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monika: i’m wondering if our focus on being good teachers, even less helpful teachers, is still keeping our students from becoming fully engaged. i’m wondering if we need to deliberately not teach.

This goes too far for me. Teachers bring a great deal of value to a classroom. Some of that is bound up in their ability to explain concepts, but students can access plenty of explanations from other sources. I also add value to a classroom when I notice different solution strategies around a classroom for the same problem, when I help students fix the incorrect strategies, and when I pull those different strategies together in a whole-class discussion at the end of the problem.

I can’t add that value in an unfocused problem space. The problem space needs to be rich but tightly focused if we’re all going to benefit from the different work that our different classroom colleagues are doing.

Multimedia gives us the opportunity to create problem spaces that are, in many cases, richer than what’s possible on paper. (Certainly that isn’t always the case.) I come to class with multimedia that’s been captured in such a way that I can anticipate what questions students will have about it. I gather as much information about that space as possible (measurements, etc) that will enable students to answer those questions. And while I’m capturing the space, I capture the answer to the question I anticipate most of them will want to answer.

Certainly, we need to keep a loose grip on the goals of our lesson. If the majority of the class wants to work on a different question (that’s still mathematically productive) I have no problem setting aside the answer video I captured. But the existence of the answer video is only adding value to the class.

blaw0013: Which seems to beg the question, why not offer the question you wish for the students to engage (rather than feign the interest in your students’ pursuit of their own question), and allow them to pursue the question in whichever manner they see fit.

Sure. I can’t say I have a problem with this. At some point, though, I need to ask a group of people: “is the question I’m going to ask students to pursue here the question that most of them will want to answer?” I can get that feedback by asking students, “what question interests you here?” Or, increasingly, by asking a group of teachers: “#anyqs.” At a certain point, I may get good enough to trust my instincts.

On the other hand, just because we don’t have the resources to take up every student’s question, it isn’t a priori insincere to ask students what they’re wondering. And sometimes we can take up multiple questions. Ten students wonder how many tickets are on the ticket roll. Three wonder how long the ticket roll would be stretched end to end. It’s a simple matter to take up both of those questions. But if I had only asked students how many tickets are on the roll, I would have missed an easy opportunity to validate student curiosity in my math classroom.

These quotes indicate a belief that there is a right way to be curious, that students should seek out the question the teacher wants them to ask, that the question should be mathematical.

Well stated. This sure is hard for me to ACT on in my classroom though. I guess I do plan for class seeking to draw out a question I wish for students to ask. To what extent can I let go, yet still create a mathematically productive environment?

And if not obvious, by selecting one question to pursue, the community of learners in my classroom are not each pursuing their own questions.

Which seems to beg the question, why not offer the question you wish for the students to engage (rather than feign the interest in your students’ pursuit of their own question), and allow them to pursue the question in whichever manner they see fit.

This seems to be the method observed by Jo Boaler in the “open” classroom described in her dissertation work, Experiencing School Mathematics.

coming from an intense year of reflection on this very thing, and knowing i have much to learn, i’m dying to know what you and others think of this:
once you yourself have
gathered info for students
recorded an answer
planned a revealing
aren’t you (we) compromising curiosity?
aren’t we blocking adjacent possibilities?
possibilities that could potentially provide a more useful answer?
but more important, and what i’m really seeking insight about,
don’t the kids see the pattern, don’t they become aware you’ll be having those answers.. i’m wondering if that knowledge of where this is headed whether or not they fully engage, encourages them to be mindless.

i’m wondering if our focus on being good teachers, even less helpful teachers, is still keeping our students from becoming fully engaged. i’m wondering if we need to deliberately not teach.