Managing Vocabulary and Conventions In A Thinking Classroom

What a moment I had in class this week.  We were doing a bit of recall practice ahead of the day's thinking task, and I had posed this question:

Why would the following question be considered a "spicy" ratio question - If thearcade basketball guy makes 15 shots every 6 seconds, how many shots can we expect him to make in 10 seconds?

Quite a few hands went up, and I got the following response from the student who answered: "Since 10 isn't a multiple of 6, we would need to go to a lower term ratio or to the unit rate instead of just skipping straight to the answer."

And the whole room nodded in agreement without hesitating.

I would consider that student's response to be not only accurate, but worded using exact academic vocabulary (multiple, lower term ratio, unit rate) with extreme fluency.  I would also consider a room full of students decoding that response and agreeing with it in a matter of seconds - months separated from last having worked on that concept - to be a minor miracle.

Building a Thinking Classroom in Mathematics has really delivered on its promises this year.  The increases I've seen in student engagement, perseverance, long-term memory, cooperation, leadership, general comfort and happiness, and even standardized test scores have far exceeded what I expected in my first half-year of implementation.

I will admit, that when I made the decision to Build A Thinking Classroom this year, I expected those increases to come with some trade-offs.  The biggest one, I suspected, would be that the huge leaps forward in thinking and comprehension would come at the expense of vocabulary and conventions.  After all, if I was expecting students to learn largely through figuring out content through hints, extensions, and collaboration, surely they wouldn't end up figuring out precise mathematical vocabulary and conventions along the way.
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And, of course, they don't.

But it has actually turned out to be incredibly easy to get students to learn, master, and retain them.
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We're currently working on the kids' first introduction to algebra, which requires a pretty heavy emphasis on conventions.

Prior to Building A Thinking Classroom, I was a big proponent of explicit front-loading of vocabulary and conventions in my lessons.  In direct instruction situations, I still believe that's the way to go.  "Here are the vocabulary words and conventions you're likely to see in the upcoming lesson, and here's what they mean or how they work."  Sometimes those vocabulary and conventions were new ones, and sometimes they were old ones that I wanted to bring back to mind.  But either way, students do best when those are presented ahead of time.

Obviously, in a Thinking Classroom, these can't be front-loaded.  If, as Liljedahl so eloquently explains, "thinking is what you do when you don't know what to do," then any front-loading prior to a thinking task reduces thinking, which we don't want.  The kids have to make their own sense of everything - including vocabulary - in the thinking tasks for maximum effectiveness.

Oh, how easy it is to teach vocabulary and conventions after thinking task, however.

Here's an example.  To introduce my students to the concept of percent ratios they worked on this thin-sliced thinking task using ratio problem-solving skills they had already developed prior.

You'll notice that the word "percent" appears nowhere in this thinking task.  The kids worked with the concept of a percentage, but not the word itself.  As you might imagine, already having good mastery of ratio problems, this thinking task hardly required thinking at all.  It was simply a bunch of ratio questions where, curiously, the "whole" in the ratio was always 100.

When we got to consolidation, all I had to do was name what they'd already figured out.  

"Today, you worked with a bunch of ratios where the whole was always 100.  In math, we have a name for ratios where the whole is 100.  They're called (vocabulary) percent ratios or percentages.  We represent them (convention) with a symbol that looks like this - %.  Let's jot that on your notes page so we remember it later."

The message - "you already figured out what this is.  Here's what math people call it, and here's how math people write it."

Our note-making page now has a section for vocabulary or conventions that need naming after the day's thinking task.  It takes 1-3 minutes of the consolidation process.

Having Built a Thinking Classroom, I spend that 1-3 minutes on vocabulary and conventions in consolidation rather than front-loading it.  Just like before, sometimes they're new vocabulary and conventions that I want to introduce, and sometimes they're older ones that I want to reinforce.  It's the same practice, just at a different point in the lesson.

I also teach science most years, and I've written about the exact same process of teaching vocabulary in the Explore Before Explain instructional model that is so effective in science.

Building A Thinking Classroom is the gift that keeps on giving.  There were a lot of benefits I was expecting, but improved student command over vocabulary and conventions was not one of them.

​It just keeps getting better.

To have a little fun with the new conventions that come with algebra, we held a funeral for the "x" symbol used for multiplication.

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