In high school I was super-obsessed with linguistics. (I still am -- I just am less likely to burst out inappropriately into linguistic asides in casual conversation.)
In my childhood my father had always treated calculus like this esoteric and super-abstract thing that only erudites could know. It was a uselessly haughty attitude in retrospect; my father was kind of a weird character -- I remember at 7 or 8, I came home with the "we worked with fractions today!" excitement, and he gave me this dismissive, "Psh! With that excitement I thought you had learnt something truly enlightening, like calculus." My father piqued my interest in science, but he was also the type to leave the family when I was 10. My mother, who works in architectural drafting and currently designs ships for a defence contractor, has only the vaguest recollection of a derivative -- her knowledge of calculus is all procedural knowledge, like how to find shear stress or dead load, moment formulas for various geometric shapes, etc. AFAIK no one talks about the elegance of the Mean Value Theorem on the job.
So my father's leaving meant I became the mathy one in my family. Which was bad, cuz when I was 14, I basically failed my secondary two mathematics exam in Singapore with a score of 47%. (OK they also let me take a makeup exam and I passed, but it was none too glamourous.) I had lost most passion for mathematics, until I picked up this book called Fermat's Last Theorem. You mean .... there are active areas of research in mathematics? I was inspired to self-study ... in Singapore everyone has private tutors or something, even the lower middle class, but my single parent household was even below that. Now I can laugh at all those people who spent thousands of dollars a year on private tutoring ... when I spent an amazing amount of $0 using Google. This is why I don't really disagree with idea of an "Investigations" curriculum -- it's just implemented horribly, when there are so many more fascinating and intellectually-stimulating investigations one could use.
Like take linguistics.
It had come to pass that in high school I had become pretty fascinated with calculus and linear algebra. I was taking linear algebra via dual-enrollment, and was trying to wrap my head around things like vector spaces and determinants. "Yeah I get how to do this problem, and I get the fact that theorem X is proven, but I still don't get why it works." I made the mistake of treating it like a regular high school class, because apparently my constant question-asking had annoyed some of my classmates, and the Dean of Students came to me and was basically recommended a remedy of asking less questions.
This was around the same time I was really into historical linguistics and phonetics, and had discovered the real truth behind English "long" and "short" vowels, and suddenly English spelling made so much sense, especially since I was also working out sound changes between French, Latin and Spanish. I felt like a child again ...
But then came my beloved math teachers -- the last ones who I expected to ask, "Why are you studying all this math? You're going into linguistics, right?"
At that time I was totally caught off guard, and could only come up with replies like, "Well uh.... it's kinda interesting," or "It's good to know, if I ever switch fields..." or "There's so much physics in phonetics! Well, kinda...."
Well, I'm glad to report that the suspicions of my math teachers were wrong. Other than the fact that I suddenly became interested in materials science in college, there is so much abstract math in linguistics it's not even funny.
[the above is a CPG mutual-inhibition diagram for a nonlinguistic circuit, but I can't believe that some people -- math teachers of all people -- don't seem to get that in order to study acoustic signal processing, especially in the brain, you need to understand a) how to analyse a periodic function b) the general solution to the differential equation y'' = -ky]