WRITTEN FEEDBACK
INJECT NEW EXPERTISE
and their written work 
includes revised explanations and justifications.
PRINCIPLE: Revising explanations solidifies understanding. As students become more mathematically proficient and their reasoning improves, they should be able to identify flaws in their own and others' thinking. Revising work as a routine matter leads to better problem solving. 
CLARITY THROUGH WRITING
I DON’T GET IT
QUESTION SESSIONS
Student Vital Actions
REVISION SESSIONS
Students revise their thinking,
MOVES TO SUPPORT THIS STUDENT VITAL ACTION
QUOTE A CLASSMATE
and their written work includes revised explanations and justifications. 
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Most frequently used: during the initial phases of a lesson. during the "last third" of a lesson. when the whole class is discussing the mathematics. after a classroom culture is established (advanced move).
Students revise explanations.
I DON’T GET IT The problem:  Oral explanations by students can be rushed or difficult to understand for a variety of reasons. The move: If a student is presenting an explanation, play the role of not understanding and say “Could you help me make sense of your thinking? Could you revise your explanation?” Teacher Tip:  This slows down the discussion and provides an opportunity for a student to revise their thinking orally. Sometimes it is useful to model what a good explanation looks like. It is critical that the teacher is respectful of the student work and models how to think about revision without judgement.
Why does this matter?
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This move best suited for use: 
INTERJECT NEW EXPERTISE The problem:  Sometimes small group work may be unproductive becuase students don’t have the information needed.  The move: Identify a student who seems to get the missing concept or information and have him or her explain their thinking to the whole class while the class is working in small groups. Teacher Tip:  This move makes a student who has understood something that is useful for the whole class into an expert. 
Most frequently used: during the initial phases of a lesson. within small groups. after a classroom culture is established (advanced move).
QUOTE A CLASSMATE The problem:  Students need to value ideas for revision offered by classmates.  The move: Have student quote a classmate’s statement that inspired him or her to revise. Teacher Tip:  Quoting each other pushes students to listen to each other and process each other’s statements. By doing this students need to listen carefully to each other and evaluate their own and their peers’ words/statements.
Students revise their thinking.
Most frequently used: during the "last third" of a lesson. when the whole class is discussing the mathematics.
Most frequently used: during the "last third" of a lesson. when the whole class is discussing the mathematics. after a classroom culture is established (advanced move).
POST-PRESENTATION QUESTION SESSIONS The problem:  Students need to learn to ask for clarification to fill in any gaps related to another students presentation or representation.  The move: Students ask questions following group presentations to help improve their own thinking. Teacher Tip:  This move is about students efforts to relate their way of thinking to the presentation and deepen their understanding. If students don’t spontaneously ask questions, you may want to prompt. “Is anyone unclear? You can ask X to explain."
REVISION SESSIONS The problem:  Students rarely get to revise their work after they present it publcly.  The move: Students [sometimes] confer in small groups after whole class presentations to revise and refine their way of thinking Teacher Tip:  This process helps students attend to and integrate new ideas through revision. Small groups are a resource that can support learning from whole-class presentations.
Most frequently used: during the "last third" of a lesson. within small groups. after a classroom culture is established (advanced move).
CLARITY THROUGH WRITING The problem:  Students need to learn to document their thinking in writing in a way that is understandable.  The move: Students create written explanations and revise them to help clarify their thinking. Sharing creates opportunities to further improve their way of thinking. These practices also yield artifacts that students can refer to later to help with learning.  Teacher Tip:  Written explanations serve many purposes. Students who write for the above aims will get the most out of written explanations and revision.  At moments when you’d like to students to record something in writing, you can call out “Stop and Jot!” as a cue. 
WRITTEN FEEDBACK The problem:  Students need to learn to interpret and incorporate written feedback provided by others.  The move: Ask students to produce written explanations of their thinking. Then swap papers so that another student has an opportunity to give written feedback. Then swap back and ask the original student to write a revised version based on the feedback.  The same move can be done with partners or small groups.  Teacher Tip:  It is often difficult to revise without feedback. This move provides an opportunity for students to give each other feedback in writing. This feedback is then used to inform the revision of their thinking.
Why are some moves considered advanced? In general, the teacher moves in the 5 x 8 resource do not have prerequisites.  Any teacher should be able to try them and be successful. However, moves marked “advanced” may require more groundwork or particular persistence on the part of teachers in order to be successful. 
Why are some moves better for the initial phases of a lesson? The goal of classroom activities is to have students understand a concept and master the related skills. The challenge for teachers is to help the students move from their initial way of thinking about the problem(s) in the lesson toward the grade level target. In the first phase of a lesson, teachers elicit students' divergent ways of thinking about a topic by allowing students to work in pairs and small groups. Students begin with their own way of understanding, and, by working together, the class creates examples of different ways of thinking about the mathematics. The students’ different ways of thinking are the " stepping stones" that take them from their starting point to grade-level ways of thinking.  Representations of these ways of thinking (students’ work and their talk about it) are the “stepping stones” that teachers use to help students get to the target.  During this first phase of the lesson, it is helpful,teachers circulate among the groups to: 1) ensure that they are struggling productively with the mathematics and intervene to re-engage struggle when needed, 2) select student work that is representative of diverse ways of thinking and will help students step up to the target ways of thinking, and 3) determine the order in which student work will be presented. The easiest way of making sense of the problem should be presented first (usually concrete thinking), and the closest-to-grade-level way of thinking should be presented last. 
Why are some moves recommended for Small Groups of Students? While some moves can be effective across multiple class structures (pairs, small groups, whole class, et cetera), other moves are particularly effective with small groups, or are only relevant to small groups.  By noting the class structure, the 5 x 8 resource supports users who want to think about how to promote vital actions within particular class structures. 
Why are some moves better to use toward the conclusion (or final third) or a lesson? The goal of a lesson is to have all students reach a shared understanding of the target mathematics. In the first phase of the lesson, students may create various representations of different ways of thinking.  In the second phase, teachers can organize presentations of these ways of thinking and a summary of the mathematics that help students "step up to the target." Presentations begin with the easiest-to-understand way of thinking and conclude with the way of thinking that represents the lesson target. Following student presentations, the teacher can give a summary of the mathematics that involves quoting from student presentations, highlighting correspondences between the various representations shared, and opportunities for students to ask questions. By helping students connect their way of thinking with increasingly more complex ways of thinking, students are able to "step up to the target mathematics". 
Why are some moves recommended for the Whole Class? While some moves can be effective across multiple class structures (pairs, small groups, whole class, et cetera), other moves are particularly effective with the whole class, or are only relevant to whole-class structures.  By noting the class structure, the 5 x 8 resource supports users who want to think about how to promote vital actions within particular class structures. 
What is a Teaching Move?
Tap on any of the Student Vital Actions to explore teaching moves!
Students talk about each other’s thinking.
All students participate.
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What is a Student Vital Action?
First Steps:Creating a Classroom Culture
Students use academic language.
ELLs produce language.
Students say a second sentence.
Students engage and persevere.
Students say a second sentence.
ELLs produce language.
Students talk about each other’s thinking.
Students engage and persevere.
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The Common Core State Standards in mathematics are the first to articulate “practice standards:” expectations not only for what students should know, but for what they should be able to do. Teachers and administrators are now confronted with the questions: how would a classroom look if students were developing these practices? What would we expect to see students doing? A SERP team worked with Bay Area district partners to produce an answer to this question in the form of 7 “student vital actions” organized for simplicity and ease of use on a 5x8 Card. The vital actions are intended to be catalytic rather than comprehensive. There are many other things students do to learn, but these 7 are concrete, observable, and leverage related important learning actions. Learning is active; the vital actions attempt to capture the spirit of that action. They are intended as a productive starting point for shifting the focus from teacher actions to student actions–one that will be continuously improved as we learn more. We welcome your feedback! Please visit the 5x8 Card Website for additional information. 
What is a Student Vital Action?
Student action is influenced by the classroom culture and leadership of the teacher. A teacher plans, assigns, prompts, spots trouble and responds, sees opportunities and seizes them, sees disengagement and re-engages. When a teacher acts to make a teaching episode productive, we refer to the teacher action as "a move.” Every teacher has a repertoire of moves that serve different purposes in different situations.  The 5x8 “deck" lists a selection of teacher moves that promote student vital actions. Teacher moves can make lessons flow toward the mathematics of the unit, and they keep students with a variety of dispositions and prior knowledge engaged in the discussion. Teacher moves also advance the discussion from initial ways of thinking toward grade-level ways of thinking. Which move should a teacher use? It depends on the purpose and the circumstance. Often, more than one move is worth trying. If one doesn’t work, try another. Good teaching entails paying attention to students’ ways of thinking and responding to it. When observing, work from student actions (good and bad) back to the presence or the absence of teacher moves.