Last week a student of mine was curious about the quadratic formula. He had seen it before but didn’t understand why we used it. “Where does it come from?”, he asked.
I loved this question.
I did the thing any excited math teacher would do and decided to take a couple of minutes to explain to him how we can start with ax^2 +bx + c = 0 and complete the square. Luckily, this took place after school because five minutes quickly turned into twenty and soon he said “sorry, mister, I need to run!” Even though it was a concept that I understood and I have taught before, I ran into bump after bump and I found myself thinking collaboratively with my student about the problem but ran out of time and couldn’t quite figure it out in time!
Luckily, I didn’t feel too defeated because I figured it out a few moments after he left, but it got me thinking… Often as a teacher, I feel the need to be fully prepared – down to the last detail. I feel like any example I show or any question that I answer must be done to perfection. And yet, learning is the exact opposite. Learning is messy and bumpy.
If I would have prepared a lesson and taught the quadratic formula explanation perfectly by detailing every step would more learning have occurred? What is the value of modeling a perfectly solved problem? Would it be more meaningful to model good questioning and struggle through a problem? How do we let students solve questions like that while still allowing them the support to access it?
I don’t know the answer to it all, but definitely some questions worth grappling with. Curious if you have thoughts or similar situations to this!