My teaching and scholarship have always centered around striving for understanding, and so I settled on the title "...do we understand" as I reflected on the types of questions I anticipate exploring here. These are the questions that interest me as a teacher, as a researcher, and as a human being.
So I expect I'll be exploring questions like:
- Do we understand the content we are teaching and learning? How? What? Why?
- Do we understand our students' ways of thinking? How? What? Why?
- If not, how can we find out?
And probably questions like:
- Do we want to understand? Children strive for it, always asking why, but older students begin to replace why with is this going to be on the test? Why??
- Do we understand each other? How can we be sure we're talking about the same thing?
And almost certainly questions like:
- Do we understand the effects of our instructional choices on learning? Can we anticipate and check for unintended consequences?
- Do we understand the strengths and limitations of the tools we use, both mathematical and pedagogical?