Further, there’s still just going to be a ton of teacher resistance to the amount of time it takes to do inquiry right. If there’s a sense you can’t cover enough ground, teachers are going to panic and go with what moves students through the material at a brisker clip. Again, mastery through inquiry will only work well if happens once a week or more. But on the other hand, there’s the possibility of going too far: one truly masterful teacher that I know runs inquiry 50-60% of the time and thinks this has hurt her scores because she didn’t push fluency enough.

So, did the kids learn/grow more (in the big picture) because of 60% inquiry, or was that too much and they really do need more fluency? No really easy way to answer that question in the current environment, much less any easy consolation if everything has to be done based on scores and a strict curricular schedule that fits testing windows in February and May.

I love inquiry, and I think it is really great for kids’ minds. But I don’t think we should kid our selves into thinking that there’s not a pretty big role for problem-based learning that still must exist.

Well, yes, it is a false choice. That’s my point.

I believe we need to drill, and we need to open minds to what that drill allows us to do.

But that’s not what those Krall and Gillard quotes say. A person could quite reasonably take from them that practice of skills was unimportant. After all, in their discussion of what is important in a Maths class they do not mention anything about teaching of skills.

I appreciate Brett taking a charitable reading of the commentary. And Dan for challenging me on imprecise language.

Same. Brett’s mediation has made our marriage 10x stronger. Appreciate your follow-up post too, Geoff, which I’ve added to the body of the post.

Ethan:

I wonder in terms of formalizing 3-Act Math as a routine if the shift to the teacher posing the “productive question” might eventually lead to students losing motivation for questioning since they know that Act One is “rigged,” so to speak.

Probably. Except I run back to their questions at the end of the period, many of which have been answered in the course of answering our focus question. I say, “I love these questions and I hope we get to all of them by the end of our time today,” and they know I mean it because we do.

Does that mean that if the teacher asks a provocative question that stimulates student thinking in mathematically meaningful and productive ways (or a student asks such a question or answers a teacher or student question in a way that leads to meaningful mathematics, etc.), that the Standardista in the corner gets to blow a whistle at the end of the lesson, should not only the “right standard” not get pointed to, but perhaps no immediately identifiable standard (as in, could there be important, powerful mathematics that arises in problem-based math lessons that is outside of the rather narrow confines of our current national standards or some other set of standards in the future?)

Maybe this is a trivial point, or “too political,” or just not getting at anything folks here want to discuss. If so, my apologies. It’s just the rebel in me, I suppose.

The possibility of student learning needs to rely on something sturdier than “hope,” is what I’m saying.”

I really appreciate your and Geoff’s posts on this. I wonder in terms of formalizing 3-Act Math as a routine if the shift to the teacher posing the “productive question” might eventually lead to students losing motivation for questioning since they know that Act One is “rigged,” so to speak. I definitely agree with needing more than “hope” when designing a lesson, but I wonder the extent to which flexibility can come into play in putting more student control on the “productive question.”

I’m not sure IF there is a way to resolve this with your valid critique of needing more than “hope,” but that’s one thing spinning around my mind after reading your and Geoff’s posts. I think he’s also circling around this idea in his reply to this post.

Ah, now I see and understand the criticism a bit better. Perhaps ineloquent, perhaps semantic, the phrase “right question” understandably rubs folks here the wrong way.

That said, in my practice I am looking for a student question that relates to the intended content on which I can pounce, to ask more probing questions and dig deeper. To me that’s the whole point of sense-making. While (of course) honoring and exploring unanticipated questions.

I appreciate Brett taking a charitable reading of the commentary. And Dan for challenging me on imprecise language.

Also, don’t lump all PBL advocates in the same boat. Many are much more eloquent and precise than me.

PBL takes time to perfect if it ever can be perfected.

We can’t neglect the idea of lesson study, action research, and growth mindset to help us shape the “right” problem and equip us to answer the questions (right/appropriate or not appropriate) students will generate.

This doesn’t negate the value I see with the format but it does provide some comfort when I go around and try to facilitate students who are stuck.

In his original post, I think Geoff is pushing on the idea that we want to have kids explore math, but that we want them to explore a particular topic on any given day, so we need to design our tasks to guide our discussions to that topic.

Dan read that as the stronger claim that we are trying to manipulate kids into asking a very particular question so that they can discover just the right answer. This feels like massive coercion. What’s worse, it is disguised as free exploration (disguised, because we were funneling them to this question all along). While I think that reading is stronger than Geoff intended (given his follow up responses), it also seems an understandable reading of the excerpted paragraph, which reads as more than a little Machiavellian to my eyes.

And here is where Pershan’s Maxim may come into play: The more specific you get, the less disagreement there is. My lessons are significantly more structured than 3 Act Tasks. I am very explicit about what I want them to explore. I simply emphasize that we are _exploring_ that area, not marching forward to the Truth. I am not a fan of unstructured Discovery learning. (Nor is Dan, who opined on twitter about being lumped in with them in the infamous 2006 Cognitive Load article from Kirschner, Sweller and Clark.) I want kids to focus their explorations on a given topic in a given area. Ideally, they will _eventually_ make some practical discoveries related to a given standard.

My description that Dan quoted above has more to do with how I view the process of learning and concept acquisition- lots of exploration, rarely linear, and activating/modifying existing schema during exploration of a topic, _even when performance is not actively improving_- than it is to do with much of anything else. Thing is, I don’t think Geoff is that far off from where I am (if there is a difference at all). I just think he stated his case with an unfortunate word choice that suggested strong external control of student thought patterns, something which I am pretty sure Dan finds reflexively objectionable.