We believe that productive talk about teaching and learning practices begins with the development of a shared language. We adapted many of the terms below from a variety of sources, and continue to push ourselves to refine our working definitions.

• add-on - A teacher move in which students are asked to add ideas to their own or other students' thoughts which may be used to prompt additional discussion or encourage other students to become a part of a discussion.
• audience shift - The shift of talk or interaction from teacher-to-student, student-to-student, and/or student-to-teacher that occurs as a result of class discovery and discussion during a math activity.
• celebrate meaningful success - Recognizing in a public way, significant mathematical statements or accomplishments of students.
• classroom norms - Practices such as exploring, thinking, sharing strategies, and collaborating that afford opportunities for students to engage in conceptual thinking.
• IRE- Initiation (by the teacher) Response (by the student), and Evaluation (by the teacher) One of several talk formats.
• listening - A classroom norm that allows students/teachers opportunity to learn from each other's  ideas, strategies, or conceptual understanding of mathematics.
• making judgment calls - Knowing when to use your teacher moves to get the class back on track and knowing when to let the class take you down a different path.
• making reasoning public - Sharing and recording students' ideas for the purpose of reflection and revision.
• mathematical knowledge for teaching - This refers to the knowledge, skills and habits of mind a teacher must have in order to effectively support student learning.  Examples include knowing mathematical content, knowing when to scaffold a student’s mathematical thinking and being able to analyze student misconceptions.
• mathematical participation - Present throughout  student-centered instruction, it requires students to think conceptually about mathematics in order to defend an argument or to understand relationships among multiple strategies or math concepts.
• mathematical practices - The tools, skills, habits of mind, actions  involved in learning and teaching mathematics. 
• revoicing - Repeating all or part of something a student says to help clarify or make meaning available to others, give students an opportunity to hear something again, connect students ideas or focus on a change in a discussion.
• richness of task - Degree to which a task leads the students to further insights, requires multiple strategies and resources, or generally challenges the student to reach beyond a simple understanding.
• socialmathematical norms - Standards that guide the quality of mathematical discourse which  support high cognitive demands.
• status - A term used to describe interactions of students in a particular group setting. 
• student agreements - When a student supports or challenges another student’s answer, method, or statement.
• student restatements - Asking a student to rephrase another student's explanation/conjecture.
• teacher consistency - An important element in establishment of social and sociomathematical norms in the classroom.
• teacher demeanor - A teacher’s attitudes and actions that influence  rapport with students .
• teacher moves - Teacher actions used to keep the class focused on  learning objectives.
• teacher questions - Questions a teacher asks to direct the discussion, obtain a particular answer, or bring the discussion back to the intended focus.
• teacher response - The verbal and non-verbal responses teachers give to students.  Examples: questions; validations; teacher moves
• wait time - A period of at least 10 seconds used to give students time to think before answering.
• what is valued? - The social or sociomathematical norms that establish what a teacher considers important.