“If I drive 60 miles per hour, my journey will take 4 hours. How long will my journey take if I drive 80 miles per hour?”
Paulina volunteered, “I did sixty divided by eighty—that equals point seven five, or three-fourths. So, it would take three hours.”
When I asked Paulina why she divided 60 by 80, or what the quotient 0.75 meant, she struggled to explain her reasoning. She also couldn’t quite connect how “three-fourths” led her to “three hours.”
We have to keep asking why–why–why, all the time.
Our job is to help students ask better questions. One of my favorite metrics for question quality is this:
If a student asks a question that makes the class say
Oh-shit-I-did-not-think-of-that!
— that's a great question.