They are mostly about engagement (it's the student's fault and/or responsibility) or about selling something.chemprof:
and "docent science," which is what my colleagues and I call it. Science appreciation is another good term. I guess I can see that they figure that most students won't actually go on and do STEM in college, but they are really limiting their students' options. Plus, I can't tell you how many students come to college thinking that there are careers in science appreciation.I've always had a simmering interest in math, and for years I bought 'math appreciation'-type books, which I always found somewhat unsatisfying and never finished reading.
Finally, after writing ktm for awhile and teaching myself math so I could re-teach math to C., I realized I didn't want to appreciate math. I wanted to learn math.
"Understanding math" - which I think of as a kind of feeling I have at times - is tremendously fun, but it's not fun when I can't actually do the math I'm "understanding." Hard to explain.
I've also learned the importance of "getting used to" math as opposed to understanding it. Or, at least, I've had the experience of learning to do something I can't understand and then, after awhile, coming to feel that it's "natural" and "logical" to do whatever it is I've been doing.
This process is starting to happen a bit with counting, which I have found utterly mystifying. Recently I discovered that a great deal of what I've been doing in counting problems involves the commutative property and the definition of multiplication.
I can't tell if all this self-teaching I've been trying to do is a good thing or a bad thing.