The Power of Student Talk in the K12 Math Classroom
What is the function of student talk in a math classroom? And what is the role of a math teacher in relation to student learning?
Consider two very different students. One is an at-risk ninth grader taking Algebra for the first time. They already believe they’re going to fail even before setting foot in the classroom. The other, a college-bound senior taking AP Calc. They love math so much, they almost don’t even need a math teacher to guide them.
In Joseph Hyun’s 11 years teaching math to San Diego high schoolers, he noticed that all of his students had one thing in common.
No matter their starting point, they were more likely to move forward in their mathematical journey and their understanding of math concepts if they were an active participant in their learning.
Dr. Derek Williams, Assistant Professor of Math Education at MSU, noticed the same in his own classrooms.
That’s why he’s made it his life’s work to research student engagement and student talk in the math classroom, and to work with math teachers to create the kinds of learning environments that get our math students talking.
In our recent Office Hours session, Dr. Williams discussed his work exploring the teaching moves, the pedagogical practices, and ways to structure math classrooms to get the most out of student engagement. And the connection between student engagement and what students learn in math classrooms.
We’ll share with you here what we learned in that conversation. Take a look at the complete recording here.
Who is engaged in your classroom? Who isn’t? And how do you know?
We all have a sense of what student engagement is. But it’s hard to monitor.
Student engagement is actually made up of four components. And we can only see one of them.
Social: How are students interacting with each other in regards to the topic or the content? What’s the on-task interaction between students? With whom did they choose to work, if it’s optional?
Emotional: How are students feeling? What are their effective responses as they go through a lesson?
Behavioral: What are students’ outward behavior showing us? What do we observe in their body language or facial expressions?
Cognitive: What’s going on within students’ minds? How are they actually absorbing the material? What are they missing?
Our ability to directly observe student engagement is limited by a number of things.
We can only actually see one of those four key components – behavioral.
But implicit bias has been directly connected to misinterpreting who is or isn’t engaged in our classrooms.
For example, the student leaning back with their arms crossed, their feet stretched out. Their body language might suggest they are less than attentive. But at the same time, we don’t know what’s going on in their mind. They could be very much paying attention to what we’re doing, and we just don’t know.
And if we ask students if they’re engaged, we break the moment. We distract them from that engagement.
So how do we measure student engagement? How do we get this information, in a meaningful way, and not disrupt or distract the learning experience, or make judgements grounded partly in our own implicit biases?
Why is student engagement important? And how does it connect directly to student talk in the math classroom?
Researchers have found student engagement to be fundamentally inseparable from the learning that’s taking place in the classroom.
Consider how emerging mathematical ideas are created and shared. What’s the consensus-building process that groups go through to form those math ideas? And how do they then become the normal ways of thinking within the space? It’s through dialogue.
In the same sense, both learning and student engagement are directly connected to our students talking.
To boost our students’ grasp of the material, we have to boost both student engagement and student talk in our classrooms.
TeachFX surfaces for teachers specifics about student talk, like when a student is able to speak for more than eight seconds. In Derek’s program, we can now see that nine times per hour on average, their teachers are getting those types of responses.
To increase student engagement in the math classroom, change how we teach – not what we teach
The first step in building student engagement in the math classroom is to establish the expectation that students are supposed to think out loud together when working on things.
This is one of the insights that came out of Dr. Williams’ teachers’ own reflections on their TeachFX data. They’re not changing what they teach, but how they teach it.
Right from the beginning of a lesson, with warm-up problems, teachers can engage the class in dialogue. The warm-up problems are the same ones the teachers have used before. What’s changed is how they implement the activities, while paying attention to their specific teacher practice and student engagement goals.
It might be a primer set of a few problems that are foreshadowing what the rest of the lesson is going to be like. Or, the one or two really challenging homework assignment items from the previous night or the previous week. Things that teachers anticipate students might need a bit more time to think about or work together on.
With any given warm-up, students are expected to work with each other and to share their thinking with others in the room.
You might assign small groups to the warm-ups. Or have students work with the person sitting right next to them.
In either approach, you’re setting up a classroom culture, such that working together with other students about the mathematics material is the expectation in the room.
What impact would structured student talk during a warm-up have in your math classroom?
The profound power of wait time to facilitate an engaged culture in the classroom
Wait time sounds simple. Be cognizant of how long you’re pausing after asking a question or after a student asks a question.
But it’s actually quite profound. In the message that it sends to students, in the norms that it can establish in the room. And in its power to increase student engagement and student talk, and to help facilitate more equitable classrooms by helping every student use their voice.
For example, the teacher says something to the effect of, “What answer did you all get?”
The same two or three students who always jump in first yell something out. The teacher accepts that as the answer everyone got, and moves on.
In that scenario, there’s very little wait time.
And the fact we’re just getting those same two or three responses, we’re only hearing from those same two or three students, is directly connected to that lack of wait time.
When we’re deliberate about pausing, and letting students sit in the discomfort of the silence that happens during wait time, we send a message to students.
We’re saying that we, as their teacher, very much value their thinking and their response. And we’re going to give them the time and space to share that.
What’s more, wait time has the power to influence the conversational pattern in the room.
If you’re facilitating a student-to-student conversation, the talk pattern doesn't have to be student->teacher->student->teacher->student->teacher.
Instead, can we get student->student->student or teacher->student->student->student as the pattern for how those conversations take place. And that happens when we allow the space for students to think and jump in.
TeachFX helps the teachers actually visualize those talk patterns in their classroom, and to see what practices – like wait time – help facilitate meaningful dialogue between students.
A sample lesson to increase student talk
Here’s a real example from a typical algebra 1 math class. Derek’s teachers were blown away by how much their students were bought in with this approach. They were interested in what they were doing. And some really fun mathematical intuition came out.
Stretching over one week, this lesson adapts the popular smartphones plan to a new context:
If you’re looking at getting your dream car, which is more cost effective? Buying that car or leasing that car?
How can we compare those two situations? And why would we even want to compare them?
Day One: Students research their dream car to create their linear equations.
They go straight for the slope intercept form. We want them to interpret down payments as the Y intercept and monthly payments as the slope.
To expedite things, provide students with tools like online calculators to help turn the information from a car dealer’s website into an estimated down payment or monthly payment.
Additional prompts can help them think about their own equations. What does the input mean? What does the output mean?
Day Two: Ask the students to compare the plans.
Start with the opening question: Which plan is more cost effective?
Then use follow-up questions like: How do these compare over time? What’s the significance of the intersection? How could you know? How could you be more sure that the lines will or will not ever intersect in a meaningful way?
Derek’s teachers’ students gravitated towards using tables and graphs to represent the information they had from the equations and use those graphs to answer the question. Because they could see it, teachers could ask: If your graphs don’t intersect, should they? The kids were reasoning about whether the slopes of the two equations were the same or not.
Day Three: Focus specifically on solving with substitution.
The driving questions here are: Why does it make sense to set up a single equation?
Why are we allowed to take these two related but different contexts for buying and leasing a car and set pieces of those two things equal to each other? What are we actually equating?
Day Four: Solve with elimination.
Here, students write the equations in standard form. Ask them to reinterpret what the bits and pieces of standard form mean. This is challenging for students. An interesting prompt to get students to think about and have them solve with elimination is: Then what does an X intercept mean in this context, if there is one?
Day Five: Special cases.
Typically, special cases are when the two lines are the same line. We might see that the lines are parallel and they’re never going to intersect. The students can explore what that means. They can see, as time goes on, one of these things is always more cost effective than the other. But the two lines will, as lines as mathematical objects will, intersect.
The students get to reason together about the previous days of work and about their interpretations of the different equations. The questions asked are built from student thinking. It’s constantly checking in with what the students are thinking about, how they’re reasoning about their equations or the equations of their neighbors to make sense of what’s going on.
Setting goals for student engagement in your math classroom
Goals are directly connected to promoting student engagement and deep learning when they focus on increasing student talk and opportunities for students to interact with each other.
Then, professional development activities throughout the year should align with the specific goals that teachers are working towards.
The teachers in Dr. Williams’ program have set both instructional practice goals and student learning goals.
Instructional practice goals include focusing on attention to wait time, more intentional group work, and working towards an average of teacher talk time of, at most 40% - 50%, per lesson. (That last one seemed an ambitious goal at the outset.)
Their student learning goals include increasing the number of times that students speak for prolonged periods of time, to promote more student engagement as demonstrated by how much time they’re interacting in class with each other, and to be more intentional about group work and direct instruction.
Measuring progress towards those goals with TeachFX
Dr. Williams incorporated TeachFX into the program in order for teachers to have objective, on-demand feedback showing them where they started and what progress they made over time.
Using TeachFX either on their phone or a laptop, they simply record a class and then get data with insights and visualizations.
With TeachFX, Dr. Williams’ teachers can see their talk time ratios, length of student talk time, and more. They get objective data. And they don’t have to spend time reviewing a recording themselves — TeachFX’s AI technology does the work for them.
Word clouds that actually represent the academic vocabulary kids are using, with a distinction between the teacher versus students vocabulary used. You can imagine the actionable next steps that teachers can can go forward with after that.
A timeline reveals for teachers specific instances of things like wait time and the types of questions being asked, when a teacher is talking or there’s group talk or silence. You literally see what a lesson looks like. Was the teacher talking for a long stretch? Is student talk happening in short bursts, with the teacher doing most of the talking?
“I thought we were being really, really ambitious with the average teacher talk between 40% and 50%. It was amazingly exciting to see the aggregated response come back in that range.”
- Dr. Derek Williams
For example: TeachFX tracks two types of wait time in the classroom. Wait Time 1 is when a teacher will pause and give time after a student speaks. Imagine asking that question, allowing that space of three seconds — or in a virtual environment even longer. While that time might be painful to have that much silence, it actually is a chance for students to be able to process and think through their questions; to have an opportunity to engage. While the more confident students might have to actually wait and hold their horses for a moment.
And Wait Time 2 is when you allow for space and time after a student response. So instead of immediately evaluating an answer, saying, “Great job, John, that is the correct answer,” giving a chance to wait and allow other students to contribute to that conversation.
With TeachFX, Dr. Williams’ teachers can see that both types of wait time are trending upwards.
It’s hard, especially when introducing new topics, to let students talk. But seeing the baseline, and using TeachFX to get a snapshot of what those baselines look like for each teacher, each teacher can see, visually, what the students are able to think through.
And because TeachFX class reports are not evaluative, the teachers in Dr. Williams’ program enjoy measuring and reflecting on what’s happening. It’s a conduit for getting together to talk about teaching, using data to reflect. Without judgment.
Plus, each teacher’s data is private to them. They can choose to share it. But others can only see the classrooms’ data in aggregate.
Part of the TeachFX philosophy is that no teacher is being judged or evaluated with what they’re gaining from their TeachFX classroom reports. TeachFX is a self reflection tool for teachers, first and foremost.
So a researcher like Dr. Williams or even a school or district leader can look at TeachFX data on a whole. But only in an anonymized and aggregated way.
Researchers and administrators get to see, high-level, the impact of the initiatives in play.
We present to Dr. Williams his program’s top trends over time, and key points like the average top percentage for the first semester (it was 44%) of the year.
And we look at that data in the context of the goals his program is aiming for. We help highlight the places where things are on track, and places where there’s opportunity for growth.
For isntance: because TeachFX surfaces specifics about student talk, like when a student is able to speak for more than eight seconds, we can see that in Dr. Williams’ program, nine times per hour on average, their teachers are getting those types of responses.
“I thought we were being really, really ambitious with the average teacher talk between 40 and 50% so it was amazingly exciting to see the aggregated response come back in that range.” - Dr. Derek Williams
Using data to reflect on teaching practice
TeachFX makes it easy for Dr. Williams’ teachers to reflect on their goals, with specific outputs about wait time and proportion of group talk vs. teacher talk. They’re able to look at those outputs, to think back to what that lesson was like, and offer anecdotal clarification on what the TeachFX class report is telling them. It starts a lot of really good conversations about teaching to promote student learning.
In their planning meetings, Dr. Williams’ group asks themselves consistent questions, to help keep the focus on the goals they’ve set.
How can we position students to interact with each other early?
The warm-up activity is one way. You might think of several others.
What key questions can we ask to get students thinking?
Without giving away too much, how can we pose a question, instead of using direct instruction to get students looking at something in the right way?
What follow-ups can we use to continue building off of students’ thinking?
If we want a lot of student-to-student interaction, and for that to be on-task interaction, then students need to have access to each other’s thinking routinely throughout the course.
In addition to asking follow-up questions, math teachers can give students an opportunity to interact with each other’s thinking in their small groups and the whole class by:
Asking students to share their response out loud
Placing whiteboards around the room and send groups of students to the whiteboards to work together and do sort of a gallery walk
Using poster paper around the room for a similar approach
Using something like Padlet or Google Slides when teaching via Zoom
What are the key ways of thinking that we want to draw attention to?
This is about reflection on what would help students drive the lesson towards the learning goals.
All of these questions are built towards positioning the students to do most of the thinking. The teachers then get to work with that foundation, to continuously draw on the thinking from the students in the room to keep moving the lesson forward in the direction we hope for it to go, that accomplishes our learning goals.
Would you like to explore bringing these practices into your math classroom?
What strategies do you use now, or have you seen teachers use, to get kids talking in the math classroom?
We believe the way forward in math education is in providing more meaningful and equitable classroom dialogue. And that happens when teachers are doing this work in their classrooms and are provided with the data and the support that the TeachFX team can give and the support that Dr. Williams gives in this program, to give teachers the feedback they need.
That’s why we help our partners establish goals like those set in Dr. Williams’ programs, and help our partners track those trends over time. If you’d like to learn more about partnering with TeachFX, we’re love to talk with you.
And if you’d like to learn more about Dr. Williams’ work, connect with him here.
