday a high school student may laugh condescendingly and say, and they got graduate credit for that!" (Shrader, 1967, pg. 274). 

     The first quote surprises me by how serious the Greeks/Plato were about education, because of the plan to dedicate 35 years of a man’s life purely to learn before being ready to be known as a useful person to society. This makes me think of how this idea may have been expanded on for the concept of schools and universities to come into fruition. That is, the idea that one goes through an education phase before they can go out and build their own careers. The second quote makes me wonder at how powerful institutions or movements control education in some form, to further their own agendas. I was shocked to read the final quote, because I was so surprised to hear that there was a time when math that is at a high school level now was considered university math then. It makes me wonder if high school students a hundred years from now will also be at shock to hear that the math they are currently studying in high school was the math that we studied in university. This also fills me with hope thinking about the fact that math will be much more advanced in the future. 

 

References 

Shrader, D.V. (1967). The Arithmetic of Medieval Universities. National Council of Teachers of Mathematics, vol. 60(3), pp. 264 –278. https://www.jstor.org/stable/27957550