Question

true or false
monasteries became the center of learning and education in medieval society

Answer 1

True.
I found an answer online to back up my statement:

In medieval Europe, often monks were the only literate people around. So monasteries held libraries of hand written books - and were likely the main places people went to learn about what went on before them.

Most of medieval Europe was not literate (able to read and write), so they weren't collecting their favorite reading materials at home. As a matter of fact, there were no printed materials around because Guttenberg had not yet thought up movable type (which is where books as we know it got their start). Monks spent days and years copying books over and over by pen and ink.

But if education is what you wanted, you went to see the monks to learn.