Honor your Dissatisfaction

Two things I forgot to say last night.

I. The reason I’m excited about the idea of having my class use its own self-made definitions to try to prove things is not just, or even primarily, because it will help them realize the inadequacies in their definitions. Although it will do that for sure. Even more than that, it seems to me the perfect way to support them in coming up with better definitions. This is what happened to Cauchy: he defined the limit verbally and a little vaguely, but then when he actually tried to use his definition to prove things, he started writing down precise inequalities. He didn’t have a teacher around to point out that this meant he should probably revise his definition, but my class does.

II. Yesterday when I asked my class to try to make a precise definition for what it means to converge, or for something to have a limit, some of them who took real analysis long ago began accessing this knowledge in an incomplete way. They started to talk about \epsilon and \delta, but in vague, uncertain terms. It looked as though others might possibly accept the half-remembered vagueries because they seemed like they might be the “this is supposed to be the answer” answer. I had to prevent this. (The danger would have been even greater if these participants had correctly and confidently remembered the definition.) I stepped in to the conversation to say, yes, that thing you’re half-remembering is my objective, but what’s going to make you understand it so you never forget it again is to fight till you’re satisfied we’ve captured the meaning of convergence. You can either fight with the definition you half-remember or you can fight to build a new definition, but you have to go through your dissatisfaction to get there. You have to air all this dissatisfaction.

Afterward, I thought of a better language. I’ll give this to them next time.

Honor your dissatisfaction.

Dissatisfaction is the engine that created analysis. This content, more than any other content, is both confusing and pointless if you bury your dissatisfaction rather than allowing it to thrive and be answered. The primary virtue of the tools of analysis is that they are satisfying. Only if you bring forth your dissatisfaction will this content have a chance to show you its value. So. Honor your dissatisfaction. It is the engine that will move us forward.


11 thoughts on “Honor your Dissatisfaction

  1. Ben:

    Honor your dissatisfaction! What a great concept. Sounds like an update of “leave no stone unturned,” but yours is more appropriate for mathematics. We miss you at UFTSCS.


  2. Found you through Dan Meyer’s link to your Waiting for Superman review…and got a little sidetracked paging through your posts 🙂

    I love this idea. I’m a 2nd grade teacher in my third year. Above the entrance to my education building at OSU were the words “Prize the doubt.” These words are hands-down the most relevant words I’ve ever been “told” about teaching. They are scrawled on a post-it that’s been in front of my planning binder since grad school. It seems like this connects with the idea of cognitive dissonance. When our minds are uncomfortable, they are flexible (if we run with it). Then great learning happens.


  3. Hey Ben,
    Got on to read your ‘Stuporman’ post and saw this. I really love it as a concept for teaching and for life!


  4. @ Elizabeth, Laura and Ann – as an update, the phrase has now become part of my vocabulary with this class. (And I think with all future classes I teach.) One of the participants has totally taken it on and I hope that the others will too so it can become part of the class’ culture.

    (p.s. Hi Ann! Say hi to Frances for me too.)

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