The author of the blog Math with Bad Drawings is a current math teacher (and former math student) and discusses the feelings and actions of someone who is floundering at math from both his teaching and his own experiences.
As a math teacher, it’s easy to get frustrated with struggling students. They miss class. They procrastinate. When you take away their calculators, they moan like children who’ve lost their teddy bears. (Admittedly, a trauma.)
Even worse is what they don’t do. Ask questions. Take notes. Correct failing quizzes, even when promised that corrections will raise their scores. Don’t they care that they’re failing? Are they trying not to pass?
I noticed the same things while teaching Algebra I and geometry in Austin. I would offer to help during class or in after-school tutoring sessions, but they would simply decline. They would NEVER remember to bring their books to class. And boy, did they show their despair over no calculators on tests and quizzes! I realized then that many of my Algebra I students did not know 6 x 7 and had no clue about negative numbers. These students were able to pass into 9th grade while having failed the previous middle school math courses. While I did as much pre-algebra review as I could, I offered extra drill practice to the students who hadn’t memorized the basic facts yet. Of course, they declined those as well. Six weeks into the year, one failing student simply remarked, “I’ll retake it in summer school.”
The author of the blog had success with math until his senior year topology course at Yale. Then he started to struggle and wasn’t sure how to handle it.
My failure began as most do: gradually, quietly. I took dutiful notes from my classmates’ lectures, but felt only a hazy half-comprehension. While I could parrot back key phrases, I felt a sense of vagueness, a slight disconnect – I knew I was missing things, but didn’t know quite what, and I clung to the idle hope that one good jolt might shake all the pieces into place.
But I didn’t seek out that jolt. In fact, I never asked for help. (Too scared of looking stupid.) Instead, I just let it all slide by, watching without grasping, feeling those flickers of understanding begin to ebb, until I no longer wondered whether I was lost. Now I knew I was lost.
So I did what most students do. I leaned on a friend who understood things better than I did. I bullied my poor girlfriend (also in the class) into explaining the homework problems to me. I never replicated her work outright, but I didn’t really learn it myself, either. I merely absorbed her explanations enough to write them up in my own words, a misty sort of comprehension that soon evaporated in the sun. (It was the Yale equivalent of my high school students’ worst vice, copying homework. If you’re reading this, guys: Don’t do it!)
I had a similar experience with an upper level college math course, Real Analysis, which I have so blocked from my memory I can’t even tell you what it was about. While I didn’t seek out help either (even though I should have!), I made it through due to the curve as it seemed most people were more clueless than me.
The author, finally desperate, did what he should have done all along. Ask for help from the professor!
I was sweating in the elevator up to his office. The worst thing was that I admired him. Most world-class mathematicians view teaching undergraduates as a burdensome act of charity, like ladling soup for unbathed children. He was different: perceptive, hardworking, sincere. And here I was, knocking on his office door, striding in to tell him that I had come up short. An unbathed child asking for soup.
Teachers have such power. He could have crushed me if he wanted.
He didn’t, of course. Once he recognized my infantile state, he spoon-fed me just enough ideas so that I could survive the lecture.
Teachers want their students to TRULY understand the concepts. Almost all are happy to give extra explanations when asked, but they aren’t mind readers. Encourage your children to not be shy.
Sometimes a student starts a question with, “Sorry, but I need help with…” as if they should be ashamed they haven’t mastered it already. I always remind them, “Don’t apologize. This is my job! You are learning, and this is why I’m here.”
I tell my story to illustrate that failure isn’t about a lack of “natural intelligence,” whatever that is. Instead, failure is born from a messy combination of bad circumstances: high anxiety, low motivation, gaps in background knowledge.
Most of all, we fail because, when the moment comes to confront our shortcomings and open ourselves up to teachers and peers, we panic and deploy our defenses instead. For the same reason that I pushed away Topology, struggling students push me away now.
Not understanding Topology doesn’t make me stupid. It makes me bad at Topology.
And I would argue that like many things had the author had more time and asked for more help with topology (or me with Real Analysis) he would have likely gotten a lot better at it. Writing this blog post has me wishing to be able to retake the class, but I imagine that will wait for another day.
Read the rest of this great blog HERE.