I'm a big fan of learning for the sake of learning and loved Val's example of connecting geometry to essays. I recall a conversation a couple of years ago with my DD (who is more passionate about language arts than math) who was trying to make sense out of negative numbers. She understood the rules, but was bothered that she didn't feel like she understood the reason behind the rule for multiplying a negative by a negative. It was the "double negative" in grammar that helped her grasp it as a concept instead of a rule and to then move onto a more mathematically based understanding.
I took alot of courses that, looking back, were a huge waste of time and taught me little in terms of knowledge or skills.
I suspect we all look back on classes that seem like they were a waste of our time in retrospect. These are usually classes that we wouldn't have chosen simply out of interest, and which we end up not really needing. I think though about how many people start out on one path in a general area of study and then, based on some experience or another, veer onto another class in the same general area. I think sometimes there is a general pool of related pre-requisites or requirements that lead to a few different specific paths. I'm thinking it might just make sense because it's more cost effective to create a foundation that allows for more than one possibility, particularly if the foundation is at the undergraduate level for a course of study that requires grad school, med school, etc. If you are a college or a university, you don't want to waste time teaching what students should have learned in the previous level, but specialization may not be decided upon until a student is involved in a graduate level course of study. Just a thought....
