#DebateMath in 3rd Grade

Last month I spontaneously took part in a Twitter chat about Chris Luzniak’s book, Up for Debate! – about using techniques from debate to encourage engagement in mathematics. The book says it’s for grades 6-12, however, as a 3rd grade teacher I was curious anyway and wanted to learn more.

I won the book through the chat & look forward to diving into it deeper (what I’ve read so far has been great!) – but I was inspired by what I learned and wanted to try a little bit with my students right away.

Warming Up

The next day, the students’ morning task was to write a CLAIM (their position) and a WARRANT (a justification for that position) to the question “What’s the best pizza topping?” The goal was to get students familiar with the claim/warrant terminology and push them to think of justifications others might find compelling (rather than “I like it”, “It tastes good”, etc.). I also hoped to familiarize students with justifying their answer to a subjective question, which we would be exploring more of later.

Some especially creative answers:

  • Artichokes because they add a nice salty flavor
  • Ice cream on a “polar pizza” because it goes nicely with the oreos

I wanted to give students a chance to practice thinking of claims and warrants to solve the type of math question we’d been working on, while also switching up the prompts from “best” to “coolest” (Chris has a lot of variations in the book, but I particularly liked the idea of starting with these).

How do you think students might have answered these questions? One student said the best way to solve #1 was 36 + 36. Another said the coolest way to solve #2 was to cut the rectangle in half to make two squares. They were still working on coming up with justifications.

Ideas like “best” and “coolest” are subjective, so there’s a lot of room for disagreement – but students still have to work to convincingly justify a subjective claim. I also wanted to get them thinking about if the “best” way to do something might be different from the “coolest”.

DEBATING COUNTING COLLECTIONS

All of this was a warm-up to extending #DebateMath to Counting Collections. It was a routine to count on Wednesdays, and this week I asked students (in partners) to come up with either the best way to count their chosen collection, or the coolest. I wanted to keep the vocabulary the same from the morning but bring it into a new (but familiar) context.

Once students chose their collection, decided how they’d count & began counting, we paused partway to make sure everyone wrote down their claim and warrant so we could use this language when we came back together as a class.

In thinking about how to best share our claims and warrants (and then discuss them), I decided to have students come to the rug & sit down, with one pair at a time sharing their claim/warrant – those who disagreed would stand & push back on the idea/justification presented while those who agreed remained seated. (Side note: doing this again, I’d re-think this a bit. It’s important to have those who ‘agree’ be part of the conversation as much as those who disagree.)

One pair said the best way to count their collection was to split it into groups of 100, because there were less groups to count, and counting by 100s is easy. Others disagreed and said it takes too long to count to 100, so making groups of 10 would be better, because that’s also an easy number to count by. Some disagreed – you have to count more groups of 10 so it’s just as difficult. Some thought maybe groups of 50 would be a good compromise.

In particular, one pair of students decided the coolest way they could count their popsicle sticks was to use rulers to measure the length of a stick. They determined 2 popsicle sticks = 9 inches. For every 2 sticks, they added 9, then divided the total by 9, and finally doubled the total. They argued this was the coolest way because it got measurement involved and that’s unique!

Some ideas to push their thinking further…

  • A lot of the justifications for why one way was “best” seemed to be that it was “easiest”. Are the “best” and “easiest” ways to solve a math problem always the same?
  • Could we write an equation or equations to represent the way the popsicle stick group counted? What do we notice about it?

DEBATING VISUAL PATTERNS

The following week, we did this as our morning warm up (we got in the habit of independent think time, small group talk, then whole class discussion for a variety of math warm-up tasks each day – including a few different visual patterns.)

To be completely honest…we never got around to a whole group discussion about our claims and warrants (we did this over a couple days right before winter break and only got through #1 as a group). Some students did individually come up with ideas and justifications for the “easiest” way to find the area in Step 43, but unfortunately the whole class wasn’t quite ready for this discussion).

So…what do you think the easiest way is to find the area of Step 43? What do you think students might say?

What I love about #DebateMath

As stated above, concepts like “coolest”, “best” and “easiest” (and others mentioned in the book/on the Twitter chat) are fairly subjective, which means using this kind of language can elicit a range of strategies from students, and also push them to keep looking for more (could another way be even easier?) The language scaffold of “My CLAIM is _________” and “My WARRANT is _________” is immensely helpful for students to clearly express their thinking in a structured way that 1) helps the teacher understand their thinking and 2) orients other students to their thinking and helps them respond to a classmate’s argument.

I also appreciate the way this routine really de-centers the teacher and leads to authentic engagement amongst students. When leading our #DebateMath discussion post-Counting Collections, I was sitting back and observing as students shared their argument and called on others to respond, interjecting only to pause occasionally to slow down and dissect an argument or response more.

Given the proper tools & scaffolds, students can essentially lead this discussion with little to no input from the teacher. The teacher may be strategic in who they call on, or the specific task students will be debating and the question around it, but otherwise, it’s really the students who are engaged in debate with each other.

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