One of the jobs I have as a math teacher is to coach students to become more and more confident in their own ability to think and reason.
Recently, I was working with a student. She is an incredibly hard worker, but lacks confidence when it comes to math. So naturally, when she comes for extra help, she looks to me constantly to reassure her that she is doing the “right thing.” She will say things like:
“Would I add x to both sides now?”
“Should I set them equal to 180?”
“Do I use CPCTC now?”
And yet, I don’t want her to be looking to me for whether or not she’s on the right track. I want her to first look to her own reasoning abilities. So we have worked to change her language from “Should I,” “Would I,” and “Do I” to:
“I think _______________ because _______________.”
Starting that very day, she really took my suggestion to heart. For example: she was working with a complicated diagram trying to find angle measures. She started to say: “Would I add these up to equal 180?” But she caught herself and said instead: “I think I should add these angles up to equal 180 because they make a straight line.” To which she responded (to herself) “oh wait…no they don’t. They make a line with a third angle, though. I could add all 3 up to equal 180.”
It seems like a small thing, but a teacher is there to coach students through the process of learning math, not to be the arbiter of all truth. Students are empowered when they learn to think of themselves as critical thinkers, capable of reasoning through complicated problems.