0 The Question Reveals . . .

I saw this quote somewhere a while ago, I don't remember where:

"It is better to solve one problem five ways than to solve five problems one way."

Recently, for bell work, I asked my students to give a response to that quote. I was kind of proud of myself, because it might be the first time my bell work has been something other than a problem to solve. The lesson for the day was solving quadratic inequalities both algebraically and graphically (they have done both, but I wanted students to see them side-by-side), so it seemed to fit.

The responses were limited to just a few thoughts:

You can use one method to check another method.
Sometimes one of the methods may not work.
You might forget one method so you could use another.

I am not sure what I was looking for. Maybe I was hoping that someone would think about how solving a problem multiple ways helps you better understand the concepts and how they all fit together?

What I think is interesting, is how much these answers reveal about where my students are at in their understanding of math. To my students, math is still a bunch of procedures to remember and repeat.

And here's the thing:  I think I am still mostly teaching that way.