Encouraging Student Listening

Talking Points

(If you haven’t heard of the Talking Points activity yet, Cheesemonkey gives a great breakdown here.)

I’ve used Talking Points at the beginning of the year before to uncover student learning mindsets and to hear a little about their predispositions for math. Here are the Talking Points I used:

  1. When working together on math, if one person knows what to do, they should let other group members try first.
  2. Being good at math means being able to do math problems quickly.
  3. Getting a problem wrong means you’ve failed.
  4. A person is either good at math or bad at math.
  5. Drawing a picture is always helpful when doing math.
  6. Math is easier to learn when it involves the real world.
  7. There is always one best way to do math.

While these conversations were good to hear, I thought they did little to build on students’ current thinking. They felt a lot more like me, throwing statements (that I felt had obvious answers) out to my students, and waiting for them to come to what I felt were the correct conclusions. I think my students must also have felt there were correct answers and were just saying what I wanted to hear. In short, it felt artificial.

While combing MTBoS this week, I uncovered that Brian Miller uses the Talking Points protocol differently. He uses them to develop a classroom culture of listening. His Talking Points are:

  1. It’s impossible for other people to tell if you are listening.*
  2. Talking is more important than listening.
  3. Group activity can be good for learning.
  4. Listening and thinking are different things.
  5. Learning to listen and collaborate well with other people is important.
  6. If you think someone is wrong about something, it is more important to tell them right away than to listen to their reasoning.
  7. Everyone can learn to be part of a learning conversation.

*This one is his favorite. Mine too!

But I think one of the reasons Miller’s Talking Points activity seems less artificial is in his whole class reflection after the activity. He asks his classes,

Do you feel like you were being listened to? Why?


Were you listening to others? Do you think they knew you were listening?

In his words, “the conclusion at the end is that just listening is not enough.” These reflection questions urge his students to convert the thoughts on listening they just discussed and turn them into actions that will enhance their classroom community. Reviewing the Talking Points that I’ve used, I wonder what reflection questions I can ask about them to achieve a similar outcome!

Students Summarizing Students

From Research in Practice,

This summer, when I or a student put forth an idea, I regularly followed it with, “who can summarize what so-and-so said?” Or (even better), “so-and-so, can you summarize what so-and-so just said?” Following the models of Lucy West and Deborah Ball, I carefully distinguished summary from evaluation. “Not whether you buy it, just the idea itself.” When dipsticking the room on an idea, I would also make this distinction. “Raise your hand if you feel that you understand what was just said; not that you buy it, just that you understand what they’re trying to say.” Then, “leave your hand up if you also buy it.”

Two weeks ago, I wrote about using language that supports students seeing the class as a learning community. One way to do that is to frame classroom discussions as ways to build consensus. Moreover, looking at discussions this way encourages students to construct viable arguments and critique the reasoning of others.

I love this idea of asking students to summarize one another and am looking forward to implementing it more in my classroom this year. I’ve lived with a secret fear that students who are paying attention to the class discussion will find the summaries repetitive. (I find it hard to distinguish between my preferences as a learner and best practices for students when I’m the teacher.) Happily, Kelly O’Shea reminded me of the importance of not falling into The Right Thing, Said Once trap.


Centering Learning Around Mistakes

Some of the hardest students to reach in my classroom are those who have already written themselves off as a “failures.” I think it is the particular and central challenge of math teachers to help students overcome years of being told they’re “just not good at math” and, along with that, that it is okay to not be good at math.

I find that in my classroom, students who use this kind of “fixed mindset” thinking are the quickest to give up when they realize they’ve done something wrong. Learning from “failure” is a valuable life skill that everyone is quick to preach, but we all know it’s a hard one to practice. It is so disheartening to watch a student feel crushed after a lot of hard work to discover that they arrived at the incorrect answer. It is even more disheartening when you show them the tinytinytiny mistake they made and try to encourage them and point out that it isn’t a big deal…only to find that the student thinks that mistake they made means all their work was for not.

Happily for me, I am not the only teacher working to show students they can be good at math. Here are some of the ways I’ve seen teachers help students learn to learn from their mistakes.


Posters like the one to the left remind students that making mistakes are an integral part of the learning process. I’ve heard this poster mentioned at PCMI this year twice already!

The video from the Teaching Channel on “My Favorite No” has received a lot of attention as a way to help all students develop the routine of learning from their mistakes and valuing mistakes as learning opportunities. I’ve added this routine to my classroom this past year and found it not only gave me a valuable way to applaud vulnerability in class, but also a space in the class to publicly honor smaller mathematical practices. By that I mean things like solving equations linearly going down or fully showing evaluation work. While I look at a lot of student work, before I implemented this routine, students in my class did not. When students made mistakes, they thought they were the only ones making them. I’d be willing to bet that when I asked students to show all of their work, at least some of them were unsure what I was looking for. My Favorite No Mistake gives me a way to begin those discussions with students.

Sarah Carter (of Math = Love fame) and a number of other members of MTBoS attempted in this post to classify the types of mistakes/errors that students make. (I learned while reading this post that there is in fact a difference between the two…) The original classification of was:

  • Careless mistakes
  • Arithmetic mistakes
  • Process mistakes

But upon collaboration other teachers, a second method of classification was invented:

  • Careless errors
  • Computation errors
  • Precision errors
  • Problem solving errors

Although the classification method that works best for your classroom may depend on the age of your students, I think these classifications provide students with a valuable framework with which to think about mistakes. I frequently tell my students that not all mistakes are created equal, but have had a difficult time elaborating on this idea. Next year, I hope to have a poster of my own mistakes classification. To build on the My Favorite Mistake routine, when student work is presented, I will ask students to identify the mistake, classify the mistake, and then revise it.

Barriers to Mathematical Discussion

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:

  1. I’m doing too much of the talking.
  2. Student’s contributions are difficult to hear or comprehend.
  3. 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!