Conducting mathematical discussions in my classroom can sometimes feel like pulling teeth. Sometimes it’s me who feels uncomfortable. Sometimes it’s my students. It seems there are a number of factors keep us from being able to optimally benefit from the exercise. The major few, though, seem to be:
- I’m doing too much of the talking.
- Student’s contributions are difficult to hear or comprehend.
- Crickets and more crickets.
Before I launch into different ways to address these issues though, I should probably share what I *want* class discussions to look like:
- ALL students participate. Not all students need to speak whole class, but everyone should be sharing their ideas in some form, written or out loud in smaller groups. Students who are not speaking should be listening, thinking, or taking notes.
- Students listen to and build on each other’s ideas. Students pose their own questions as they arise.
- Everything said leads to further understanding for someone. No fluff. No talking for the sake of talking.
- Teacher is a participant in the discussion of students’ ideas, not the leader.
Barrier #1: I’m doing too much of the talking.
Oftentimes, in my class, I’ll pose a discussion question, a student will boldly kick off the conversation, and then the room is quiet again and all eyes are move back on me. I feel the need to pose a second question to keep the “discussion” going, and the process repeats. A map of our classroom conversation would look like a game of ping pong rather than a game of volleyball. I’m aiming for volleyball.
Something to try #1.1: Ask questions with many possible answers.
The easiest and quickest way my class and I fall into the ping pong conversation trap is when I ask questions with obvious, right answers. Asking students to share their “noticings” and “wonderings” in class can be a great way to stimulate class conversation. Max Ray has a post of additional questions that teachers can ask to get students talking. My favorites are:
- What’s making this hard?
- What is the first thing that popped into your head when you saw this? What is the fourth?
- What do you think a mathematician might notice about this?
- What is an answer that is definitely wrong for this problem? How do you know?
- How would you explain this to a _____?
- If your math fairy godmother appeared right now and offered you a helpful hint, what would you ask her for?
Something to try #1.2: Give discussion questions ahead of time.
I’ve read, and I’m sure you’ve read, in countless blogs and education articles that giving students time to think before asking them to share their thoughts helps improve both the quality and quantity of student responses. I would also posit that, if students are given discussion questions ahead of time, the discussion can be re-organized and lead by students easier. The structure* goes like this: Halfway through an activity, I’ll give students a list of 5 potential end of class discussion questions. At the close of the activity, I’ll remind groups to discussion the questions together, choosing whichever they find most interesting to answer first, then continuing on to the rest if they have time. Again, the emphasis is on quality of their discussion, not the quantity of “answers” they can come up with. Then, as a class, I’ll randomly select a group to kick off our discussion. The responsibility of the chosen group will be to identify for the class the question they found most interesting, eliciting a response from at least one other group on the same question, and then the facilitating group will share their own thoughts. Once the question is answered, the facilitating responsibilities will shift to a new group and the process will repeat.
Asking the facilitating group to withhold their thoughts until the end will force them to listen to the responses of their classmates so as not to look silly repeating. It will also give them time to reformulate their share-out based on the thoughts of their peers. I like this format for facilitating a class discussion because it hands the reigns of the class discussion to students in a manageable and structured way.
*Disclaimer: I haven’t tried this! But I’m looking forward to trying in the fall. If you’ve attempted something similar, I’d love to hear your thoughts.
Barrier #2: Student’s contributions are difficult to hear or comprehend.
In math conversations, my students have a tendency to overuse pronouns. “It’s 30.” What’s 30? “It crosses at 5.” What is crossing? What is the thing “it” is crossing? Which 5?
Something to try #2.1: No “it” Sherlock.
I think what my students struggle to understand is, when someone can see your paper or knows exactly what you’re pointing at, context-specific language using lots of “its” can be fine. In whole class discussions, however, when we’re talking about more than one question and all looking at different papers, pronouns make sentences very difficult to follow. When I push students to be more specific, students stumble or don’t see what the problem is. They sometimes think I’m telling them in different words that what they said is wrong.
This is where “No ‘it’, Sherlock” comes into play. (Thank you to the great, Benjamin Walker for introducing me to this.) It’s a quick, fun response that can be said when students use “it” in a sentence when there’s a piece of math vocabulary or some other more specific word they could be using. When used often enough outside of whole class contexts, this saying just becomes a prompt for students to pause, think clearly about that they’re saying, and then rephrase what they just said more specifically. Hooray for attending to precision and making explanations more comprehendible!
Something to try #2.2: Use a mini-lesson to motivate the need for context-independent math explanations.
Because we use pronouns so often in everyday speech, it can be hard for us to recognize when we’re using them. #2.1 helps us help our students address that. Another barrier students may struggle with is why context-independent explanations are needed. In my classroom, it is very important to me that I explain at least some of the “whys” behind my decisions. Is Miss Lam saying “No ‘it’, Sherlock” constantly just to be annoying? No! So, here’s how I go about motivating the need for context-independent explanations, as inspired by Lisa Delpit’s Other People’s Children.
Think of a simple, non-math task that all students can do. Build a sandwich. Fry an egg. (Most of my thoughts outside of teaching are dedicated to food.) Walk from a certain community landmark to school. Ask students to write down directions for how to complete this task. Part of the fun is picking a task that can be accomplished in different ways and letting students see the variances…but the real fun is when I, the teacher, act out the tasks exactly as students wrote them. Exploit the ambiguities and hilarity ensues. For tasks that can’t be done right in front of students, I’ll do them at home and take pictures of myself while going through the steps so that I can put together a PowerPoint the next day.
The first time I do this in class, I’m usually the actor going through the task. If it seems later in the year that students need a refresher, I can ask them to recall our first run through and allow them to be the actors.
Something to try #2.3: A hand signal to ask students to speak up.
This Try is self explanatory. I’ve seen many teachers circumvent that annoying “May I use the bathroom?” question by giving it a hand gesture. Do the same for asking students to speak up! This can be a signal that you direct to students, but more powerfully, it can be used by students to other students.
Barrier #3: Crickets and more crickets.
When students are silent in my classroom, it’s usually because they’re feeling unsure about their ideas and are too nervous to admit it. I admit to being bad with wait time, so it may be that they haven’t had enough time to digest the question being posed. Here are some ways I’ve found to silence the crickets and encourage my students to speak. (Most of these ideas are drawn from this lovely article from the University of Maryland Teaching & Learning Transformation Center.)
Something to try #3.1: Allow students a “pass.”
I remember when I was in high school, the minute my teachers started cold calling, my palms began to sweat. Looking “dumb” in math class is a scary thing, but when students are thinking about if others are questioning their intellectual abilities, they’re not thinking about math. We want our students to be thinking about math.
Something to try to help alleviate some of this anxiety in students is to allow students a “pass.” In other words, I set the expectation that I will be cold calling, but I also explain that if I ask students a question they genuinely have no idea about, they can say “pass,” knowing that I will return to them later in class. This “pass” moves the spotlight off deer-in-headlights students quickly and also helps reinforce the expectation that student’s don’t need to know 100% of the answers 100% of the time. When a student passes, it is important to return to them later in class so that they know passing on a question is not just an easy out. The follow up can happen whole class or individually, with the same question or a different one. The important thing is that it happens.
Something to try #3.2: Use phrasing that implies students are a learning community and invites students to the conversation.
Here are some example questions:
- We’re about to move into work time. Who can repeat the directions for anyone who may have missed them?
- What do you rest of you think about that?
- Are we in agreement?
- Do we have any differences of opinion?
- Is there anything that is unclear or needs further clarification?
- Can someone summarize our discussion in a way that a classmate who missed our discussion today could understand?
- Based on our discussion, what have we learned today?
Another great silencer of students is this idea that questions are posed in class because they need an answer and the only meaningful contribution to the discussion is the one that gives the “right” answer. Something I’d like to work on moving forward is stretching what students see as meaningful contributions to discussions. Contributions they frequently overlook are restatements of what has already be discussed, mistakes that were made and what can be learned from them, requests for further explanations, and disagreements with what appears to be the current consensus.
The questions above help to instill value in contributions like this by explicitly requesting that they appear in the class conversation. The ultimate idea is, when students realize their is more than one way to participate, they will be more willing to participate!