I just had a conversation with a student in my class that made me really happy. I got a student to believe that her figuring out information, made her a lot happier than me giving it to her. I got her to impress herself, and to believe that she can impress me.
Completing the square is part of our curriculum, and we teach it as just a way to change standard form to vertex form when it comes to a quadratic relationship. So after doing a lot of fun tasks around modelling situations that end up being quadratic, we have to … complete the square.
Bottom line is that I could easily tell my students that in order to complete the square in , you take half of the “b” value and square it, but what’s the point???
My students have worked with algebra tiles before, so I just ask them to take and arrange it as close as possible to a square. So for a while, their desk just looks like…
After a bit of thought and some talking and arguing…it eventually turns into…
And then I just ask them…”what’s missing to make it a square?” and they’ll very quickly show me this:
The Side Conversation
So while this is going on, one of my students who, before this semester, had a tough time with math class, starts a conversation with me:
Student: (Quietly) Sir…is it four?
Me: What do you think?
Student: (Louder) I think it has to be four…
Me: Could it be anything else?
Student: (Confident) Nope! It has to be four.
Me: Ok then…
Student: (With a big grin) I’m so smart!
So into the second question I asked them, another student at her group says…”I’m pretty sure that its just “b” divided by two squared”, and the girl asks “Sir…why wouldn’t you just tell us that???”
The Teachable Moment
Me: How did you feel when you figured out that the answer is 4?
Me: So what kind of person would I be if I took that away from you?
Student: Awwww… Thank you sir!
The Bottom Line
We have many answers… answers that can impress students… make them say ooooohhh and aaaaaahhhh, but why??? Why take those moments away from them? If we give them the chance, they can make their own moments, impress themselves, and most definitely impress us.