Practice Puzzles: Math Practice Three

Math Practice One and an explanation of the puzzles
Math Practice Two

There is nothing more charming (and alarming) to me than to listen to a child try to explain themselves mathematically. I truly do love every second of it...I never tire of it, and it never gets old. Having said that, I'm not the only teacher who has to reconcile the balance between pushing past, and lingering in, the nonsense. In all of these Math Practice Puzzles that I am sharing, there is way more to the practice than I have given rise to here in these captured moments. The point was to find ONE thing we could use as an entrance to the practice...I wasn't looking to frontload it in its entirety, I just wanted one shared, contextualized experience to draw out the practice. The rest has unfolded as it has, with some practices more easily expanded on than others. Which feels exactly as it should for working with the Littles. They have Kindergarten until Senior Year to sort it all out. I'm just doing my small part.

So, Practice Three....there are so many deep and important truths in this practice, but the one that we have cleaved to early on is the idea of revision. This practice is tightly wound with other practices, and as we see more patterns, learn more structures, take command of more precise language, and test more solutions and strategies, our communication and explanations will continue to evolve. But these are lofty aspirations indeed, if you consider how we start on this path. There is no primary teacher on the planet who hasn't heard such carefully crafted nuggets as: "I know it's five because that is my favorite number." Or, "I know because I knew it in my head" (which is MOST exciting when it comes with a wrong answer...."8 + 3 =12, because I knew it in my head"). Other oldies but goodies include "I counted on my fingers" and "I guessed".

Early on, I introduced the notion that the onus is on the explainer....if somebody doesn't understand you, it's your job to keep revising your explanation until they do. It's not because they aren't listening to you (they aren't though) and it's not because they aren't smart (they really are) it's because the explanation wasn't sufficient. The correlating piece to this is it doesn't have to be perfect to get started. Focusing on revision means that all you have to do is start. Just say SOMETHING. Then you'll get some feedback, and you can add on/change/delete to make it more clear. Get more feedback. Make more changes. And so on. You don't have to wait until you know exactly what to say or how to perfectly explain something. Just say anything.

From the classroom: Afoa had JUST told us that the two numbers we were going to use to solve our problem were written on the poster, 37 and 43. I turned to Natalia and asked, "So...which numbers do we use?" And she says, I swear, "I don't know." I want to cry haha but instead I tell Afoa, "Well, I'm afraid that explanation wasn't enough for her to understand" and bless his pea-picking-heart he immediately updates it to, "It's the purple numbers on the bottom, 37 and 43." I made SUCH a big deal about this to the whole class! "HOLD UP!! Did everyone SEE what Afoa JUST did???" and then I explained that what he had done was soooooo mathematical because he didn't tell Natalia that she wasn't listening, he didn't tell her oh well you just don't get it, he CHANGED what he said to make it a BETTER explanation." Then Afoa talked about what he had said before and how he changed it. Natalia confirmed that NOW she understands what to do.

Look. It was only marginally mathematical and even calling it an "explanation" is a stretch (it was more like a clarification) but it was all we needed. We have talked about this idea over and over and, in conjunction with a few other key moves, my second graders have made enormous leaps in their ability to explain and question each other. I'm taking it!