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.