Some things just take a while to sink in. This summer I was studying my class textbooks in advance because the ideas just simmer in the back of my brain and then make so much more sense when we actually get to them in class. However, my number theory class this semester is different. The class textbook is super thin and holds a few axioms to learn, but then asks us, the students, to explain them and to prove other theorems based on them. Sure, I can read in advance and try to work my way through, but it’s difficult without any feedback. With all these worries, can this still be a better way to learn?
This is a way of teaching known as the Moore method. Instead of the standard lectures, this method allows students to experiment in a way by doing proofs and seeing how what we already know applies to new situations. We all progress at the same rate by presenting what we’ve learned in class and discussing what we did differently or anything that still doesn’t make sense.
Though this method is also used in our logic course, most computer science classes follow the standard lecture and lab format. Professor Gordon Novak told us, “CS is an experimental science,” but by this he didn’t mean that we discover new data structures just by trying to solve a problem and seeing that that would be the best possible solution. Instead with some exceptions, we learn most of the time we don’t need to reinvent the wheel. The focus is on learning about many different data structures, gaining experience using them, and figuring out how to decide which is the best solution to any particular problem.
Of course, the concept of number theory is completely different than most of what we encounter in computer science. The method of proving the theorem (which may be as close to programming as math gets) isn’t so important as the fact that you can prove it and really understand why something’s true. It’s still kind of a shock being in a Moore method class, but it’s only been two weeks, so I still have most of a semester left to see if this works for me.