Friday, April 18, 2014

Get Students to Argue in Math Class

I recently submitted my speaker proposals for both 2014 CMC conferences. One of my proposals is for the following session:
Title: "Get Students Arguing in Math Class with Number Sense Activities."
Description: Get students to productively argue about math situations. Participate in number sense activities requiring students to construct viable arguments, critique the reasoning of others, and use sense-making. Get ready to throw down.

I also had to answer a few questions justifying the session and connecting it to the CCSS and 8 Mathematical Practices. I provided the following connection:
The presenter will use number sense activities to get participants to construct viable arguments and share their reasoning like students. Using presenter-made tasks (Estimation 180) and other online resources appropriate for grades 3-8, attendees will be able to see the importance of student reasoning and creating productive discourse in the classroom. Teachers will also be provided with sentence frames and stems for all students, especially English language learners.

I'm really excited at the thought of this session getting accepted so I figured I would jot down a few ideas here and see what you all have to contribute. Even if I'm not accepted, I think every math class has to have students productively arguing at times. Doing estimation challenges with my students has been so beneficial for them to get better at the art of arguing. However, I know it could be better. I'm not sure if you've ever experienced it before, but it's a treat to stand off to the side or in back of a group of students arguing about a question in math. They have no idea you're nearby because they are so caught up in the argument. Don't get me wrong, it's not like they're swearing at each other and calling each other names. They are having a rich discussion, sharing conjectures, examples, counterexamples, etc. and I have the pleasure of spectating. I usually turn to an innocent bystander (nearby student) and whisper, "Awesome, look at them arguing. Isn't it great?" The student usually looks shocked that I'm happy their classmates are arguing. I love it!

I'd like this session to place a big emphasis on two mathematical practices:
MP 3: Construct viable arguments and critique the reasoning of others.
MP 1: Make sense of problems and persevere in solving them.

I plan to break these two practices down more in my session. For now, I feel I need to focus on three major parts to arguments: having excellent content, capturing the arguments, and indirect facilitation.

Content: There's a wealth of content available, but I think the more controversial the point of contention, the better. One of my favorite moments in math class was when we did Mathalicious' Datelines lesson. Students were arguing about which celebrity shouldn't date another celebrity because of the age discrepancy. Some students disagreed about the rule of (n/2) + 7, especially since I was teaching 14 year-olds at the time. It was awesome.
Here's my current list of resources that have given my students great things to argue about:
My kids went nuts arguing about a similar question to this "Would You Rather" found here.

These don't have to be full-on lessons. They can be warm-ups, math talks, used during classroom transitions or to break up your direct instruction, etc. I'm really looking forward to using @MathCurmudgeon's site
Imagine your students arguing about which student should pack your parachute based on this data.
Another up and coming resource is Open Middle by Robert Kaplinsky and Nanette Johnson.

What resources would you add to my content list?

Capture: I need to capture these arguments for a few reasons. Students need to listen to other students argue, especially from different classes. My memory is very porous, and I can't remember what students say verbatim. Students can listen to the recordings and pick a side, or provide their own agreement or dissent. I'd also love to share student arguments with other teachers, especially at this session. How do I capture this?

I just downloaded Voice Memos for iPad onto my school iPad. I will test it out next week with students. Wish me luck. Here are the features I'm optimistic about:
  • It will record in the background while another app is running.
  • It was $1.
  • I can pause the recording.
  • I can trim audio clips.
  • I can sync with Dropbox.
Have any tips for capturing student arguments?

Facilitation: Here's where I need to do a better job. For many of my students, English can get in the way of them articulating their point. I'd like for students to listen better to each other and respond accordingly. I want to hear what they have to say. I want them to be a contender in their disagreement, but I don't want them to be held back because of language deficiencies. Therefore, I need to provide them with sentence starters and stems. Fortunately, these can be used with any student. Here's a few:
  • My opinion about this is _____________.
  • I could argue that _____________.
  • I disagree with your statement that _____________ because _____________.
Have any stems or sentence frames you're already using with students to help them articulate their thoughts?



  1. Another idea is to capture on video the argument as a socratic circle. Inner circle disusses (argues), outer circle observes and notes behaviors or math practices you want to monitor.

    I've done this and have had the opportunity to present Socratic Circles with a focus on literature. Perhaps I can "pass the baton" and you can include it from a math perspective.

    If you do this format I suggest a few "practice" sessions before recording one. The video then lends itself as an exemplar--future students know your expectations--and you have a great example for your adult audience.

    Another tip: to free you up as a facilitator, have a colleague record the video and place a wireless mic in the center of the inner circle to pick up the audio. I planted the mic in a basket. When it came time for the outer circle to comment, the students passed the basket so we could hear the students.

    I also obtained parent permission to record.

    Good luck!

    1. Thanks Mary. I appreciate the tips and will check out Socratic Circles.

  2. *Have any stems or sentence frames you're already using with students to help them articulate their thoughts?*

    I try to stay away from negative feel statements since I want my classroom to be a place to share ideas without pressure of being wrong.

    I really like what ____ said about _____, it made me think about ________
    I agree with ______ because __________
    My idea of ________ builds on ________ idea
    I like what _____ did, but I looked at this this way _________

    1. Hi Bryan. Thanks for the suggestions.

  3. I feel like something critical here is the last part about capturing the student argument as students often have a challenging time transitioning from oral explanations to written explanations. Here are some ideas off the top of my head:
    - In pairs students have to copy down their partner's reasoning so that they can explain it to someone else.
    - Students have to write down their argument (perhaps in bullet points?) and can only talk about something they have already written down?
    - Maybe some sort of graphic organizer that has multiple sections like: "I believe that...", "I know this because...", "The evidence I have to support this is...", "Someone might incorrectly disagree with me because they think..."

    1. Good ideas Robert. Getting students to organize their arguments is a great idea and I'd work to utilize that process when students are given the chance. I'm curious what graphic organizer you'd come up with and we can compare notes.

  4. Cool idea for a sesh! You might want to maybe talk to the author of he just led a series of PD around debate in the math classroom, he has some great videos of his classroom on PBS showing math debate, and he's one of my best friends (so you know he's super awesome/nice). His twitter is @pispeak and I can send you his email if that doesn't work (he sometimes does MTBoS stuff and sometimes not... but he IS coming to TMC14!!!)