GET READY
ELICIT ELABORATION
(spontaneously or prompted by the teacher or another student) to explain their thinking and connect it to their first sentence.
FIND THE LOGIC
MAKE REASONING PUBLIC
MOVES TO SUPPORT THIS STUDENT VITAL ACTION
PRINCIPLE: Logic connects sentences A hallmark of the understanding prioritized by the CCSS-M is the ability to use mathematical reasoning to construct and defend an argument (this is what I did and why it makes sense). Brief, single-sentence student utterances are generally insufficient for a viable argument. Teacher questioning can facilitate students’ logical thinking and explaining.
IS THAT LEGIT?
Students say a second sentence.
TRY TO GENERALIZE
Student Vital Actions
LISTEN FOR IDEAS
Most frequently used:
Students say a second sentence. 
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.
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ELICIT ELABORATION The problem:  Sometimes students answer with one-word or unelaborated responses. The move: Ask and encourage students to ask: Can you tell me more about that? Why do you think that?How do you know...you have more/less? It is growing/shrinking? It is faster? Slower?What changed and what stayed the same?Teacher Tip:  Students may be accustomed to providing a one-word answer and having the teacher turn in into an “explanation.” These questions help to elicit the student thinking and change their expectations. They need to know that you have the patience to give them the time they need to construct an explanation. 
Why does this matter?
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Most frequently used: during the "last third" of a lesson. when the whole class is discussing the mathematics.
IS THAT LEGIT? The problem:  Sometimes students don’t notice that a solution is completely incompatible with the situation presented in the question. The move: Ask and encourage students to ask: Is that an answer that makes sense for this problem? How do you know?Teacher Tip:  Requiring students to connect their conclusions with the problem context builds the habit of examining the plausibility and meaning of solutions. 
GET READY The problem:  Some students have trouble developing thoughtful explanations spontaneously.  The move: Students are given time to develop their ideas and prepare to explain their thinking so the other students can understand them. Teacher Tip:  Some students are much quicker than other. If some students are done and looking impatient, you might: A) ask them to prepare an explanation for a student 2 years younger; B) have cards on hand with wrong answers. You can have them choose a card and explain why the answer is wrong; C) let them start on a homework problem. 
Most frequently used: during the initial phases of a lesson. within small groups. when the whole class is discussing the mathematics.
LISTEN FOR IDEAS The problem:  Students are hesitant to share ideas "along the way” when discussing math (in contrast to when they have a solution to offer).   The move: Pay attention to and engage with student thinking prior to solution sharing. Teacher Tip:  Help students develop the language to express their ideas and keep the student thinking the subject of the conversation. Students will be more willing to share their thinking when they know their ideas will be considered.
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).
MAKE REASONING PUBLIC The problem:  When students present an answer to the class, they may perceive that they are responsible only for sharing an answer instead of sharing the thinking and process that led to an answer. The move: Ask and encourage students to ask: How did you get that answer? Why did you (reference student work e.g., put a 1 over there; divide both sides by six)Teacher Tip:  Some students will have better or more efficient strategies than others. Remaining neutral about the student’s approach allows all strategies to be considered before the benefits of some over others are called out. 
TRY TO GENERALIZE The problem:  Student perceive math as many isolated and unrelated activities.  The move: Ask and encourage students to ask: Is it always true? Sometimes true?  What about with very small, large, or negative numbers?Teacher Tip:  These questions may be helpful additions for students who work fast and begin to get bored. When they share their answers, you might ask a student who find generalizing more more challenging whether they understand the explanation. It contributes to a productive classroom culture if students are valued for being able to be clear enough for other students to understand. 
Most frequently used: during the "last third" of a lesson. within small groups. when the whole class is discussing the mathematics.
FIND THE LOGIC The problem:  Students present an explanation that contains two statements that are not connected logically (but could be). The move: Ask and encourage students to ask: “You just said [sentence A] and [sentence B] (quote students work). Could you help me understand how these sentences are connected?” Teacher Tip:  In earlier grades in particular, students frequesntly assume that if something makes sense to them, it makes sense to others too. They need reminders that logic that connects their sentences needs to be clear if others are to understand. 
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. after a classroom culture is established (advanced move).
This move best suited for use: 
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. 
Tap on any of the Student Vital Actions to explore teaching moves!
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ELLs produce language.
Students engage and persevere.
First Steps:Creating a Classroom Culture
Students talk about each other’s thinking.
Students say a second sentence.
BETA VERSIONPlease email us comments and corrections at mellinger@serpinstitute.org Thank you!
Students use academic language.
Students revise their thinking.
All students participate.
What is a Teaching Move?
What is a Student Vital Action?
ELLs produce language.
Students talk about each other’s thinking.
Students engage and persevere.
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. 
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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.