Some interesting criticism of my most recent post on question mapping from Dan: the idea of considering questions you want your students to ask that will enable the teacher to more readily get into content.
There seems to be two strains of criticism, which I’ll attempt to distill here.
Criticism 1: By designing tasks to elicit specific questions, you are not allowing students to offer up their genuine questions and denying them a mathematical voice in the classroom.
Either I was unclear or it takes a pretty disingenuous reading of my post to land here, with me dismissing every question except the one I’m hoping to hear. In case it was the former, let me be clear: student ingenuity is great. There’s nothing better than when students ask a question I hadn’t thought of and we can explore it together. Students asking interesting questions is literally the best part of teaching. Full stop.
Perhaps the phrase “the right question” landed wrong and/or is ill-phrased (happy to take alternate phraseology in the comments!). But yes, I am looking to elicit (and hoping to promote and answer) content-oriented questions or questions I can address with content.
Which brings us to the second strain of criticism, the one I think Dan was getting at in his follow-up to a commenter,
Criticism 2: Lashing a prescribed question to a non-routine task is not realistic and it’s folly to rely upon a task to elicit particular questions.
From (Harel, 2008):
For students to learn what we intend to teach them, they must have a need for it, where ‘need’ means intellectual need, not social or economic need.
My desire in all classrooms is to have students engage in problems that demand an intellectual need, preferably (but perhaps not necessarily always!) aligned to content I am to teach. That need often manifests itself in the form of students asking questions. In a response to a commenter, Dan says (emphasis mine):
I am interested in question-rich material that elicits lots of unstructured, informal mathematics that I can help students structure and formalize. But I never go into a classroom hoping that students will ask a certain question.
Well here is a point of real disagreement between me and Dan. I am hoping students ask certain questions: Who will win the race? When does the energy efficient light bulb pay for itself? How many sticky notes will cover the file cabinet? How many push-ups did Bucky the Badger do? These are questions I can synthesize into content. It’s more than hope though: with careful craftsmanship, I’d like to be able to predict what students will be curious about because I want to align it with my very real need to teach through my content standards in a meaningful way. Sometimes I’m able to, sometimes not. With practice I get better. These are the questions that evince intellectual need for the content I’m intended to teach.
I’ve never facilitate Bucky the Badger and not had “how many pushups did Bucky do?” be the overwhelming question in the room. I can safely predict (more than just hope) that this will be the primary question asked by students, and wouldn’t you know it? I have a “second act” ready to give you to aid you in your journey.
The point of Question Mapping is to consider how students might engage with the content in order to design a better, more clear task to hopefully alleviate the first two of four artifacts that Fuller et al describe as “problem free environments”:
Four categories of problem-free activity emerged from our analysis and reflection:
1. The situation or immediate goal is not understood by students.
2. The goal of the activity as a whole is unclear.
…
Problem-Based Learning contends that students learn best when there is an intellectual need for a concept. To me, student questions are the best evidence of that need. So as I teach content, yes, I am (hopefully!) designing tasks that gets students asking questions relating to that content while they are immersed in that scenario.
Anyhoo, comments, clarifications and pushback are welcome in the comments!
===
Harel, G. (2008b). DNR Perspective on Mathematics Curriculum and Instruction, Part II. Zentralblatt fuer Didaktik der Mathematik 40, 893-907.
emergent math 
I’m not sure I entirely get what you mean here. Do you mean, they’ll best learn the concept when there’s an intellectual need for it? Or that they best learn — in some more general sense?
Are those two different things? I guess I’m referring to the former, but it might also include the latter.
The phrase “intellectual need” is taken from the paper linked in this post, from UC-SD: http://math.ucsd.edu/~jrabin/publications/ProblemFreeActivity.pdf
Interesting commentary with both your posts and Dan’s post. I think about Dan’s posts on “____ is the aspirin, what is the headache?” and it seems to me those posts were about addressing what you are focused on here, the intellectual need. I’d be curious about your and Dan’s thoughts about how those fit in either paradigm. It seems to me that trying to create the headache is very much in the same vein as trying to get students to ask certain questions.
Geoff:
So what’s wrong with just asking those questions? Or more practically, if a student didn’t ask one of those questions, what would you do?
I hear from lots of teachers who give up on these modeling experiences (a/k/a “inquiry” maybe) because their kids didn’t ask “the question”, at which point the teachers engage in all kinds of subtle and not-so-subtle machinations to get the kids to ask the question, at which point the kids realize they were only ever playing the “guess what the teacher wants to me to ask” game. Why not just ask the question, I wonder? The outcome of the question-asking is too fragile and fickle (and inessential IMO) to serve as the foundation for the robust, dependable, and essential process of mathematical modeling.
Shorter question: a teacher says to you, “I can’t do inquiry. The kids didn’t ask the question I wanted them to ask.” What’s your response?
Nicol:
There, as here, I’m not expecting students to come up with the question or the aspirin. I’d like to put students in a position where my asking the question or offering them the aspirin seems natural or, in Harel’s terms, necessary.
That was kind of the point of the post initially, to think about how to design tasks to elicit those questions. This is a very real challenge I and other teachers have with Problem-Based Learning. And I’m not going to pretend that I had classrooms in which 100% of the instruction was entirely driven by student questions. Consider that the aspirational goal.
My response would probably consist of one of the following:
* Consider: why aren’t kids asking questions in your class? Is it because it’s just not part of their skill-set, or that they’re not used to it? Or is it the task? Or are you not leaving enough space or facilitating in away such that questions might be asked? A routinized protocol is really helpful here. Like the Need-to-Know protocol:
https://emergentmath.com/2011/11/01/inquiry-based-mathematics-the-posing-of-a-problem-is-only-the-beginning-of-the-problem-posing-process/
* The other would be to send them over to one of my favorite all time posts, “The Unengagables.” (http://blog.mrmeyer.com/2013/the-unengageables/) I really like the practical baby steps toward using student input as the driver of instruction provided there.
***
I would like to step back for just a minute and consider if there’s a difference between the Questions and the Need-to-Know (NTK). NTK is a process I (and ostensibly) all New Tech Network teachers (and many non-NTN teachers) adhere to. Robert Kaplinsky has a version that I really like and draw upon often:
Click to access Problem-Solving-Framework-v7.1.pdf
So even if we pose the problem by asking the questions germane to the scenario, there is still room for students to identify what they need to know in order to solve the problem. You can see examples in the link above. This was my median state of my classroom. Of course, this was back when 3-Acts was just a glint in Dan’s eyes.
Are NTKs the same as Questions? I’m not sure, I might have to chew on that a bit more. In both cases, I’m designing tasks that surface student needs (and/or curiosity) that I can tie into my very real need to teach my content.
It seems as though there is a bit of a false tension between Geoff and Dan. I hear Geoff saying, “Set up a situation so that students are curious about stuff, and be deliberate so that their questions are predictable.” I hear Dan saying, “If the kids don’t ask the question, don’t manipulate them, just ask the dang question!” I am finding it easy to agree with both of you. It is pretty much how I have operated my classroom for quite some time. If I don’t get the questions I anticipated, then I ask the questions, modeling what it looks like to be curious about math and science. But I will say that it has been fun to engage students in a longer-than-anticipated conversation about a topic at the start of a project, in hopes that the question emerges from that conversation. In fact, the conversation is usually just as valuable as the question.
Nice mediation. No problem here.