Expectations:

                                                                             Growth Trajectory

      Emerging  (1)                             Applying (2)                                  Transforming  (3)

A. Teachers pose high quality questions and problems that prompt students’ engagement and thinking about the content of the lesson.

Level:  (0)  (1)  (2)  (3)

• Questions are cognitively demanding (DOK Level 2)
• Questions are open-ended
• Questions and prompts are set within real-world context

• Questions are cognitively demanding (DOK Level 3)
• Prompts have two entry points
• Questions and prompts are mathematically relevant and used to solve real-world problems

• Questions are cognitively demanding (DOK Levels 3-4)
• Prompts have multiple entry points
• Questions and prompts require students to explore and understand the mathematical concepts, processes, and/or relationships

B .Teachers use variation in students’ solution methods to strengthen other students’ understanding of the content

Level: (0)  (1)  (2)  (3)

• Cognitively engage some students
• Afford students time to share out different strategies for solving the problem
• Have students write about how they solved the problem

• Cognitively engage most students
• Provide time to examine and address solutions that are incorrect
• Have students agree or disagree with each other’s solution methods

• Cognitively engage all students
• Have students expand on each other’s mathematical solutions
• Connect different students’ responses to key mathematical ideas
• Create mathematical visual records of the class discussion to show varying solutions

C  Teachers provide opportunities for students to engage in conversations about each other’s thinking, critique each other’s thinking, and construct viable arguments.

Level:  (0)   (1)   (2)   (3)

• Provide time for peer-to-peer communication and discussion
• Have students listen to and read arguments of others
• Have students use pictures and tools to prove or disprove an idea
• Promote the use of sentence starters to facilitate academic conversations
• Students use academic language, with support and/or prompting

• Facilitate peer discussion on why incorrect solutions have faulty logic
• Encourage students to question the mathematical reasoning of others
• Prompt students to challenge each other’s thinking and ask for clarification from their classmates
• Students use academic language without stems and minimal prompting

• Coach students on how to participate in peer-led mathematical discussions
• Use students’ thinking to propel discussions
• Require that students use explanations, diagrams, graphs, tables and mathematical examples to support their argument
• Students talk to each other and use academic language without prompting/ stems to engage in debates; defend and challenge thinking; explain how they solve problems.

D. Teachers ask students to explain and justify work and provide feedback that helps students revise their thinking and work.

Level:  (0)   (1)   (2)   (3)

• Use number talks that engage students in discourse
• Identify misconceptions through meaningful discussions
• Coaches students to use academic language in explanations that help clarify their thinking

• Facilitate discussions of students’ explanations and use probing questions
• Provide timely task-specific feedback after instruction
• Explore how students respond to feedback
• Require students to explain their thinking

• Prompt student to re-organize and consolidate their mathematical thinking and understanding
• Provide ongoing and timely task-specific feedback during and after instruction
• Provide time and expect that students revise their work based on feedback, including revision of explanations and justifications
• Have students explain and justify mathematical ideas and strategies with sufficient and significant mathematical details