Had my third calculus class today. Still learning about vectors. Even though they don't excite me as much as calc does, they're really cool, useful, and powerful. I'm amazed at how much simpler they make expressing fuctions in two or more dimensions, or how they can make geometric proofs that took a page in ninth grade simple.
What I wonder most, though, is why I've had so little exposure to them. In precalc we did a unit on them, but it was really no different than what you might do with lines in analytical geometry. there were no dot products or cross products. Then in physics, we learn a little more about vectors, but when it comes to dot products and cross products we are just told to plug values into some equation that magically works, with no explanation as to why.
Yet, they are so simple. You can begin learning them in middle school, and all it takes to really fully grasp them is a deeper understanding of trigonometry, something students get their sophomore year. It's like not teaching concepts like radians or limits until 10th or 11th grade, when kids would internalize them and understand them much better having been taught them from childhood.
No comments:
Post a Comment