"But what's the answer?!?" (I hear my students cry)

(Note:  this blog is posted a day after it was written, as my internet connections as down last night.  Also a really big tree came down in my neighbor's yard Monday night, and our willow tree has several fewer branches than it did Monday evening.  These phenomena may or may not be related.)

I found myself resisting the open-ended, cycling, somewhat repetitious and jumbled nature of the modeling whiteboard discussions today (Tuesday).  

At one point I thought, "I'm not sure I would have enjoyed being a student in this kind of class -- do students learn to enjoy it?".  I was mostly reacting to the frustrating sensation that there is almost never just a simple answer or conclusion to any question.  And the prompting facilitator questions sometimes feel like the "guess what the teacher's thinking" game.

I guess a follow-up question would be, "How important is it for learning to be enjoyable?"  I suppose there's an argument to be made for building moral fiber by persisting in unpleasant tasks.  On the other hand, I found it a lot easier to eat my spinach once I discovered forms of it that I find tasty.  (Slimy nasty canned spinach of my childhood - no.  Fresh spinach leaves in a salad, or sauteed with garlic, or made into saag paneer - yes, please.)  

So, what makes the circular, repetitious, jumbled nature of these discussions palatable to students who are familiar with, comforted by, and good at the traditional approach to teaching and learning, where the teacher sometimes (often) provides answers?  (Or are the discussions less circular, repetitious, and jumbled with real students?  Doesn't seem likely, but may our student mode is failing?)

As we were deep in the weeds of whether motion maps show instantaneous or average velocity with their velocity vectors, I thought to myself, "I love physics and I am bored by motion maps right now.  What will keep my students awake?"  I suppose it will be somewhat a matter of tailoring the discussion to the level of my students.  But are students really engaged by questions about whether the dot should have an arrow on it or not?  Does it depend on how deeply we're tying it to the details of the actual, real-world, physical motion?  (I did love the graphs Bryan put up at the end showing how the acceleration arrows could be pictured as the vertical side of the slope steps on the a v-t graph, adding to or taking away from the velocity lines at each position.)

I'm excited to have workshop participants try leading whiteboard discussions tomorrow.  If I'm called on to do it, I think my biggest struggle is going to be restraining myself from "giving answers".