Six Strategies That Can Lead to More Equitable Online Mathematics Instruction

By Joe Dostilio and Laurie Speranzo

Institute for Learning

Every student has the right to be engaged in meaningful learning that draws on their unique abilities and backgrounds for making sense of mathematical ideas and relationships. Educators who believe this have looked for ways to engage all students in equitable mathematics instruction that advances each student’s conceptual understanding as they navigate this new world of virtual instruction.

These are three teaching practices that work in combination and can be used in virtual spaces for keeping every student engaged, talking, and supported in online learning.

  • Keeping Learning Focused and Advancing
  • Engage Students in Talk/Hear Student Voice
  • Engage In Formative Assessment

 For each of these practices, there are strategies that support equitable mathematics instruction when teaching virtually.

NCTM (2014) research shows that “Student learning is greatest in classrooms where the tasks consistently encourage high-level student thinking and reasoning and least in classrooms where the tasks are routinely procedural in nature” (Boaler and Staples 2008; Hiebert and Wearne 1993; Stein and Lane 1996) and “Not all tasks provide the same opportunities for student thinking and learning” (Hiebert et al. 1997; Stein et al. 2009).
Even when instructional time moves online, students need time to consistently engage in high-level tasks on their own and with their classmates in order to keep learning focused on sense-making.

Strategy #1:  Use Tasks that Require High-Level Mathematical Thinking and Reasoning

High-level tasks

  • have multiple entry points;
  • include or can be solved using a wide range of representations and tools; and
  • require problem-solving.

Focus tasks, a subset of high-level tasks, are a type of cognitively demanding task that requires thinking and reasoning that leads to sense-making, but they do not require the same level of investigation or problem-solving. Focus tasks explicitly press student thinking about a key mathematical concept or relationships by leveraging one of the following methods. Try using a focus task that

  • provides a model for students to interpret and make sense of the mathematics.
  • shows an accurate and an inaccurate solution, then asks students to analyze and name which is accurate and which is not, and explain why.
  • shares a way of solving that is not a traditional algorithm. Ask students to discuss the way of solving and apply it to a new situation or set of numbers.

Use focus tasks to help provide a steady diet of high-level tasks that leads to greater and deeper learning, especially in a time of potentially decreased instructional time due to the pandemic.

Investigating and discussing high-level tasks to make sense of mathematics supports students in seeing themselves as doers of mathematics.

Strategy #2: Provide “On Your Own” Time for Students to Begin Thinking and Reasoning about the Mathematics in the Task

Students need time to generate their own thinking and solutions to a task. Consistently giving students independent work time
  • honors each student’s thinking and develops their identify as a doer of mathematics;
  • provides formative assessment opportunities for teachers; and
  • makes it possible for students’ ideas and solutions to be discussed and compared in small breakout groups and in whole-class discussions.

When time is a concern, consider sending the task to student in advance with a pre-recorded set-up that supports students in understanding the context of the task (without unpacking or giving away the math concept for them). Ask students to engage in “On Your Own” time and come to the live class meeting time prepared to share and discuss their solutions.

It is critical to provide time so that students can process the task, formulate their own mathematical thoughts and solution path, and put their thinking on paper before engaging in discussions. Providing this time makes it more likely that every student—regardless of native language, identification, background, or grade point average—will share their ideas with others, instead of just hearing from those students who work faster and/or louder.

Carpenter, Franke, and Levi (2003) talk about the importance of student voice. “Students who learn to articulate and justify their own mathematical ideas, reason through their own and others’ mathematical explanations, and provide a rationale for their answers develop a deep understanding that is critical to their future success in mathematics and related fields.”

When engaging students in virtual classrooms, look for ways to keep students generating, talking about, and making connections between their ideas and solution paths. Making time for and providing ways for students to use their voice and agency will build positive math identities.

Strategy #3: Incorporate Manipulatives into Lessons

Representations help to clarify the reasoning of specific students, while also leaving a visible trace of the strategy, which allows other students to enter into and follow the mathematical thinking of their classmates.
NCTM (2017) Taking Action

Manipulatives allow students to show their thinking and provide a reference when explaining their reasoning. Consider these options for having students use and discussion manipulatives in virtual classrooms.

Using student manipulative representations allows students to discuss their own understanding and to comment on and explain the thinking of others. When using virtual manipulatives, sending out the link in advance is a good idea, as students (and adults alike) need to “play” with the manipulatives before using them for a task.

Strategy #4: Create Space for Students to Share Their Thinking

Victoria Bill, longtime Senior Math Fellow at the IFL, always says, “The person who talks the most, learns the most!” Use ways to provide time and provide space to ensure each and every student has opportunities to talk and for their voice to be heard.

Check out 4 Go-To Learner-Centered Routines to Bolster Math Discussions, In-Person and Online to read about some routines that prepare students to engage in discussions about deep mathematics. Consistently using these and other routines that get students to share their mathematical thinking, provides similar benefits as those listed above for “On Your Own” work time, honors student thinking, develops their identify as doers of mathematics, provides formative assessment opportunities, and makes it possible for students to generate solutions to share and compare with other students.

Wiliam noted that “the important point is that we must acknowledge that what students learn is not necessarily what the teacher intended, and it is essential that teachers explore students’ thinking before assuming that students have ‘understood’ something. In this sense, assessment is the bridge between teaching and learning” (2005).

As mathematical ideas and solutions are shared, translate some formative assessment best practices to the virtual world. When students say or write about what they think, these strategies honor that thinking and students develop a sense of worth of their ideas—that their ideas are worth sharing and will be discussed in the process of learning mathematics.

Strategy #5: Ask for Agreement/Disagreement . . . Then, Ask Why?

Asking every student to weigh in on whether they agree or disagree is a simple means of formative assessment that teachers may use throughout a lesson. In virtual classrooms, identify ways to continue to use agree/disagree to keep students engaged and provide on-going formative assessment throughout the lesson.

  • Ask students to use a Reaction or an Emoji.
  • Poll students using a simple “Agree” or “Disagree”.
  • Have each student send a message through the chat box; ask that the message be sent only to you when you want to make sure students are not swayed by others’ responses.

Then, prompt students to say more about why they agree or disagree! Without the justification of their agree/disagree stance, there is a missed opportunity for students to share their mathematical reasoning. If teachers are not in the habit of asking for students to back up their thinking, students may agree or disagree out of habit and not out of math content knowledge.

Strategy #6: Provide Effective Feedback

Learners engage better when feedback is focused on their work, identifies what they have shown in their work in regards to the mathematical learning goal, and provides an actionable way for moving forward from their work. Feedback that assigns a grade or score that can often send a message that the learning is complete and has been assessed (Butler 1988, Black & Wiliam 1998, Hattie & Timperley 2007).

When providing written or verbal feedback, call attention to what work the student(s) have done and pose actionable next steps that press the student(s) toward deeper meaning-making.

Characteristics of Feedback and Guidance
Feedback Guidance
  • Highlights mathematical ideas or strategies and lets the student know the benefit or usefulness of the idea or strategy.
  • Acknowledges student’s actual work.
  • Is focused on student’s work, not the student.
  • Conveys to students that they have an audience for their work, “I noticed…” “When looking at your work…”
  • Highlights components of the program that are valued (e.g., connections between representations, communication of mathematical reasoning).
  • Extends the student’s work from where the student is in his or her work to the next stage of the work.
  • Encourages the student to do the work, serves as a call to action, “Give it a try…”
  • Presents students with a challenge or a counter to their method.
  • Prompts the learner to consider the use of alternative representations, strategies, or processes.

Check out these two examples of feedback and guidance given to two different groups by a teacher who utilized Google Slides during small group work a focus task.


Provide time for the student to take action/respond and then respond/resubmit. As time with our students is often reduced in hybrid and remote learning, this process of providing effective feedback and having students take action and respond/resubmit can create a better virtual experience for students and strengthen student-teacher relationships.

Regardless of where students are in their mathematical thinking—not yet fully expressing their reasoning, exhibiting faulty or overgeneralized thinking, or even having the correct answer with sound justification— they all deserve feedback and guidance. Every student should be pressed to move forward from where they are to deeper mathematical understanding. This makes the instruction both equitable and differentiated!

Tell Us About the Strategies You Use When Implementing High-Leverage Teaching Practices in Virtual Classrooms

  • Which of these strategies that support equitable mathematics instruction do you already use in virtual classrooms? How is it going?
  • What other strategies that support equitable mathematics instruction do you recommend for virtual classrooms? Why?

Share your story here.


    Black, P. & Wiliam, D. (1998) Assessment and classroom learning. Assessment in Education: Principles, Policy & Practice, 5(1), 7-74.
    Boaler, J. & Staples, M. (2008). Creating mathematical futures through an equitable teaching approach: The case of railside school. Teachers College Record, 110(3), 608-645.
    Butler, R. (1988). Enhancing and undermining intrinsic motivation: The effects of task-involving and ego-involving evaluation on interest and performance. British Journal of Educational Psychology, 58(1), 1-14.
    Carpenter, T. P., Franke, M. L., & Levi, L. (2003). Thinking mathematically: Integrating arithmetic and algebra in elementary schools. Portsmouth, NH: Heinemann.
    Hattie, J. & Timperley, H. (2007). The power of feedback. Review of Educational Research, 77(1), p81-112.
    Hiebert, J. Thomas, P., Carpenter, E., Fennema, K. C., Fuson, D., Wearne, P., Human, H. M., & Alwyn, O. (1997). Making-sense: Teaching and learning mathematics with understanding. Portsmouth, NH: Heinemann.
    Hiebert, J., & Wearne, D. (1993). Instructional tasks, classroom discourse, and students’ learning in second-grade arithmetic. American Educational Research Journal, 30(2), 393–425. Retrieved from
    Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K., Human, P., Murray, H., Olivier, A & Wearne, D. (1997). Making mathematics problematic: A rejoinder to Prawat and Smith. Educational Researcher, 26(2), 24-26.
    National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. Reston, VA: Author.
    Smith, M. S., Boston, M., Dillon, F., & Miller, S. (2017). Taking Action: Implementing Effective Mathematics Teaching Practices in Grades 9-12. Reston, VA: National Council of Teachers of Mathematics.
    Smith, M. S., Huinker, D. & Bill, V. (2017). Taking Action: Implementing Effective Mathematics Teaching Practices in K – Grade 5. Reston, VA: National Council of Teachers of Mathematics.
    Smith, M. S., Steele, M. D., & Raith, M. L. (2017). Taking Action: Implementing Effective Mathematics Teaching Practices in Grades 6-8. Reston, VA: National Council of Teachers of Mathematics.
    Stein, M. K., & Lane, S. (1996). Instructional tasks and the development of student capacity to think and reason: An analysis of the relationship between teaching and learning in a reform mathematics project. Educational Research and Evaluation, 2 (1), 50–80.
    Stein, M. K., Grover, B. W., & Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. American Educational Research Journal, 33(2), 455–488.
    Wiliam, D. (2005). Keeping learning on track: Formative assessment and the regulation of learning. In M. Coupland, J. Anderson, & T. Spencer (Eds.), Making mathematics vital: Proceedings of the twentieth biennial conference of the Australian Association of Mathematics Teachers (pp. 26–40). Adelaide, Australia: Australian Association of Mathematics Teachers.

    Accountable Talk and Learning Walk are registered trademarks of the University of Pittsburgh.

    Tagged with: Academic Rigor, Agency and Voice, Equitable Instruction, Formative Assessment, High-Level Tasks / Curriculum, High-Leverage Teaching Practices, Math, Multi-Lingual Learner Instruction, Online Instruction, Principles of Learning

    Using 4 Learner-Centered Routines to Build Positive Math Identity in Equitable Classrooms

    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.

    Tagged with: Accountable Talk® Discussions, Agency and Voice, Equitable Instruction, High-Leverage Teaching Practices, Multi-Lingual Learner Instruction, Principles of Learning

    Translating Accountable Talk® Practices Between In-Person and Virtual Teaching

    By Jazmin Rotger de Parra and Kristin Nuñez

    Teaneck Public Schools

    Like many of you, we are still navigating the world of remote instruction and virtual classrooms while wanting to stay focused on providing academically rigorous instruction and having high expectations for all students.

    At the center of most of our decisions is the idea of instructional equity. Equity does not mean that every student should receive identical instruction. Instead, it demands that reasonable and appropriate accommodations be made as needed to promote access and attainment for all students (NCTM 2000)[i]. Up until now, the decisions that led to a greater degree of instructional equity largely occurred in schools and classrooms. But now we are having to apply all that we know about teaching and learning to maximize equitable opportunities for every one of our students in a world outside the school walls.

    …we are having to apply all that we know about teaching and learning to maximize equitable opportunities for every one of our students in a world outside the school walls.

    During the 2019-2020 school year, the use of Accountable Talk practices was a pedagogical foci for our Grades 3–5 mathematics classrooms. Through our work, we incorporated and refined our use of discourse and supported students as they engaged in verbal, visual, and written communication. We increased opportunities for students to learn from one another through the collaborative clarifying of ideas, unpacking misconceptions, and making connections across different ways of doing mathematics. Because of our focus on the use of Accountable Talk practices in the classroom, we know how important talk is to developing mathematical understanding. And even in the time of COVID we are continually trying and tweaking different ideas and approaches during online instruction to foster a learning community that engages in meaningful math discussions that advances student understanding.

    Mrs. Nuñez is one of our third grade teachers, and she continues to reimagine instruction while holding students and the role of instructional conversation at the center of her efforts. Read on as she describes her first-hand experience with establishing Accountable Talk discussions in her classroom and then transitioning to accountable communication between and among her students and herself in an online world.

    Why focus on talk, and specifically, the use of Accountable Talk practices?

    From the moment a new group of learners come together, establishing community is vital for their academic success, and the foundation of the community is talk. Skillful teachers recognize the power in leveraging talk to guide understanding and collaboratively construct knowledge.

    Building the community this year has been a bit different because we started the school year working online. For the first couple weeks of virtual learning, we engaged in many whole group conversations about respect, uniqueness, and culture. We centered our conversations around read alouds that focused on different social emotional skills. Over the course of a week, we developed class promises to hold each other accountable for our learning and make the most of our time together.

    How have you been able to capitalize on the unique opportunity to build community from a distance while students are at home?

    Even though I miss teaching in-person, one of the advantages of our current situation is that we have been able to truly expand the walls of the classroom to better encompass students’ lives at home. We unpacked and shared elements of our cultures to learn more about one another. From morning meetings and brain breaks to icebreakers and structured assignments, our classroom community is building a foundation of patience, perseverance, and celebration, which is integral to establishing community both virtually and in-person.

    How did you start using Accountable Talk practices during instruction?

    There is an assumption that students know how to talk about their thinking; however, this specific type of discourse needs to be explicitly modeled and practiced. Students need opportunities to engage in academic talk that leads to learning. Accountable Talk stems on charts or flip-rings can be used as scaffolded support and referred to during discussions. Similar approaches can be used when working online. Talk stems work because they provide students with diverse backgrounds a common language with a specific, intended conversational purpose to use during our discussions. As students take ownership of what it means to be accountable to their learning community, to accurate knowledge, and to rigorous thinking and truly internalize the expectations, academic conversations flourished, providing rich opportunities for students to build knowledge together and think deeply about content.

    What conversation dynamics do you plan for during your instructional minutes?

    At the beginning, we do a lot of partner and whole group discussion, and within that I balance student voices and keep mine to a minimum.

    After routinely hearing and engaging in Accountable Talk discussions as a whole group, the students adopt the language practices and lead their own conversations—acknowledging and building on each other’s ideas, questioning one another, and supporting claims with evidence. The conversations can seem almost natural in small group discussions, partner conversations, and conferences with me.

    I plan for a combination of teacher to student(s) and student(s)-student(s) discussions.

    What challenge(s) have you faced integrating Accountable Talk practices into instruction, in person and online? How have you met the challenge(s)?

    Though the path to having a language-rich classroom sounds easy, it is not. Not all students are comfortable exposing their thinking, especially when they are aware of the expectation that thinking can (and should) be questioned and challenged. As an adult, it is hard to feel comfortable with the idea that after sharing my best thinking, I am going to have to explore it more deeply—and publicly.

    It takes time and intention to create an instructional space where students feel safe enough to willingly take these risks. Since some students may feel more comfortable than others with this exploratory thinking and talking, I have to think critically about the ways in which equity and engagement intersect.

    One of the ways I’ve met this challenge, both in person and online, is by establishing expectations for participation. Within the structure and routine of a lesson, I find a variety of ways for students to participate. Everyone gets time to work on and is responsible for working on the problem independently. When working in-person, I have them talk with a partner who works at a similar skill level and pace. Then I have two partner groups talk with each other before we have our grand conversation as a whole class.

    When working online, the students share their thinking in a variety of ways. One low-risk way I got them started was by using polls. The polls let me do quick whole class snapshots, and, using follow up “why” questions, let me hear from individual students about their thinking. I also have them use a collaboration board to share their thinking with others after working independently. They use a shared white boards or Google slide in breakout groups. I’ve had students take pictures and send them to me to share with the group. These intentional decisions are the scaffolds for supporting students as they grow their own Accountable Talk practices. Through these efforts my students are more comfortable taking academic risks and have learned the value in hearing and seeing diverse ideas from all members of our classroom learning community.

    Say more about how and why you used the collaboration board with students.

    When we first started digital learning, I was losing students left and right. Students and families struggled with using the attachments in “order” or had difficulty toggling between multiple sources. I needed to regain control of the wheel, so I researched and experimented with different apps and resources to better guide students in their virtual learning spaces. I searched for digital ways to increase and improve collaborative interactions among the members of our learning community.

    I embedded virtual drawing and collaboration boards to engage students in our learning community. Virtual drawing boards allowed students to share their processes and thinking. These boards gave me an opportunity to digitally “walk” through my classroom—to listen in on student conversations, provide feedback through assessing and advancing questions, and make adjustments to my instructional practice. Collaboration boards provided students the ability to respond to the content and each other.

    What else did you consider when making decisions about platforms?

    These instructional decisions empowered students and created space for them to use their voices. It was important that I strategically chose platforms where they could share their diverse ideas in this virtual space not just with me, the teacher, but also with each other.

    Jazmin Rotger de Parra is the Supervisor of Instructional Programs – Mathematics and Kristin Nuñez is a Third Grade Teacher at Teaneck Public Schools.

    IFL Step Back

    Mrs. Nuñez’s story illustrates the art and science of teaching. She tried several small tests of change as she translated her Accountable Talk practices from in-person to online instruction.

    • Honor students for who they are and all that they bring to the classroom.
    • Make time for and expect talk from students.
    • Provide scaffolds for students to support them as they engage in learning discussions.
    • Allow for a range of communication dynamics.Plan and experiment with different ways of getting students to collaborate and communicate with each other using pictures, images, and written words in addition to spoken words.

    Click here to tell us how you are translating Accountable Talk practices during your online, in-person, or hybrid teaching. We want to celebrate your successes and support you in facing the challenges.

    [i] p. 12. National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. Reston, VA: Author.
    Accountable Talk is a registered trademark of the University of Pittsburgh.

    Tagged with: Accountable Talk® Discussions, Agency and Voice, Equitable Instruction, High-Leverage Teaching Practices, Math, Online Instruction, Partner Spotlight, Principles of Learning

    Focusing on the Instructional Approach Nurtures Agency

    By Kristin Klingensmith

    IFL Mathematics fellow

    Sara DeMartino

    IFL English language arts fellow

    Many educators name student agency as something they want to work to develop within their schools and classrooms. But what is student agency? And, more importantly, what can we as educators do to foster student agency?

    To start, we should work from a common definition of agency. The Achievement Gap Initiative at Harvard University defines agency as “the capacity and propensity to take purposeful initiative […].” In their work they frame agency as being on a continuum from having a sense of agency to expressing agency.

    If we keep their definition of agency in mind, then we have to acknowledge that agency is not something that is given, but rather is something that can be nurtured in others. And because students spend most of the school day participating in learning activities in classrooms, we have to consider what agency looks like during the learning process and the impact teachers have on students’ development of agency.

    To foster agency in the classroom, students should have opportunities to be active participants in their learning and be asked to think deeply about content. Students are the meaning makers in the room, and the teacher provides support through feedback and scaffolding that allows students to do the heavy lifting.To better understand student agency and the impact teachers can have on its development, let’s compare two scenarios from second grade classrooms. The students in both classrooms are working to solve the
    Doubles Task. As you read, look for instances where you believe students are expressing agency.

    Scenario A

    Mrs. Miller begins when everyone is sitting silently with the task and a pencil. She tells the students to watch what she does so they can learn how to solve addition equations with double-digit numbers quickly.

    Mrs. Miller says, “I know that there are 49 cookies in each box, and there are 2 boxes, so I have to add 49 + 49.”

    She writes 49 + 49 = ___ on the board.

    Then she says, “I add the tens together and then add the ones together. Then I will put the tens and ones together. 4 tens + 4 tens is 8 tens—80.” Then she says, “9 ones + 9 ones is 18.” She continues, “I know the total amount of tens, 80, and the total amount of ones, 18, so now I put the tens and ones together.” Mrs. Miller says to the students, “Write the amount we get when we add the tens and ones.”

    She sees some students write 80 + 18 = 98. Other students shout out their answers: I got 98. There are a lot of cookies. Wait, I got 88. No, it is 80 and 18, so it has to be 98, don’t you know?

    She is disappointed that they shouted out and did not wait to be called on. Mrs. Miller says, “I wish you would follow the directions. But two of you shouted out the right answer, so good job.” Mrs. Miller writes the final step on the board: 80 + 18 = 98.

    Mrs. Miller then turns to the class to check their understanding. She asks, “Why did we add 80 + 18 to get 98?” The students look at her and then at one another. One student says, “Because you told us to.”

    Scenario B

    Ms. Franklin tells the students to get ready for math and posts the Doubles Task on the board. As students move into their math groups, they begin to work on the task in groups. Ms. Franklin walks around the room, listening to their conversations and providing support as needed. She notes that some of the students have made diagrams of base ten blocks while others are using manipulatives. Some students are working more abstractly without the use of visual models.

    As she approaches one of the groups, she hears a student say, “I added 50 + 48.” Another student says, “I think we made a mistake. We have to add 49 + 49.” Another student says, “It’s okay because it’s 98 either way. It is just easier to add 48 + 50.” Ms. Franklin asks where the 48 + 50 came from, and a student answers, “We moved 1 from this 49 to this 49.” Then Ms. Franklin asks, “Are you allowed to move some from one addend to another? Why or why not?” The students pause and then start to talk as a group. Ms. Franklin hears several students say that both 49 + 49 and 48 + 50 equal 98. One student says that moving 1 from 49 over to the other 49 does not change the answer because they are moving 1 not adding 1. Ms. Franklin says, “Get your reasoning on paper. Be ready to explain to the class why changing 49 + 49 into 48 + 50 does not change the answer.”

    Ms. Franklin continues to circulate among the group listening for their mathematical reasoning and asking questions to stretch their thinking.

    You probably noticed instances of student agency in both classrooms, but recognized that there were more instances where student agency was being expressed in Ms. Franklin’s class than in Mrs. Miller’s class. Though Mrs. Miller’s students were willing to share their answers and be heard (without waiting for her to call on them), Ms. Franklin’s students expressed agency more consistently and in more ways.

    The evidence of student agency in these scenarios is directly related to the instructional decisions that Ms. Franklin and Mrs. Miller made that worked to either “boost” or “dampen” student agency. Both Ms. Franklin and Mrs. Miller start by selecting a task that is of high cognitive demand and that allows for multiple student solution paths, which provides students something worthwhile to talk about and figure out. This instructional decision serves to boost agency. Unfortunately, after the selection of the task, Mrs. Miller works in a way that dampens student agency because opportunities for students to think, reason, and even interact are taken away. In contrast, Ms. Franklin continues to boost student agency. She creates an additional challenge when she asks a small group of students, “Are you allowed to move some from one addend to another? Why or why not?” which leads students to think more rigorously by working to understand why moving an amount between addends does not change the whole, rather than simply report the steps they used to arrive at the answer. The challenge works to captivate the attention of the students and requires them to engage in meaningful discussion of the mathematics. Based on their interactions, it is likely that students in Ms. Franklin’s class regularly participate in meaningful classroom discussions.

    If student agency is to remain a goal, then looking at what is happening in the classroom must be the focus. We have to recognize that students from every background deserve and have the right to experience classroom environments designed to foster agency. We have to believe that students are the most valuable resources in the classroom and come to us as thinkers whose contributions have merit. We have to ask if the materials we put in front of students are worthy of serious thought and cognitive effort. And we have to consider how instructional practices subtly, or not so subtlety as in the case of Mrs. Miller, convey beliefs about students and work to boost or dampen their agency.

    Tagged with: Agency and Voice, Equitable Instruction, High-Leverage Teaching Practices, Math

    Agency and Voice: A Push for Greater Equity and What it Looks Like in Math

    By Laurie Speranzo

    IFL mathematics fellow

    Asale Harris

    Supervisor of mathematics (Grades 1 to 6), New Brunswick Public Schools

    Jamie Gulotta

    Supervisor of mathematics (Grades 6 to 12), New Brunswick Public Schools

    JoAnna Castellano

    Mathematics specialist, New Brunswick Middle School

    In her article “Framing Equity: Helping Students ‘Play the Game’ and ‘Change the Game’” (2009), Rochelle Gutiérrez lays out the four key dimensions of equity: Access, Achievement, Identity, and Power, which sit on two axes. Access and Achievement create the dominant axis, and Identify and Power create the critical axis.

    Many of our partners in education have been working to secure access to high-quality education for every student to ensure that each of them can achieve. Their efforts often focus on the dominant axis to ensure that students have access so that they can move towards achievement. While work in this area is necessary, the critical axis allows students to see themselves as mathematicians and changers of the world around them. Honoring and leveraging the identity of each and every student, and transferring power to students in classrooms must also be considered to truly address equity. Gutiérrez writes that attention to identity includes that “students’ frames of reference and resources are acknowledged in ways that help build critical citizens.” Power is not just about who owns the airtime in class: “While teachers in interviews may say they ‘want to empower students,’ they almost always mean it only as it relates to achievement, not with respect to helping students reach personal goals of excellence that may intersect with the doing of mathematics.” However, if students are to be empowered to excel outside of school, opportunities need to be provided in school.

    One partner district, New Brunswick Public Schools, has taken on equity, with a focus on providing students greater agency and voice. If one definition of voice is students having choice, control, challenge, and opportunities to collaborate, how are district teachers and leaders building voice?

    Asale Harris and Jamie Gulotta, the district supervisors of mathematics, name that it all starts with access to high-level tasks: Students try different pathways and strategies and then discuss these with peers. By making discussion the norm in the classroom, students are empowered to share thoughts and ideas without the fear of being different or wrong. During instruction, teachers place value on student ideas and discussion, which then, in turn, increases student voice.

    The mathematics specialist at New Brunswick Middle School (NBMS), JoAnna Castellano, who supports teachers in use of high-level tasks and facilitating productive discussions, adds this:

    Our students at NBMS are utilizing their voice and agency by taking ownership of their work. The students at the middle school have committed to persevering through high-cognitive tasks. Teachers are intentionally making moves that are making students focus on three components when working on a high-cognitive task, emphasizing the student’s mathematical explanation with a visual model, while focusing on the precision of their work. Students are taking a more direct role in their work.

    The New Brunswick district’s vision is “to create lifelong learners and leaders.” This takes into account agency being defined as the capacity and propensity to take purposeful initiative (Ferguson, Phillips, et al., October 2015). Agency starts in the classroom, with the ultimate goal that students use their agency to navigate and impact the world around them. Students build voice and agency through the opportunities provided to them.

    New Brunswick teachers have been working at making classrooms places where there are opportunities for students to develop voice and agency. Castellano talks about what she sees. “With focusing on student voice and agency, students are always asked to justify their work. As educators, we try to create a ‘safe place’ for errors, even when the students can reason how they came up with their solution.”

    The district supervisors share that “Throughout [our] math classrooms, students are more willing to dive into solving tasks and rely on the discussion around strategies to persevere through solving them. By creating opportunities to talk through strategies for tasks, students are given the stage to express their thinking and reasoning about how they see the math. The more opportunities we create for students to discuss with each other, the more empowered students will feel to do so.” And with the district goal of creating lifelong learners and leaders, students will be better equipped to leverage their voice outside the classroom as well.

    Transitioning from traditional classrooms to ones that support student struggle and the opportunities for student voice and agency also requires supporting teachers. Harris and Gulotta share how teacher voice is fostered and heard:

    In New Brunswick, we consistently attempt to create opportunities for our educators to form communities that invite different points of view and reach solutions that not only reflect the views of all but also ultimately positively reach and affect our children. Teacher voice plays a commanding role in our steering committees, during our common planning time sessions with specialists, vetting our district-wide assessments and rubrics, and actively participating in professional development sessions that are ultimately adjusted to our students who present with varying needs with our strategic plan, vision, and PD goals in mind.

    Working toward stronger student agency requires the intentional creation of opportunities for students to be empowered and build voice, and that takes the concerted commitment and effort of dedicated educators at all levels.

    Tagged with: Agency and Voice, Equitable Instruction, Leadership, Math, Partner Spotlight