So the other day I read a tweet by Justin Lanier that really sparked my interest.

 We all know the scenario in classroom discourse where a student asks a question – a really great question – and you know the answer, but you hedge and you say something like, “That’s a great question! I wonder what would happen if…”  So you reflect it back to the students so that they have something to think about for a little while longer, or maybe even ask a question like “Why would it be that way?” or “Why did you think or it like that?”  to try to get the student to think a bit more.  But what Justin, and the person who coined the phrase “authentic unhelpfulness” Jasmine Walker (@jaz_math), I believe were talking about was hedging because you really don’t know the answer – sincere interest in the uniqueness of the question – not because you’re so excited that student has helped you move the conversation forward, but because of your own excitement about the possibilities of the problem solving or the extension of the mathematics.

I think what got me so excited about this idea was how it connected to something that I was discussing earlier this summer with a group of teachers in my scaffolding in PBL workshop in late June.  In a PBL curriculum, the need to make sure that students have the right balance of scaffolded problems and their own agency is part of what Jo Boaler called the “Dance of Agency” in a paper she wrote in 2005 (see reference).  My understanding of this balance goes something like this:

So initially, the student is confused (or frustrated) that the teacher refuses to answer the question although you are giving lots of support, advice and encouragement to follow their instincts.  The student has no choice but to accept the agency for his or her learning at that point because the teacher is not moving forward with any information.  But at that point usually what happens is that a student doesn’t feel like she has the authority (mathematical or otherwise) to be the agent of her own learning, so she deflects the authority to some other place.  She looks around in the classroom and uses her resources to invoke some other form of authority in problem solving.  What are her choices?

She’s got the discipline of mathematics – all of her prior knowledge from past experiences, she’s got textbooks, the Internet, her peers who know some math, other problems that the class has just done perhaps that she might be able to connect to the question at hand with previous methods that she might or might know how they work or when they were relevant – that discipline has had ways in which it has worked for her in the past and lots of resources that can help even if it may not be immediately obvious.

But she’s also got her own human agency which is most often expressed in the form of asking questions, seeing connections, drawing conclusions, thinking of new ideas, finding similarities and differences between experiences and thinking about what is relevant and what is not.  These pieces of the puzzle are not only important but a truly necessary function of the “dance of agency” and imperative to problem solving.

Interweaving both of these types of agency (and teaching kids to do this) have become more important than ever.  Yes, being able to use mathematical procedures is still important, but more important is the skill for students to be able to apply their own human agency to problem and know how and when to use which mathematical procedure, right?  This “dance” is so much more important to have every day in the classroom and if what initiates it is that deflection of authority then by all means deflect away – but the more we can “dance” with them, with “authentic unhelpfulness” and sincere deflection because we need to practice our own human agency, the more we are creating a true community of practice.

Boaler, J. (2005). Studying and Capturing the complexity of practice – the Case of the ‘Dance of Agency’