By Laurie Speranzo and Kristin Klingensmith

Institute for Learning

Equitable mathematics instruction that honors the lived experiences, ways of knowing, and linguistic and cultural assets of students should always be at the forefront of our minds. Each and every student has the right to ongoing, high quality, rigorous instruction that recognizes them as learners and that is designed for students to advance their conceptual understanding. Both inside and outside of the classroom, students are thinking, reasoning, and problem-solving daily. It is imperative that we honor the fact that students are doers of mathematics and that the lives students lead provide greater context for mathematical knowledge than what our lessons alone provide. Black and Brown students are doers of mathematics. Emergent multilingual students are mathematicians. Students identified as needing specialized educational support are “math people.” So how can teachers use learner-centered routines to support students in seeing themselves as doers of mathematics?

This article is the second of a two-part series focused on four learner-centered routines:

  • Turn and Talks
  • Stop and Jots
  • Step Backs
  • Quick Writes

It explores how these four routines can be used to foster a positive math identity in students by creating space for voice, agency, and actually doing mathematics. For more information about these routines, check out the first article 4 Go-To Learner-Centered Routines to Bolster Math Discussions, In-Person and Online.

Using Routines to Invite Student Voices and Promote Agency in a Math Classroom

Voice: Students have choice, control, challenge, and opportunities to collaborate.

[Toshalis, E. & Nakkula, M. J., (2012). Motivation, Engagement, and Student Voice]

Agency: The capacity and propensity to take purposeful initiative…

[Ferguson, R. F., Phillips, S. F., Rowley, F. S., & Friedlander, J. W., (October 2015). The Influence of Teaching Beyond Standardized Test Scores: Engagement, Mindsets, and Agency]

Having students build their identity as doers of mathematics starts with providing opportunities to access voice and employ agency in math classrooms. Student voice in class does not just mean hearing from a student. It means they have the opportunity to share their thinking and to challenge the thinking of others; it means they have the opportunity to work together while engaging in the math so they are constructing meaning, not just taking in information. It also means that they see their words and their mathematical activity as having an impact on the outcome of the classroom discussion. When teachers make the deliberate move of talking less, it leaves more space for students to share their thinking, understanding, and lived math experiences. By attending to student voice in the classroom and providing opportunities that foster agency, students can build agency.

Turn and Talks & Stop and Jots

Imagine this happening in a classroom:

Two students have just shared their solution paths – Josiah used repeated addition to solve the task and Martina used multiplication. The teacher asks, “Can both solution paths be correct? Be ready to say why.”

Four hands shoot up, the same four that are always up.

Though it is exciting to see students ready to share, in an equitable classroom all students are given a chance to process their thinking and be ready to engage in the discussion of the task.

The Turn and Talk and Stop and Jot routines can be used to create time and space for all students to think about and construct a response to the question. Providing opportunities for students to get their own thinking out verbally or on paper honors what every student brings to the table, such as use of a language other than that of instruction, algorithms more dominant in other countries, representations that are not traditional in American classrooms, and student connections to a context related to their own experiences. Consider these examples.

Learner-Centered Routine Example for Use in the Scenario Recognizes Students as Doers of Mathematics
Turn and Talk Ask students to turn to a partner and discuss their thinking. After a minute or so, make sure that the second person in each partnership has had a chance to share so all of the talking is not done by one person.

Every student has the opportunity to verbally share their reasoning to a rigorous mathematics question with a peer. Additionally, every student has the chance to

  • talk with a peer before attempting to express their thinking to the class, which is especially valuable when the language used during a Turn and Talk differs from the language of instruction.
  • rehearse putting their own thinking into words and changing their words to make their ideas clearer.
  • hear other students’ thinking and language.
  • grow more confident in their reasoning because it has been compared and possibly defended with a peer.
Stop and Jot Pause and say, “Take a moment. Stop and jot. Can both solution paths be correct? Why or why not.” to allow students time to process their thinking.

Every student has the opportunity for and responsibility to privately respond to a rigorous question about mathematics and construct a response that may be shared with the whole class. Additionally, every student has the chance to

  • organize their thinking.
  • reflect on and maybe clarify their thinking about the question.
  • feel more prepared to share their thinking.
  • refer to their Stop and Jot when contributing to the discussion.

Turn and Talks and Stop and Jots provide opportunities for students to process independently or collaboratively the question posed by the teacher.

Take a look at these two routines being used in math classes.

In this grade three classroom, they are working on unpacking patterns in multiplication (when doubling one factor, the product doubles). The teacher uses a Turn and Talk to ensure every student has a chance to work through their thinking before hearing from a few students publicly.

In this seventh grade classroom, watch as the teacher uses a Stop and Jot that turns into a Turn and Talk to give students the chance to process their ideas while she uses the time to formatively assess where students are in their understanding.

Step Backs & Quick Writes

Return to the scenario from earlier involving the two solutions paths (multiplication and repeated addition scenario) and think about how the conversation may have progressed. Step Backs and Quick Writes can be used later in such a discussion to build in additional opportunities for student voice and agency, but these would likely be done with a slightly modified question.

Learner-Centered Routine Example for Use in the Scenario Recognizes Students as Doers of Mathematics
Step Back Use one of the other routines and then after students have heard from multiple classmates, ask the step back question “Why is multiplication with [whole] numbers the same as repeated addition?”

Students benefit from repeated public marking of the key structures of the mathematics being studied, by teachers and classmates. Asking students to respond to step back questions, shifts the responsibility of pulling the ideas together to students.

Students are expected to

  • process and synthesize contributions from multiple peers.
  • unpack their own thinking related to the thinking of others.
  • articulate the understanding they’ve constructed so far.
  • listen and weigh the synthesized ideas of others.
Quick Write Because this is an opportunity for a major “a-ha” moment for students, it offers the chance for students to dissect a more narrow piece of the thinking to be able to apply it to the question of if both paths are correct. Start with an independent Quick Write of “How are repeated addition and multiplication similar? Different?”

Using the more narrow Quick Write allows students to be ready to add their voice to the discussion by

  • having them name what they can share with the class (in this case, similarities and differences).
  • allowing them to identify a specific piece to contribute to the conversations (in this case that both solution paths yield the same answer).

Using Routines to Build Positive Student Identity in Math Classrooms

We have all heard people say, “I’m not a math person.” The reality is that math is all around us and impacts how we interpret the world. Therefore, we all need to feel that doing math and thinking mathematically are a part of who we are.

“How students are positioned to participate in mathematics affects not only what they learn but also how they come to see themselves as learners,” according to NCTM (2018), Catalyzing Change, p. 28. Ensuring that student voice is at the forefront of the classroom experience builds students’ confidence, honors the lived experiences they bring to the table, and sustains a belief that they can do the math and that their thoughts matter. As students’ positive identity grows, their voice will be leveraged even more. Students’ math identities are a reflection of the opportunities that have been provided in the classrooms to build voice, agency, and the belief in being a doer of math!

Letting only the four students, who first raised their hands, be the only ones who contribute to the discussion, reinforces the false narrative that math is about speed and that the few whose hands went up first were those “good in math.” By utilizing the learner-centered routines, more students are going to feel that their thinking is worthy of sharing, both in writing and in discussion, and, therefore, build a cadre of learners who believe they can do math! It is incumbent upon us as educators to not only hear student voices in the classroom but listen to what the students are telling us about how what they know and can do as mathematicians.

To read more about instructional approaches that foster student agency, check out the article Focusing on the Instructional Approach Nurtures Agency.

Tell Us About How the Routines You Use Led to Greater Voice

  • Which of these student-centered routines have you tried?
  • How did the routine(s) allow for more student voice in the classroom?

Tell us here.