‘To listen well is to figure out what’s on someone’s mind and demonstrate that you care enough to want to know.’ (From ‘You’re Not Listening: What You’re Missing and Why It Matters’ by Kate Murphy)
Listening is the heart of good teaching. Not only does attentive listening tell us how to act pedagogically, it also fosters a sense of belonging. We can feel when someone is listening superficially to us, or when they are deeply interested in what we are saying. It’s in their demeanour, how they react, and what they do or say in response.
Brent Davis, who has examined how mathematics teachers listen as a way to help them better understand their practice, calls listening a ‘fundamental competency of the mathematics teacher’. Yet there seems to be little guidance about how to listen effectively as teachers, what we might listen to, what gets in the way of listening, and how listening can shape our teaching.
What should we be listening to and how?
In her book ‘Listening: A Framework for Teaching Across Differences’, Katherine Schultz defines listening ‘as an active, relational, and interpretive process that is focused on making meaning’. So what should we be listening to? Schultz describes four kinds of listening:
- Listening to know particular students — a deep knowledge of each student’s preferences, needs and strengths
- Listening to the rhythm and balance of a classroom — the underlying structures and patterns of the classroom interaction (rhythm) and the class as a whole (balance)
- Listening to the social, cultural and community contexts of students’ lives — the whole world a student inhabits beyond the classroom
- Listening to silence and acts of silencing — missing conversations, overlooked perspectives, and moments when students are actively silenced by individuals or institutions.
All four are essential to teaching responsively. However I want to focus on one that Schultz seems not to have explicitly captured: listening to students’ thinking, which may be offered to us in written, spoken, pictorial and gestural forms.
Of course, every teacher is (or should be) listening to their students’ thinking. But are we really listening to their ideas or are we listening for a particular response? Davis (1994, 1997) elaborates this distinction further by identifying different forms of listening as evaluative, interpretive, and generative which he illustrates with classroom vignettes. (Davis originally termed the third level ‘hermeneutic’, but I prefer to follow the framing of Yackel et al (2003).) Evaluative listening seeks a particular response; interpretive listening seeks to make sense of an individual’s thinking; generative listening seeks to transform both individual and shared understandings.
What does listening require from us?
Davis asserts that the ability to listen is dependent upon the presence of particular virtues. If we believe that students have something worth saying, if we are curious about what they think, if we trust that there is reason in their actions, then we are more likely to listen to them. Our beliefs about learning mathematics also come into play. If we believe it is mastering a system of pre-established, formal truths, then we are more likely to listen for particular responses so as to correct misunderstandings. However, if we believe that learning mathematics develops through the exploration of concepts, then we are more likely to listen to students’ interpretations of ideas.
Listening requires us to be active participants. Good listeners physically convey their interest—they might lean in, make eye contact, offer an encouraging smile or a ‘thinking frown’, tilt their head—and listen with total focus. They respond in ways that support the speaker to elaborate rather than shift the conversation elsewhere.1 Marilyn Burns, a long-time listener to student thinking, has written an excellent blog post outlining ‘Nine ways to have deeper conversations with students about math‘ that demonstrates many elements of supportive listening.
If I’m meant to be listening, why am I still talking?
Good listeners also ask good questions. In the mathematics classroom, questions serve many different purposes. They may be framed to help students get started on a problem, to try and ‘unstick’ them, to sharpen their reasoning, to cause reflection, and more. To draw out mathematical thinking, we might ask:
- What makes you say that?
- How do you know?
- Can you tell me more?
- How did you figure out … ?
- Why did you decide to … ?
John Mason (2010) calls these genuine enquiry questions, and encourages us to use them as much as possible. Mason, who has written extensively about questioning, co-authored a book2 with Anne Watson that presents an invaluable framework for generating questions and prompts in mathematical thinking (the title of the book). This sits on my bookshelf alongside ‘Thinkers: a collection of activities to provoke mathematical thinking‘ (Bills, Bills, Mason, Watson) as my go-tos for asking questions with rich possibilities for listening to how students make sense of mathematical structures and processes.
With the right questions and a generative listening stance, student thinking can shape the trajectory of the lesson and transform the classroom into a community of genuine mathematical inquiry where ‘classroom participants (teacher and students) lay down a mathematical path as they go, rather than follow a well-trodden trajectory’ (Yackel et al 2003).
Features of different modes of listening
My current view of the typical features of different modes of listening is summarised in the table below. Much of this is gleaned from the literature, and was partially sparked by David Butler’s 2018 tweet summarising his interpretation of Yackel et al (2003). I also recommend the papers by Davis and Mason for closer reading. The book by Kate Murphy is insightful, and addresses the prevalence of poor listening in society.
|Listening for||Listening for / listening to||Listening to|
|The purpose of the listening is …||To seek a particular response.||To make sense of an individual’s thinking.||To transform both individual and shared understandings.|
|The questions are typically …||Funnelling questions.|
|Probing questions.||Genuine-enquiry questions.|
|The motivation for questioning is …||To ensure that learners are themselves listening.|
To evaluate the correctness of the contribution.
|To decipher the sense that a student appears to be making.||To generate a new space for mathematical exploration.|
|The teaching style is …||Transmission.|
Telling students what they ‘need to know’.
Discussion-based to engaged interest and stimulate thinking.
Inquiry based with joint exploration guided by students’ responses. Learning is viewed as a social process.
|The interaction between the teacher and students is …||Unidirectional.||Bidirectional.||Multidirectional.|
|The role of the teacher is …||To present and ensure mastery of material.||To guide the discussion along a pre-defined trajectory.||To be a participant in exploring the mathematics.|
|The role of the student is …||To acquire and internalise pre-specified concepts.||To model the mathematics.||To be a participant in exploring the mathematics.|
|Student explanations …||Are expected to fit a pattern.||Are modelled on teacher explanations.||Are used to generate new avenues of exploration.|
|The mathematical authority is …||The teacher.||The teacher.||The community of participants. Student and teacher ideas are on an equal footing.|
|Mathematics is conceived as …||A system of pre-established, formal truths. Knowledge is developed elsewhere and retold in this setting.||A system of pre-established, formal truths that will be uncovered through guided and carefully orchestrated activities.||A rich landscape of ideas to be explored through a constructivist approach.|
Obstacles to listening
So, what gets in the way of listening well? The obstacles can be practical. Are the desks arranged for quiet individual work, or for fostering discussion? Are the prescribed tasks formulaic, or do they offer space for exploration? Do we have the time to listen, or do we need to make a pragmatic decision to move on? Having to attend to the many moving parts in a classroom can divert our attention and lead to what Jenna Laib calls ‘play listening‘, which has all the signs of attentive listening but little of the substance.
The more pernicious barriers are psychological. Do students feel safe to share their thoughts, or do they fear being humiliated? Have we made assumptions about what individual students might be capable of? Do we feel able to interpret all ideas, no matter how unexpected or surprising? Do we have the confidence to enter the classroom as a learner as well as a knower?
One last word
As with many teaching practices, listening is nuanced. I am not advocating for a wholly generative listening approach (that sounds exhausting!). Indeed, sometimes evaluative listening is the most appropriate. What I am suggesting is that we are mindful of how we listen. The first quote in this blog post is from Kate Murphy and so it seems fitting to end with some of her guidance. Murphy says that listening is like playing a sport or a musical instrument in that you can get better and better with practice and persistence (and, I would add, reflection), but you will never achieve total mastery. Earlier in the book, she writes that listening is more of a mindset than a check list of do’s and don’ts.
More than anything, listening requires curiosity. Cultivating a genuine interest in what your students think is an excellent place to start.
 The support-response, shift-response framing is due to sociologist Charles Derber.
 Both books are available in the AAMT bookstore.
Davis, Brent. 1994. “Mathematics Teaching: Moving from Telling to Listening.” Journal of Curriculum and Supervision 9 (3): 267–83.
Davis, Brent. 1997. “Listening for Differences: An Evolving Conception of Mathematics Teaching.” Journal for Research in Mathematics Education 28 (3): 355. https://doi.org/10.2307/749785.
Murphy, Kate. 2020. You’re Not Listening: What You’re Missing and Why It Matters. Celadon Books.
Mason, John. 2020. “Effective Questioning and Responding in the Mathematics Classroom 1.” In Debates in Mathematics Education, by Gwen Ineson, edited by Hilary Povey, 2nd ed., 131–42. Second edition. | Milton Park, Abingdon, Oxon ; New York, NY : Routledge,  | Series: Debates in subject teaching: Routledge. https://doi.org/10.4324/9780429021015-11.
Schultz, Katherine. 2003. Listening : A Framework for Teaching Across Differences. New York: Teachers College Press.
Yackel, Erna, Michelle Stephan, Chris Rasmussen, and Diana Underwood. 2003. “Didactising: Continuing the Work of Leen Streefland.” Educational Studies in Mathematics 54 (1): 101–26.