At some point almost every teacher I know will get the dreaded, “Why do we have to do this stuff?” Today we were working through the verification of trigonometric identities and that question came out of the ether on a Monday morning. I have been thinking to myself, how should I answer this?
- I could just silence the student for insubordination, but that would require a misuse of authority. I distrust people who demand blind obedience.
- I could use the textbook line, “You can use trigonometric identities to rewrite trigonometric equations that model real-life situations. For instance, in exercise 58 on page 556, you can use trigonometric identities to simplify the equations that model the length of a shadow cast by a gnomon.” Wow, it says real-life, but then directs the reader back to the exercise problems. This had to be written to appease some bureaucrats that have no understanding of math. And how many people know what a gnomon is without looking it up.
- I could use the, “It is good for problem-solving and critical thinking skills.” But the flaw there is that problem-solving and critical thinking skills can be taught with other subjects, it’s not unique to math class, so why bother with the painful math?
- I could use the, “You will need this in college, work, etc.” However, do we really need the math as it is taught in school for college or work, or is it that those particular fields just use the class as a way to separate and classify people, making math class a filter? And if that is true, can I be content with my teaching knowing I am just a filter?
- I could say that, “The state requires this stuff, so there is nothing I can do.” That doesn’t sit well because now I am just passing the blame to someone else. Also, see what I said about authority in number one.
Honestly, I believe there is a kernel of truth in all of those statements, but I don’t believe alone, any one of those statements can be proper justification for the misery students feel in math class. So, what do I tell my students? What should I say when I really think their frustration stems from deeper issues of how we teach math and how shallow their understanding of mathematical concepts are? When I view trigonometric identities all I see are arithmetic expressions to be simplified. As long as I can do arithmetic, I can prove trigonometric identities. So a better question would be, “Why should I not verify this equation before me?”
Sitting in those desks though, trying to absorb the information, it doesn’t come across as relevant and pertinent. Our schools have created such a Pavlovian response to education that many students have lost the wonder of learning just for the sake of learning. Too many of them view education through the lens of correct answers and the quickest means to achieve them. Their minds have been trained to reward their emotions for extrinsic rewards like grades, meaning far too few of them ENJOY THE PROCESS.
And there I stand, at the front of the room, thoroughly enjoying the process of math that lay before me while they see a gauntlet that must be endured to achieve the grade. I’ve made up my mind, they’ve made up theirs. Our viewpoints are incompatible. We are just too different.