Monday, July 6, 2015

Growing Community, Critical Thinking, and Mental Muscle with Math Talks

One of my favorite routines in my classroom is Math Talks. For about 10 minutes each day, my kids discuss, debate, and confer, respectfully and focused on the topic at hand. They run them almost entirely on their own and when I listen to them, I feel like I might be doing a pretty good job, after all. 

What are math talks?
 In my classroom, a student, chosen randomly, places his or her solution to a complex word problem on the camera and, in steps, explains the process for solving it. Then, other students discuss the solution, adding their thinking, following some basic sentence starters that keep the conversation objective and on-task. 

How do you train your students?
At the beginning of the year, I lead as little as possible, but more than I will for long. We begin with an anchor chart:

 and I'll begin by modeling a talk. Something like this:
Jake has 163 Pokemon cards. Seth has 46 fewer cards than Jake, and Isiah has 84 more cards than Seth. How many more cards does Isiah have than Jake?

The presentation would sound something like this:
I found the numbers 163, which represents how many cards Jake has, 46, which represents how many fewer cards Seth has than Jake, and 84, which represents how many more cards Isiah has than Seth. My job is to find the difference between Isiah's cards and Jake's.

The word fewer tells me that there's a difference between how many cards Jake has and how many Seth has. Seth has 46 less than Jake. I'll subtract 46 from 163.

The words 'more' and 'than' tell me that there's another difference, this time between how many cards Seth has and how many cards Isiah has. Once I have Seth's number, I'll add 84 to it to find out how many cards Isiah has.

There's another 'more than' in the last part, which tells me that there's a third difference, but this one's between Isiah and Jake. I know how many Jake has - it's 163 - and once I find out how many Isiah has, I'll find that difference.

So, If Seth has 46 cards fewer than Jake's 163, he has 117, because 163-46 = 117 (and I'll show my arithmetic as I go). If Seth has 117, then Isiah has 201 cards because 117+84=201. Finally, to find how many more Isiah has than Jake, I'll subtract 163 from 201, which gives me 38 cards, my final answer.

Because the problem didn't give us a total for all three boys, it's tough to prove my answer, but I used a bar representation here and did the numbers again to show that my process and calculations are right. 

From here, the students may comment on my work. For the first several weeks, maybe even until the first report card, they are only allowed to begin their comments with "I agree with ________ because..." or "I disagree with ____________ because..." The because is imperative. It forces kids to reason out their responses. Until they're good at talking - and they may respond to each other's comments, but they still have to use the two available sentence starters - this is all they get.

Over time, once the routine and the language are down, I can step away from it. Sometimes, I'll need to step in to get some different voices involved, but that's about all.

How does this build community?
Respectful-but-lively discussion is good for everyone. Presenters are sometimes wrong, and that's where the "I disagree because..." comes into play. Without prompting, most kids are kind in their disagreements. I usually get, "I agree with _______ 's process, but disagree with her calculations because 7x8 is 56, not 54." If, in your classroom community, risk-taking and mistakes are a natural part of learning, then these talks are an extension of that.

How does this build math muscle?
 Every kid knows that he or she might be called up to present on any day, so there's that factor. I also structure my question sheets to make the presenting easier, with each step
in its own space, which encourages all kids to get through them. It's a little less intimidating if it's all laid out. 

I use 'CUBES' as a strategy for approaching story problems. The acronym stands for:
C - Circle the numbers. What does each represent?
U - Underline the actual question. In your own words, what are they asking?
B - Box the action words.
E - Evaluate. How many problems are in the problem? What operation(s) do you need?
S - Slash the trash (get rid of distractions) and Solve. How do you know that your process
      and calculations are correct? Did you get all of the possible combinations?
 Giving them this feels a little 'drill and kill', but it also gives my lower students a life ring when they feel like they're drowning. It also translates well to testing situations. 

The discussion, though, is the important part. Students are always encouraged to have more than one representation, which requires more creative thinking. It's not unusual, at the end of a talk, for a child to say, "I got the same answer, but did it totally differently. Can I share mine?" Whenever we can, the answer is 'Yes.' Seeing multiple ways of approaching a problem gives kids a variety of strategies, and, again, encourages risk-taking, which, in turn, values divergent thinking. Good for problem-solvers.  

Where can you find problems that work for this?
 What you'll have to decide first is if you want to do this whole- or small-group. When my class is largely at the same level, with a few on the fringes I do this whole-group. If, however, the kids are all over the place, we'll go small. If your kids are like mine, they'll be all-about-the-same on some standards and very different on others. It's OK to vary the routine. If you're doing this small-group, you'll have to simplify the steps of some questions and algebra-fy others to increase the challenge. There are a couple of really good resources available for this. I loved Minds on Mathematics and Good Questions: Great Ways to Differentiate Math Instruction

I invent a lot of my questions, but I also model some from quiz questions that kicked their butts. On Amazon, searching 'Challenging Math Problems' will get some hits, largely
based on or around Singapore Math. (Don't let the Singapore thing intimidate you. Most of the questions don't really require the bars.)

Or, you can head over to my TpT store, where I've whipped a few into shape. 4th grade whole number operations is ready. I'll be adding more to the collection as the year progresses:

Clicking the cover will take you there!

Thanks for stopping by. I hope you'll find that adding a Math Talks routine to your math instruction has the same kind of positive effects it had on mine!

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