Yopp - Response

Oh dear. Conjectures in a math high school classroom? Hmm. It's not that I don't think students are capable of doing it, nor do I feel guilty about temporarily frustrating my students so that they can learn something from the process. However, I don't know that the current sort of abstraction present in curriculum would serve students well, or even at all, when disproving conjectures. I would worry that students would get turned off completely from math. I imagine that the "math" that people say they "hate" is really all instrumental/arbitrary. In fact, math is so much more than that; what the general public thinks is math is just the methodology of processes used (mostly) in arithmetic. It seems to me that it is easier for a teacher to use and teach methodology than it is to effectively teach someone how to solve a problem or disprove a conjecture. And on that note, how do we wish to mold students? Do we wish for students to have a high aptitude of mathematics, logic, and abstraction, for students to be laborers capable of completing conversions and estimating necessary materials, functioning taxpayers (or both)? Given that arbitrary math is so disliked, is it worth using conjectures in a classroom? I remember rolling my eyes at any proof that came my way in a high school, because nobody ever bothered to explain why proofs were useful/necessary. My logic said, "I could see it, why did I need to prove it?". Also, at what age level would this be done? Grade 11/12? Earlier? Would the conjecture methodology be a lens or occasional teaching tool? I would like to learn more about this!