PLASTIC BRAIN

VARIETY OF SKILLS

at points of difficulty, challenge, or error.

IT’S NOT A RACE

HIGHLIGHT THE ARC OF LEARNING

PRINCIPLE: Productive struggle produces growth.
When students persist in making sense of a challenging problem and trying different strategies for solution, they are more likely to learn the mathematics than students who give up quickly or avoid challenge to the greatest extent possible.

NOT ABOUT INTELLIGENCE

Student Vital Actions

CONVEY THE MESSAGE

Students engage and persevere

SHOW CONFUSION

MOVES TO SUPPORT THIS STUDENT VITAL ACTION

MASTERY AND EXTENDED PROBLEMS

Next

Students engage and persevere.

Why does this matter?

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.

IT’S SUPPOSED TO BE HARD!
The problem:
Students often do not understand the learning purpose behind struggle. Students often make negative self-attributions when they struggle and disengage as a result.
The move:
Showing what you already know is not learning. Explain to students that learning requires struggle. Working hard to make sense of new concepts for themselves allows them to build a deep and lasting understanding. Praise effort and persistence. Use prompts to help students reflect on the effectiveness of their strategies.
Teacher Tip:
Students sometimes need support to struggle with the mathematics in ways that will result in learning. It is helpful to anticipate misconceptions and be prepared with prompts and questions that can help student move beyond them. It can also help to teach more generic strategies for managing “being stuck” and related frustrations so students can become re-engaged with the mathematics.

Previous

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).

ASK ANOTHER QUESTION
The problem:
When students provide an incorrect answer, teachers sometimes move on to another student quickly in order to avoid embarassing the student.
The move:
Ask a student who has given a wrong answer additional questions to explore his or her thinking. Demonstrate curiosity about that thinking.
Teacher Tip:
Moving on when a student gives a wrong answer signals that the teacher doesn’t think the student is capable of thinking and revising. If the student is genuinelt stuck, expand the conversation to include others, but point out how valuable the wrong answer was in launching a productive learning opportunity.

EFFORT OVER SMARTS
The problem:
Students believe that if getting an answer correct means they are smart, then getting an answer wrong demonstrates they are not smart.
The move:
Do not praise intelligence. Do praise effort.
Teacher Tip:
Draw attention to the value in considering and learning from mistakes.

PLASTIC BRAIN
The problem:
The concept of brain development in unfamiliar. Students often think that people are born more or less intelligent.
The move:
Provide evidence of brain plasticity.
Teacher Tip:
Research has shown that students can internalize the message that the brain changes with effort by writing to real or fictitious students about hoe the brain grows…
When students work hard and struggle, you may want to remind them that they are growing new dendrites.

Most frequently used:
during the "last third" of a lesson.
when the whole class is discussing the mathematics.

USE BOTH MASTERY EXPERIENCES AND EXTENDED PROBLEMS
The problem:
Students may expect that they should immediately know how to do any assignments they are given.
The move:
Structure mastery experiences for students at the start of course. Then, introduce harder “thinking problems” and discuss their value openly with students so they are aware that they are not expected to progress through them quickly, and may not be able to get the right answer. But you made the problem hard to get them thinking hard.
Teacher Tip:
If assignments are going to be challenging, require extended exploration, and/or may not necessarily yield solutions, help students anticipate these experiences.

Most frequently used:
during the initial phases of a lesson.
within small groups.
when the whole class is discussing the mathematics.

ARC OF LEARNING
The problem:
Students experience anxiety when confronted with with challenging new topics.
The move:
Describe for students how they have developed understanding in the past during previously unfamiliar learning activities.
Teacher Tip:
Remind them that they aren't supposed to understand at first, and help them recognize the facility they develop over time. Highlight that things that once seemed difficult are now easier because they are developing new capacities.

Most frequently used:
during the initial phases of a lesson.
when the whole class is discussing the mathematics.

CONFUSION ABOUT CONFUSION
The problem:
Students often fear that they will not be able to solve a problem if they do not see a path immediately. Frequently, to manage emerging negative feelings (frustration, anger) they disengage. Making a space for students to share thinking that has not yet proven productive can promote perseverance and help students recognize that confusion is part of the learning process.
The move:
Students share their thinking and attempts even when they have not found a viable solution. Sometimes teachers share initial uncertainty in response to questions from students and model the process of figuring something out.
Teacher Tip:
You may want to demonstate being in “learning mode” by telling students you’re not sure of something from time to time. You might ask, “Was this a good problem, or did I just choose something too confusing?” “Was that a helpful assignemnt, or was it too easy?” Model asking for feedback and getting it wrong as a strength.

IT’S NOT A RACE
The problem:
Effort and engagement is what leads to growth. Rewarding groups that finish quickly undermines this message.
The move:
When some groups are “finished” earlier than other ask them to analyze their work and seek places to revise their explanation so more students will understand it, or look for an alternative approach.
Teacher Tip:
Provide multiple avenues for students to demonstrate their mathematical knowledge that count towards grades. If students believe that they will be able to demonstrate what they have learned and it will influence their grades they will be more likely to persevere. They will be more focused on the goal of learning. In-class assignments, presentations, homework, one-on-one interviews, journals etc., can all be valid forms of assessment. If students who learn material more slowly than their peers are regarded positively for having learned, they will be more likely to persevere.

This move best suited for use:

Most frequently used:
during the "last third" of a lesson.
within small groups.
when the whole class is discussing the mathematics.

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 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.

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.

ELLs produce language.

BETA VERSIONPlease email us comments and corrections at mellinger@serpinstitute.org
Thank you!

Students engage and persevere.

Students talk about each other’s thinking.

First Steps:Creating a Classroom Culture

Students say a second sentence.

All students participate.

Students use academic language.

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Students revise their thinking.

What is a Student Vital Action?

Tap on any of the Student Vital Actions to explore teaching moves!

What is a Teaching Move?

Students say a second sentence.

ELLs produce language.

Students talk about each other’s thinking.

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.