Multiple choice. A student looks at the graph on his calculator and concludes the minimum is at x= “a little past negative 8”, so he chooses (C) -8 because “it’s the closest one so it’s the best answer.” General consensus among the vocal. They wait for me to move us on to the next thing, I wait for them to tell me they’re done.

Some whispering. One or two students have noticed choice (D) -25/3. Three students turn to me separately and mouth, “Isn’t it D?” I deadpan. A minute goes by. Three minutes go by. Finally, my quietest student makes a noise I can’t make out. The student at the board hears her and repeats out loud, “Is it D?” Now they all know they’re done.


  1. What am I going to do next year to build number sense?
  2. What am I going to do with my underclassmen this year to build number sense?
  3. Most importantly, all year I’ve been deliberately emphasizing the importance of putting ideas and objections out for the group, but somehow I must be unknowingly communicating something different, because they are still afraid to do that.

That last may be too harsh. I think they feel safer questioning each other on the calculus than on fractions – if you reveal yourself as confused on calculus, hey join the club, but if you’re confused on fractions, that’s embarrassing. Hmm.

One more note – as I moved us on to the next thing, I definitely articulated my impatience, not with their not recognizing -25/3, but that three people had a different idea and didn’t put it out there. I wonder if showing my frustration when they don’t take a risk is the best way to encourage them to take a risk. I suspect not.