Trivium and quadrivium

The first stop I had when reading this article was from the discussion from Plato in which he believed that education should be the sole occupation of the first 35 years of a man’s life, with the first 20 years spent on gymnastics, music and grammar; next 10 years on arithmetic, geometry, astronomy, and harmony; and the last 5 years on philosophy (Schrader, 1967, p.264). Essentially, that could be equivalent to today’s time of a person going to school from Pre-K to grade 12, then immediately going into a 5-year post-secondary program, 2-year master’s program, and 3/4-year doctorate program with still 11 years to go. If a person today spent the first 35 years of their life devoted to education, they would have so much time for mastery learning of subjects before moving onto new topics. There were various views by Greeks and Romans; Greeks who were concerned with the education of free men (non-slaves) as future citizens and Romans who expected a boy to be ready for advanced work before he turned 16.

I did not know that arithmetic was considered an essential part of the curriculum in cathedral schools and was taught in all monastery schools (Schrader, 1967, p. 267). They emphasized computations as they were seeking to determine the date of Easter. It was also mentioned that numbers were identified with various gods and that odd numbers were considered male and even numbers female (Schrader, 1967, p.267). This reminds me of Alice Major’s (2017) paper from last week that discussed Ordinal Linguistic Personification (OLP), which was the automatic, involuntary tendency for individuals to attribute personal characteristics to sequences like numbers.

Finally, the comparison between university during the Middle Ages and present-day was interesting. Schrader (1967) mentions that university instruction was based on lectures and there were no exams; to qualify for a degree simply required a student to defend or oppose a proposition by another student (p. 272). Schrader concludes that most of material for medieval universities is equivalent to common third grade knowledge today and much of arithmetic taught on ratio and proportions are taught in modern eighth grade mathematics. Though this should not discount the fact that medieval arithmetic concepts are just as challenging today as they were back then.

 

 

Reading:

Schrader, D.V. (1967). The Arithmetic of the medieval universities. The Mathematics Teacher, 60:3. 264-278.