Inquiry-Based instruction, in a PNG-nutshell

In talking to math teachers about an Inquiry- , Project- , or Problem-Based approach, these are the following questions that come up most often.

1) “How am I supposed to cover all the standards using this approach?“

and,

2) “So, when do I actually teach?”

An attempt at the first question is reflected in the Great Inquiry-Based Curriculum Mapping Project, from a couple weeks ago.

The second question can be a bit loaded, especially when you move the emphasis from word to word (as I did, by emphasizing “actually“).

We can discuss the second question a bit more in-depth going forward, but I’d like to attempt to simplify the nebulousness of “inquiry-based instruction.” When teachers ask “when do I actually teach?” I think they’re asking when do they stand up in front of the class and demonstrate examples and processes? And is such a time ever appropriate for an inquiry-based classroom environment?

But before we get into the weeds of such a rich topic of discussion, let me posit this to you: I would suggest that the change from a “traditional” approach to an “inquiry-based” approach may be as simple as moving from this

to this:

(apologies for the computer science jargon)

Now, obviously there’s a lot more to it than just a couple diagrams, but the point is this: instruction still happens, but it simply happens after students have attempted a problem and within the context of a problem. Instead of saying “Today class, we’re learning about slope, here’s a lecture,” followed by a lecture, followed by a problem set, the practice is in some sense, simply reversed: “Today class, here’s a problem,” followed by instruction about,say, slope.

So yes: instruction is still useful and necessary for an inquiry-based environment. And I would also say yes: lecture or direct instruction is often a appropriate tool to transmit mathematical knowledge in an inquiry-based environment. (Although, I would warn against it’s overuse, lest it become the default mode of instruction.)

The deeper questions of when and how do I instruct is a bit more of a dance that I hope to at least partially address in the coming posts. But in the meantime, let me hazard a broad-brush answer at these.

When: after students have had a goodly amount of time to discuss the problem with each other, and at least begin to attempt a solution. Maybe at least 30 minutes?

How: it depends in part on the number of students struggling with the content. If every group is having difficulty even starting the problem, then a whole-class lecture may be appropriate. If half the class is struggling, maybe some share-out, gallery-walk, and/or group-student-exchanges may be appropriate (or better yet: Kate’s “Speed Dating” activity). If only a few students are unable to jump into the problem, a small workshop may be necessary, while groups discuss and assess their solutions.

But these are broad-brush, haphazard solutions to potentially a much bigger question. I’d love to begin aggregating and categorizing math scaffolding activities and to have a discussion about when they may be appropriate.