Rosita’s Reads December 1

This talk is rooted in the belief that self-organized learning will shape the future of education and that children with access to the internet can learn anything by themselves. Give it a listen and consider the possibilities for the changes that may, inevitably, come.


The Future of Learning

Sugata Mitra
October 2018

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

Rosita’s Reads November 24

This four-part report compiled by the LIFE Diversity Consensus Panel explores a set of principles that educational practitioners, policy makers, and future researchers can use to understand and build upon the learning students from diverse groups have coming into school. The assumption and challenge are for educators to honor and make use of the informal learning that occurs in the homes and communities of students—which is where most learning takes place—to reduce the “gap” between marginalized students and mainstream students. 


4 Go-To Learner-Centered Routines to Bolster Math Discussions, In-Person and Online

By Laurie Speranzo and Kristin Klingensmith

Institute for Learning

Educators who believe that every student has meaningful ideas to contribute can use learner-centered routines to ensure that every student is actively engaged in a math discussion. These routines create space for students to reason about the mathematics of the task in ways that make sense to them using their knowledge from both inside and outside of the classroom. Using learner-centered routines gives teachers multiple opportunities for formative assessment within a single lesson from which they can make adjustments in real-time to better meet where students are in their understanding.

To School Leaders & Coaches

These routines support learning at all ages, so consider if and how you might use these routines during in-person and online professional learning to support deeper understanding of the ideas being explored and discussed with other educators.

Based on two decades of experience with in-person teaching and learning and several years of engaging in online teaching and learning, here are four go-to learner-centered routines to use while facilitating meaningful mathematics discussions in-person and online.

  1. Turn and Talk
  2. Stop and Jot
  3. Step Back
  4. Quick Write

When used consistently, these routines enhance Accountable Talk® discussions in mathematics, support engagement, and scaffold learning.

1. Turn and Talk

Why Use a Turn and Talk?

Turn and Talks create space for students in groups of 2 to 3 to share their ideas related to the mathematics being explored and hear the ideas of others. Turn and Talks are an informal way for teachers to assess (little “a”) where students are in their thinking. Teachers can and should use the insights gained from a Turn and Talk to inform the direction of the mathematics discussion.

Tips for Using Turn and Talks

Turn and Talks are low-risk talk opportunities that can be useful throughout a discussion because students get a chance to “try out” and “rehearse” their thinking alongside others. Turn and Talks are a great go-to after 10 seconds or more of wait time when students need to talk through their thinking before being ready to share with the whole group. If you are familiar with Accountable Talk moves, Turn and Talks are particularly beneficial when used in combination with the moves: challenging, pressing for reasoning, or expanding reasoning.


Adapting Turn and Talks for Online Discussions

In person Turn and Talks are as easy as turning and talking with a neighbor, and allow the teacher to listen in to get a feel for student thinking. Turn and Talks are not as easy to replicate online but are still important for supporting student thinking and engagement.

For online Turn and Talks try

  • moving students into breakout rooms with just 2-3 people for a very brief amount of time.
  • asking students to mute their mics and say their thinking aloud to themselves.
  • establishing Turn and Talk partners so that students can chat privately with a pre-assigned peer via the chat box.

Though online Turn and Talks do not afford the opportunity to “overhear” the Turn and Talk of others, all of the adaptations offer students’ the opportunity to put their thinking into words and to rehearse how they want to express their understanding. Because students cannot be overheard, teachers may want to have a few students share out to the class what they said aloud to themselves or what was shared during their exchange with a peer. If planned in advance, a teacher may pair a Turn and Talk with a multi-select poll to see which ideas resonated with the students following their Turn and Talk.

2. Stop and Jot

Why Use a Stop and Jot?

Stop and Jots provide each student time to collect and record their thinking as it relates to the mathematical idea or relationship currently being discussed. Stop and Jots are commonly used during critical points of discussions and usually involve students adding something new to their written work. This provides teachers the chance to casually check on student thinking as they walk around and glance over students’ shoulders. The information gathered from glancing at students’ Stop and Jots can be used to determine the pathway of the discussion.

Tips for Using Stop and Jots

Because Stop and Jots start out as private thinking time, students tend to feel more comfortable expressing their initial, and possibly incomplete or unfinished, thoughts. Stop and Jots can ask students to write about how two concepts are related, create another or connect two representations, record another/different equation, describe a situation, etc. When using a Stop and Jot, teachers may look for patterns in responses, unique responses, and responses that suggest over-generalizations, to determine what to “take up” next in the discussion.


Adapting Stop and Jots for Online Discussions

During online discussions, it isn’t as easy to sneak a peek at what students jot, so consideration has to be given to low-risk ways for students to share their jotting.

For online Stop and Jots try

  • asking students to write their thoughts on paper and having those who are comfortable share orally or, in the case of visual models or equations, by holding the paper up to the camera.
  • inviting students to type or draw in a shared document.
  • having students use the chat box to share their thinking with the teacher only or with the whole group.
  • using (or a similar platform) so that students can text their responses anonymously and have them collected on a single shared screen.

When making a choice about how to have students share their ideas after a Stop and Jot, keep in mind that some students may feel more comfortable sharing what they wrote verbally than actually sharing their writing. Things like spelling, sentence construction, and use of formal math language are not and should not be a focus during Stop and Jots.

3. Step Back

Why Use a Step Back?

Step Backs offer an opportunity for students to reflect verbally on key learnings from across the entire discussion and to share their conclusions or generalizations with the whole group. Step Backs offer teachers a glimpse into how students are taking stock of the ideas being discussed and their progress toward the mathematical learning goal. They also allow students to again hear the salient and mathematically critical ideas that surfaced during the discussion.

Tips for Using Step Backs

Step Backs are best used following big “ah ha” moments related to the learning goals for the lesson. These moments may occur in the middle or at the end of a discussion and sometimes both. Use Step Backs to create space for students to ponder and consider the Why of the big “ah ha” moment(s).


Adapting Step Backs for Online Discussions

Step Backs do not need to be adapted for online discussions, but they may be used more frequently to help students hold on to critical ideas as understanding is constructed.

For online Step Backs try

  • pre-determining several places during the discussion to do a Step Back so that the discussion has multiple summary points that culminate by the end of the discussion.
  • having at least one or two students “say back in their own words” the teacher’s summary so that others can hear it more than one time and students have a chance to paraphrase the key ideas.
  • varying who is responsible, teacher or students, for summarizing the discussion at a given point.

4. Quick Write

Why Use a Quick Write?

Quick Writes create space for each student to put their thoughts into writing, allowing them to take stock of their knowledge, reflect on their learning, and/or apply their insights, generalizations, and conclusions in a new way. Quick Writes can and should be used as formative assessment because they contain evidence of each student’s thinking and reasoning, especially after engaging in an Accountable Talk discussion.

Tips for Using Quick Writes

Quick Writes can be used at the beginning of a unit of study to learn about students’ prior knowledge. Quick Writes can also be used toward the end of or following a math discussion or summary. In this case, it is important to make sure that the Quick Write relates directly to the mathematical learning goal of the lesson.  Additionally, students and teachers can gain insight about how learning is progressing over time by using Quick Writes after each lesson in a series.


Adapting Quick Writes for Online Discussions

Quick Writes can be used when teaching online in much the same way they are used in-person. The adaption to Quick Writes is mostly about how students will submit them.

For online Quick Writes try

  • having students write a response in the chat but wait until everyone is done writing before sending it so that no one’s thinking is compromised by reading others’ responses.
  • setting up a Padlet (or similar applet) for students to submit their responses and comment on the thoughts of others, using a combination of multi-media options: text, pictures, drawings, and video.
  • having students submit their response via an online form or through email.
  • using a shared document or slide deck.

When making a decision about how to have students submit their Quick Writes, consideration should be given to what the submission option affords. Some options only allow written responses, while other options offer the ability for students to create images and upload pictures or video.

The second article in this two-part series will be released December 1 and will explore how these four learner-centered routines can be used to foster student voice and agency and support students in developing positive mathematical identities as doers of mathematics.


Tell Us About the Learner-Centered Routines You Use

  • Which of these routines do you already use? How is it going?
  • Which of the routines might you add to your toolbox? Why?
  • What other routine do you recommend? Why?

Tell us here.

Tagged with: Accountable Talk® Discussions, Equitable Instruction, Formative Assessment, High-Leverage Teaching Practices, Online Instruction, Principles of Learning

Rosita’s Reads November 17

Read the 1987 AERA Presidential Address by IFL founder Lauren Resnick, who speaks to the popular wisdom that common sense outweighs school learning for getting along in the world—that there exists a practical intelligence, different from school intelligence, that matters more in real life. Recognizing the duality of learning can help us understand the various ways to honor and leverage learning done outside of schools to complement and balance the education done in-schools.