INTERESTING IDEAS
DISCUSSION DYNAMICS
(not just their own).
STRATEGIC SEQUENCE
Student Vital Actions
ALONE TOGETHER
PRINCIPLE: Understanding each other’s reasoning develops reasoning proficiency.  Students learn about mathematics by exploring their own and others' reasoning in problem-solving situations. Actively listening to peers increases the time focused on mathematical thinking and promotes the cognitive flexibility that is so highly prized in college and career. 
WELCOME CONJECTURES
EYES ON YOUR NEIGHBOR’S WORK
MOVES TO SUPPORT THIS STUDENT VITAL ACTION
TEAMWORK
Students talk about each other’s thinking
START SMALL 
PRINCIPLE: Understanding each other’s reasoning develops reasoning proficiency.  Students learn about mathematics by exploring their own and others' reasoning in problem-solving situations. Actively listening to peers increases the time focused on mathematical thinking and promotes the cognitive flexibility that is so highly prized in college and career. 
Next
EYES ON YOUR NEIGHBOR’S WORK The problem:  Students are not accustomed to learning from the work of their classmates once they have a problem solution, and they rarely aware of the value of thinking about problems and their solutions in different ways.  The move: Show and discuss work generated by students when working with mathematics concepts. Questions that may be used to prompt student are: "Did anyone approach the problem a different way?" “How is your thinking different than Damien's?”"What does Julie’s way of thinking help you understand?"“Do you think the Darryl's method would work with this kind of problem? Why or why not?”Teacher Tip:  If a suitable work sample is not available from a student, for example if no students are on the right track, use a fictional sample “from another class” and discuss that. 
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).
Why does this matter?
FOSTER PRODUCTION DISCUSSION DYNAMICS The problem:  Students may believe that the purpose of speaking in class is to give the right answer. Initially, students may focus on evaluating the performances of their peers. It is an innovation for students to approach whole class discussions as opportunities for everybody to learn.  The move: Assign students tasks that require responding to others’ thinking. (e.g. compare your approach to X’s… Identify the question to would ask Y...) Teacher Tips:  It will help them learn from these experiences if they have concrete tasks to do during presentations that orient them toward learning. They also benefit from being held accountable for restating the thinking of others.  Some teachers find sentence frames to be helpful in focusing students on the thinking of their peers and in encouraging intellectual consideration (e.g., “your approach helps me understand...” “I agree with this part of your idea because...” “I don’t think your approach will work because... ”). Following an important contribution, ask: “Who can repeat that? Who can say that in their own words? Who can restate what Juan just said?”
Previous
Most frequently used: during the initial phases of a lesson. during the "last third" of a lesson. within small groups. when the whole class is discussing the mathematics.
WELCOME CONJECTURES The problem:  Students may believe that teachers are only interested in the correctness of student answers. They will become more willing to share their thinking when they feel it is valued because it provides a learning opportunity. They will also be more likely to view their peers’ thinking in the same way.     The move: Model the atmosphere of conjecture that you would like to see in the small groups by demonstrating a genuine interest in the thinking of all students.  Teacher Tip:  Tell students that you are evaluating the quality of their engagement with the group and make these evaluations transparent and synchronous (e.g., participation quiz). Students are likely to be focused on producing answers. Developing norms of collaboration can take practice and persistence. Students believe that what is important is evaluated. Therefore, evaluating their collaboration can help improve it, especially if the evaluations are transparent.  
Most frequently used:
INTERESTING IDEAS The problem:  Students may not be aware that a problem they are working on can be approached in a variety of ways. The move: Call out students ideas about how to approach a problem as students are working.  Teacher Tip:  You can help students develop the language to express their ideas by giving them time to explain and offering them precise words to clarify their meaning.  Curiosity about various ways of approaching a problem will help students become flexible thinkers. In upper grades students may need frequent demonstrations that you are genuinely interested in their thinking, not just their answers. 
Most frequently used: during the initial phases of a lesson. within small groups. when the whole class is discussing the mathematics.
START SMALL The problem:  Being called upon to share an idea to an entire class or group can be overwhelming and prevent some students from focusing well on the math question. The move: Try these approaches from time to time: Ask students to work individually for a minute or so before sharing their thinking within groups.  Structure pair and small group work so that students explain the thinking of their partner(s). Ask students to explain their thinking in small groups prior to whole class discussions.Teacher Tip:  These practices gives students a chance to develop their thinking in lower-stakes settings, and increases the quality of presentations so that others can learn from them. It can bring more voices into the conversation. This practice is similar to sharing drafts in a writer response group. 
ALONE TOGETHER The problem:  Students work in isolation even during group activities. The move: Sometimes require sharing of scarce resources, (e.g. deliberately limit the number of cards, manipulatives, etc., to make sharing necessary.)  Teacher Tip:  Forcing students to share can help create a single object for group reflection. This move can be powerful for students that like to work alone. It is important to make sure resources and tools are shared equitably. You might want to assign one student the task of making sure sharing is equitable. 
Most frequently used: during the initial phases of a lesson. within small groups.
Most frequently used: during the "last third" of a lesson. within small groups. when the whole class is discussing the mathematics. after a classroom culture is established (advanced move).
TEAMWORK The problem:  Students do not see helping others understand as part of the mathematical work.  The move: Sometimes when working in small groups or pairs, require groups to come up with a single shared explanation. Tell students that you will ask anyone in the group to explain the group’s answer. Everyone in the group must come to a consensus understanding and be able to articulate it. Also try only responding questions from groups when nobody in the group can answer the question and everyone in the group can ask it. Teacher Tip:  It may seem frustrating to some students who work quickly to have to attend to the thinking of others. But research shows that the student explaining gains as much or more than the student being helped. 
STRATEGIC SEQUENCE The problem:  When students work in groups and then present to the class, other students may not be engaged in mathematical thinking.  The move: Choose the order of the groups presenting so the sequence is instructional and demonstrates a useful progression related to the mathematics. Call attention to how students represented the same thing differently. If a group's way of thinking is at or close to the instructional target, ask other students what is good about this way of thinking.  Teacher Tip:  Make sure students get to see and handle the work their peers create. Technology such as cameras and projectors can help with this.
Most frequently used: during the "last third" of a lesson. when the whole class is discussing the mathematics.
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 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 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 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. 
Students talk about each other’s thinking.
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. 
Students talk about each other’s thinking.
First Steps:Creating a Classroom Culture
BETA VERSIONPlease email us comments and corrections at mellinger@serpinstitute.org Thank you!
Students use academic language.
Back
Students revise their thinking.
Students say a second sentence.
All students participate.
Tap on any of the Student Vital Actions to explore teaching moves!
What is a Student Vital Action?
What is a Teaching Move?
Students engage and persevere.
ELLs produce language.
Students say a second sentence.
ELLs produce language.
Students engage and persevere.
Return
What is a Student Vital Action?
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. 
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.