We started our Intro to Calculus unit in precalc today. This is the time of year I get a little anxious as the AP Calc test is just days away and it dawns on me that I have exactly one year to get my precalc kids ready for one of the longest and most tiring exams they will ever take. With every blank stare, panic starts to set in as I remember how much work it takes to get them to the finish line. 

We reviewed derivatives and tangent lines today before the kids started working on their packet. I said time and time again (as I had done earlier in the semester also), “As soon as you see ‘Write the equation of the tangent line…’ think point-slope form.”

So the kids got to working and I started answering questions as they came. One boy asks a lot of questions every single day, and I love him for it. I know others have the same thoughts: he’s just brave enough to ask. 

I had been by his desk several times already, when he said, “I just don’t know where to start.”

“Ok. See how it says, ‘Write the equation of the tangent line’? As soon as you see that, you’re supposed to think of what?”

“I honestly don’t know.”

And that’s when I did something I very much regret. I sighed. Audibly. 

And I saw it on his face immediately. I saw the shame. 

And a memory came rushing back to me of when I was in his same shoes, asking a professor in graduate school for homework help, only to be told, “The answer is obvious. I can’t help you any more. That wouldn’t be ethical.” I remembered my shame and my frustration with myself. Why couldn’t I figure this out? Was the solution really that obvious?

And you know what happened? My brain shut down. Oh, I remember it so well. I couldn’t process anything else the professor said after that. I closed my books and left the office, knowing my heart needed to heal before my brain could do what I knew it was capable of doing. 

I looked at my student, cussed myself out without speaking, and purposed to rectify the situation. 

Armed with new patience and empathy, I helped the student work the calculus problem. I knelt beside him and encouraged him as I could see him puzzling the problem together piece by piece. In the end, he was able to figure it out. And I was convinced that he made some mathematical strides. But I still worried I had been too harsh. 

Several minutes later, a young lady asked me a similar question.  Once again, I asked, “Ok, when you see, ‘Write the equation of the tangent line,’ what do you need to think?”

“Uh…I don’t know…”

I turned around and called to the previous student. “S, can you help us out?” And I repeated the question. 

“y minus y-one equals m times the quantity x minus x-one,” he said with the proudest smile on his face.

That’s what I needed. It was clear he had forgiven me. And he remembered the math. 

He’ll pass the test in a year. Mark my words. 


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