Finding the "Hidden Wows"

I was working with some middle school teachers-to-be who are noticing some of the aspects of algebra we tend to take for granted after years of practice and application, and they are noticing how difficult it can be to anticipate the strategies and struggles of students who are just learning algebra.
 
One way I get around that is to try to hold myself still with a problem for a bit and look for the hidden connections. With kids, I might tell them we're looking for the Hidden Wows.

Suppose I am preparing a lesson for sixth graders to introduce problems of this form:

Solve: ax = b

 My planning might start out sounding a bit like this:

What's with that title anyway?

Let me say a bit about the title of this new blog of mine.

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?