Talking in Math

Author: Arlene Vinion Dubiel

We need to encourage student discussion in the math classroom. Classroom discussion has a substantial and positive effect on student learning, as explained by John Hattie in his book “Visible Learning.” Common Core Mathematical Practice Standard 3 is to “construct viable arguments and critique the reasoning of others.” Students who achieve this standard listen to others and communicate their ideas. Furthermore, communication is one of the top skills needed to be successful in the workplace. The bottom line is that talking in the mathematics classroom is an essential skill for students. But HOW do we get students to talk math with one another? What steps can we take to support discussion in the mathematics classroom?

Discussions and PBL

In project-based learning (PBL), students must communicate and collaborate to complete their projects. Often, the conclusion of a project-based learning unit involves a presentation or sharing session with the class. There may be a whole-class discussion to reach a consensus and reflect upon the project as a whole. Each of these components within a problem-based learning unit requires communication skillsets for students and teachers.

Student Prompts

Whenever students gather in small groups, they talk with one another. Usually, they talk about music or their weekend plans, but if they are motivated, they will talk about the classroom task at hand. This talk can be superficial or productive. Features of productive talk include students speaking directly to one another in respectful tones and consistently referring to the task. Students will refer specifically to the learning objectives and make connections to other content. As the instructor, it’s essential to listen to students talk without judgment and only prompt further discussion when necessary.

In casual everyday conversation, students don’t usually engage in productive talk. They may need prompts to help further the discussion. This is especially true of students for whom English is not their first language. This half-page talk moves handout by John McCarthy of Opening Paths is one of my favorites. This sheet has beginning prompts to help students begin conversations with one another. The prompts are organized into five categories: agree, disagree, add on, ask a probing question, and ask a clarifying question. These student talk moves should be introduced early in a course and then be a resource available for students to use. The provided prompts can be handy when disagreements arise, keeping the debate focused on the task and not directed towards the person making the argument.

Teacher Prompts

As mentioned previously, you want to listen quietly, allowing students to talk with one another without interruption or judgment. But sometimes, the discussion and progress on the task fall flat, and you may need to intervene. If student talk isn’t task-focused or if students aren’t communicating with one another, you may need to prompt them. For example, you could ask them for a progress report. You may also ask them to explain the learning objectives in their own words or ask a good robust question or two. Letting students know you are present and listening can help them refocus on the project.

To help with question phrasing, Tracy Zager has a printable two-page handout with several prompts that encourage students to use intuition when solving problems. The questions come from her book “Becoming the Math Teacher You Wish You’d Had” and is organized into seven main types. Having this kind of available resource can help manage small group work that keeps students thinking about the task and how they can critically think about their work.

When managing a whole-class discussion, it’s essential to use speech that redirects the conversation away from yourself and back onto the students. This takes time, and practice as students are not always comfortable talking with a whole class and often look towards you for guidance, approval, or attention. This list of nine talk moves from The Inquiry Project is organized into four goals and can help you redirect attention back onto students. Other tricks for managing whole-class discussions include using a soft or squishy ball (that can be easily thrown) to designate the speaker or choose one or two students in advance to lead the discussion. Using any of these practices encourages students to talk to one another rather than use you as the go-between.

If you want in-depth discussions in the mathematics classroom, I recommend the book “5 Practices for Orchestrating Productive Mathematics Discussion” by Margaret Smith and Mary Kay Stein. This text starts with selecting tasks, going through purposely direct classroom discussion by anticipating student responses, monitoring students as they work, selecting and sequencing the work to be shared, and connecting student responses.

Enjoy the silence

Using prompts and talk moves are essential for moving discussions along, but I argue that the most important and often underused talk move is silent wait time. In the publication “How to… Ask the Right Questions,” the late Patricia Blosser suggests singing a short song to yourself like “Baa, Baa, Black Sheep” after asking a question. I often use “Mary Had a Little Lamb” or “Happy Birthday.” The trick is to keep your mind occupied for 3-5 seconds, so you don’t jump in too early. Even if you sing in your head quickly, you are still giving enough silent time to allow students to think and formulate a response.

In addition to singing to myself, I also use a sip of water to force wait time for my students and myself. I carry a full bottle of water to every class. I take a sip after asking a question, so I don’t speak too quickly. I also take a sip when ending a discussion to allow time for students to ask questions or make comments. If students ask a question that needs a complex response, I’ll take a sip of water to give me time to formulate my thoughts. You can’t speak with water in your mouth, so you are required to slow down, be silent, and allow time to think. As a healthy bonus, this trick ensures you are well-hydrated on class days!

I’ve found with online classes that wait time needs to be lengthened by a second or two. When in person, students can look around and pick up on physical, social cues. We lack those social cues online, so students may need additional time to decide that they are the ones who will speak. Students are usually more distracted when online than in person and may need an extra moment to register the questions asked. Be prepared to not only add an extra second or two to your normal wait time but also to repeat the question as distracted students may have tuned you out!

When a student responds to a question, it is equally important to have a short wait time afterward. This allows the opportunity for other students to chime in without requiring you to prompt. Students will talk with one another in a student-centered classroom rather than wait for you to continually prompt new discussion points. This second wait time also allows you time to formulate your response to the student. Often, when we jump in too quickly, we pass a verbal judgment on the initial reaction to effectively stop the discussion or further thinking. Staying silent sends a message to students that the responsibility for discussing is on them.

With project-based learning, encouraging student communication is critical for success. Using various student and teacher talk moves and silent wait time can encourage task-focused student discussion and promote student learning.

Try using some teacher or student talk move prompts when engaging students in productive classroom discussion. And remember that silence is sometimes the best tool to further discussion.

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