Education in medieval Europe

 1) "...the Romans expected a boy to be ready for advanced work by the time he was sixteen; the Greeks considered him a beginner until he was twenty or older" 

    I find this quote particularly interesting considering that the Romans and Greeks had a different view of age. Today, in most civilized countries I think 18 would be the standard adult age because we go to high school until that age and our brains are in the developing stages. Furthermore, it is absurd to do "advanced" work at age 16; I consider this having a full time job. I wonder how over the years, countries have decided what universal age would be best appropriate. Also, I would stand more with the Greeks because even when I was 20, I had little to no clue what I wanted to do hence, beginner.

2) "It has been frequently stated and more frequently implied that the trivium-quadrivium division of studies existed in theory but that in actuality only the trivium was studied. This is not entirely true."

    I stopped and pondered for a long time when reading this sentence. When we look at gender representation today, there is without a doubt that for math I feel like is mainly male dominated. I could say this for other specialties such as physics, computer science, and engineering. While the reading established that this fact is not true, how did people conclude that trivium was mainly studied? Is it because of population representation? What other factors contributed to this? These are some questions that are lingering in my head. Today, how can we make students be more engaged and interested in Mathematics if population representation is a problem?

3) "The student had simply to swear that he had read the books prescribed and attend the lectures. To qualify for a degree, he was required to participate in public disputations, either defending a proposition or opposing one defended by another student."

    It is of particular interest to know that the standards of qualifying for a degree changed dramatically over the centuries. How is it that students simply had to swear that they read the books and attended the lectures? How can their knowledge of books and going to classes be tested during that time period? I understand that technology was quite different back, but I can't help wonder if there were students that did not read the books. On top of that, I find it interesting that public disputation is necessary to qualify for a degree. I think this whole notion would be ridiculous today because all the mathematical theories and concepts have been proven over the years. If I were to say that gravity did not exist and try to explain why, I would not have any evidence at my disposal backing up my claim. Would I fail getting a degree then? My guess is that back then, not all theories are accepted and students questioned mathematical ideas to see if there are any flaws. I found this really compelling to me.