Tonight has been weird. I left school with my mind fluctuating between anger, disappointment, and curiosity. I was curious about reflections and the thought of reflecting a triangle over a parabola came to mind, wondering if it would have some sort of fun house mirror effect. The more I thought about it on my commute home tonight I realized that derivatives would be involved, so clearly this wasn’t going to be something I could try to do in Geometry.

Then when I checked Twitter tonight I saw this.

<blockquote class=”twitter-tweet” data-lang=”en”><p lang=”en” dir=”ltr”>Reflecting over a circle <a href=”https://t.co/WaqQ04G5ji”>https://t.co/WaqQ04G5ji</a> <a href=”https://t.co/1zzqMf1nKh”>pic.twitter.com/1zzqMf1nKh</a></p>— Christopher (@Trianglemancsd) <a href=”https://twitter.com/Trianglemancsd/status/837071141873164290″>March 1, 2017</a></blockquote>

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Low and behold, nested within the Twitter stream was a question involving reflecting parabolas. I thought it was neat to watch the discussion unfold in front of me, but when I came across the term normal line, I felt stupid. I had no idea what a normal line is. I don’t know if I never was introduced to the term, or I had forgotten, but I do know it’s not that I was rusty. So rather than try to participate, I just kind of shut down because it made me feel dumb.

The problem I have is that I am the math zombie that became the teacher. I finished a math degree and didn’t really know math. I discovered I was a math zombie when I first began teaching Algebra I and I couldn’t answer a typical mixture problem. (If I had a book with me I probably could find the exact problem since it was that scarring.) Any math that I actually know has been more or less self taught with the aid of textbooks, YouTube, perseverance, an enormous debt of gratitude to the History professors at BGSU who challenged my conception of knowledge, and the students who drug me through. Hopefully that doesn’t mean I am dumb, but that does mean that my mathematical knowledge is extremely piecemeal and lacking in formality. Some of the reasoning I try to share with my high school students clearly lacks the rigor of proper mathematics, as has clearly been pointed out on occasion, but I can confidently say it is mine. Sometimes the responses sting though. I was so excited to share my explanation about rationalization with the world, but was dismissed by some because of canonical forms and the definition of radix. I had to look up canonical forms (which made me want to flip that guy the bird) and I’m still not sure what a radix is or how it impacts square roots. Kind of rips the confidence straight out from under me.

But as painful as times like these are, it helps remind me what it must be like for my students. I can empathize with ALMOST every single student in class to some extent, at least in the attitude towards academics, because I have been there. Math wasn’t, and still isn’t, always easy for me, I need moments like tonight to remind me of that. When I leave work angry and disappointed because of student work, it’s night’s like these that I remember what it was like…

to be worried about grades first and foremost.

to not wanting to focus because other assignments are due.

to just not being able to think about math because, well, just not today.

to struggle to try and remember all the steps in this witchcraft.

to look at a quiz and think, “We didn’t go over that!”

to wanting to just get by and get done.

In a perfect world all my students would come to me with amazing prerequisite knowledge and be highly motivated to learn. That’s not the world we live in though. Without empathy for all the situations our students find themselves in, to many of us wind up browbeating kids into obedient behavior, which just breeds a culture of compliance. My hope is that with some understanding and a little patience I can get a student to want to contemplate the reflection of a triangle over a parabola because…, well,…why not?