Thinking about Thinking

I remember (when I was in school) my teachers would say, "I can't open you head and see what you are thinking."  And then (I guess) they would encourage us to ask questions when we didn't understand something.

I think the biggest challenge for teachers is to try to know what their students are thinking.  We can't always "see" it on an assessment.  Even as mathematics teachers, it is not enough to see that the students are getting the right answer.  We're glad they are getting the right answer, but we don't necessarily know that they are thinking through the problem correctly.  This is particularly evident when they get some answers right and others wrong and the problems are very similar.  Teachers think, "How did you get this right and this wrong?"  We assume that they made a simple arithmetic error.  Sometimes that IS what happened.

But other times the problem is that the student isn't thinking about the problem correctly.  Their method works sometimes and not other times.

This is why it is so important to have lots of discourse in the classroom.  Teacher-to-student, student-to-student, and whole class discourse.  We have to "hear" what the students are thinking.  And if we want students to be comfortable to speak up in class, then we have to establish a learning environment where students feel safe to share their thoughts.

Someday, we might have a device that can show us what students are thinking.  But today, we have to find ways to encourage students to help us to know their thoughts; to talk about their reasoning, their "thought process"; their ideas.  It's all about the learning; which requires thinking; which requires teachers to know what their students are thinking.

Yipes!  Teaching is hard.