It’s always surprising what kids say and do when properly provoked.

In fact, I’ve taken a new stance on teaching and learning, and I’ve begun to value — above all else — the power of the provocation.  Why?  Because learning shouldn’t be prescriptive; instead, it should be provoked.  Sure, the nature of our world requires that certain skills be prescribed to our students, but even those skills, with some artistry and creativity, can at least be linked to a provocation.

photo 1
Provocation 1: The Commutative Property

So I chose yesterday to continue our math instruction through class-wide provocations.  Yesterday’s provocations were meant to help students to not only see patterns in the number system, but to also help students learn more about additive and multiplicative properties, specifically the commutative, associative, and distributive properties.

It’s funny to think about, because when I was a kid, I didn’t learn about these properties until I was in middle school, and even then I didn’t realize their foundational value to all of mathematics.  Now, as a teacher fifteen years later, it makes me wonder why little kids weren’t taught this stuff back then.  Regardless, I’ve been teaching about these properties for several years now, and each time I find a way to improve upon the process.  The first time I did it, when I was a student teacher, I simply modeled the process with counters, rearranging them to show that the two sides of the equation were, in fact, equal.  While I may have shown my “expert” knowledge of the properties, in retrospect, it probably didn’t teach them very much since it was mostly me doing the talking.

photo 2
Provocation 2: The Associative Property

But this time, I think I have a better shot of making it stick.

I posted provocations around the room, similar to the counters method I used quite some time ago, and I asked the children to wander about the room, writing down observations, questions, and inferences, very similar to the See-Think-Wonder thinking protocol I taught them a few months ago, just without structure and direction this time.  Instead, I let them choose the provocations they found interesting.  They moved about the room, casually writing thoughts and questions.

photo 3
Provocation 3: The Distributive Property

And once again, I was pleasantly surprised by my students’ seemingly innate abilities to observe and think independently.  While it could be argued that they’ve simply built upon the thinking protocols and strategies my co-teacher and I have already established, I might also argue that this is a matter of vulnerability: it’s a matter of them no longer needing a structure through which they could observe and question because, I believe, they feel much more comfortable being wrong than before.

In fact, by giving them time to muddle in the mess of a new provocation, and by allowing them the freedom to document their own thinking in the manner in which they saw fit, I saw lots of things that I wouldn’t have even thought to assess.  Some of the students actually didn’t internalize the equal sign in the middle of all of the provocations, and it wasn’t until we debriefed that some students noticed that both quantities were equal.  Some students, too, readily applied multiplicative properties, while others simple looked at shapes within the colored dots — a striking distinction between a more advanced number sense and a less developed one.

photo 4
The Product of Provocation


Regardless of the outcome, standing back and provoking learning has become an invaluable practice in my classroom.  Instead of totally prescribing what students should know and be able to do, I’ve given them a strong part in the process by letting them implicitly tell me what they know through provocations.  These provocations, in and of themselves, spark and interest, ignite a curiosity, and in the end, tap the knowledge that was already there    beneath the surface, waiting to be awakened.


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