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8. Interpreting student thinking to assess mathematical understanding, reasoning, and methods.

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8. Interpreting student thinking to assess mathematical understanding, reasoning, and methods.

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students expect to explain their thinking

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7. Anticipating what students might struggle with during a lesson and being prepared to support them productively through the struggle. 

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7. Anticipating what students might struggle with during a lesson and being prepared to support them productively through the struggle. 

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-encourages students to explain and reflect on their thinking as an essential component of meaningful mathematical discourse.

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5.  Teacher probes thinking and requires explanation and justification.  Students reflect on and justify their reasoning, rather than simply providing answers.

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5.  Teacher probes thinking and requires explanation and justification.  Students reflect on and justify their reasoning, rather than simply providing answers.

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Purposeful questions allow teachers to discern what students know.

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6.Teacher can provide students with opportunities to use their own reasoning strategies and methods for problems solving.

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6.Teacher can provide students with opportunities to use their own reasoning strategies and methods for problems solving.

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Often the emphasis on various strategies and solutions makes a simple problem much more complex than it should be. 

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Often the emphasis on various strategies and solutions makes a simple problem much more complex than it should be. 

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4. Students engage in purposeful sharing

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4. Students engage in purposeful sharing

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8. Identify what counts as evidence of student progress toward mathematics learning learning goals.

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8. Identify what counts as evidence of student progress toward mathematics learning learning goals.

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5. Allowing sufficient wait time so that more students can formulate and offer responses.

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5. Allowing sufficient wait time so that more students can formulate and offer responses.

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4. Making arguments based on evidence created by the student. How did you solve? Why does this work?

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4. Making arguments based on evidence created by the student. How did you solve? Why does this work?

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Students are active members of the discourse community as they explain they reasoning and consider the mathematical explanations and strategies of their classmates.

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3. Multiple ways to represent and not the most efficient or effective should be used. So we can see how everyone thinks.

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3. Multiple ways to represent and not the most efficient or effective should be used. So we can see how everyone thinks.

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7. Give students time to struggle with tasks. Ask questions that scaffold students' thinking.

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7. Give students time to struggle with tasks. Ask questions that scaffold students' thinking.

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4.  Teacher engages students in sharing their approach to problem solving.  Students identify how different approaches to solving a task are similar or different.

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4.  Teacher engages students in sharing their approach to problem solving.  Students identify how different approaches to solving a task are similar or different.

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4. Teachers can engage students in purposeful sharing of mathematical ideas, reasoning, and approaches, using varied representations.

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4. Teachers can engage students in purposeful sharing of mathematical ideas, reasoning, and approaches, using varied representations.

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5. Pose purposeful questions that encourage students to think and explain.

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The assumption of motivated students having a lively discourse regarding mathematical concepts is clearly evident throughout the text.

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The assumption of motivated students having a lively discourse regarding mathematical concepts is clearly evident throughout the text.

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Using multiple forms of representations to make sense of and understand mathematics.

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6. Provide students with opportunities to use their own reasoning strategies.

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6. Provide students with opportunities to use their own reasoning strategies.

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3. Ask students to make drawings or use other visual support to explain and justify their reasoning.

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3. Ask students to make drawings or use other visual support to explain and justify their reasoning.

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Use student eviden

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2. implement tasks that pomote reasoning and problem solving

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2. implement tasks that pomote reasoning and problem solving

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2. Engaged students should be discussing how to reason and solve ( beyond think pair sharing).  Discourse for understanding.

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2. Engaged students should be discussing how to reason and solve ( beyond think pair sharing).  Discourse for understanding.

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Sometimes conceptual understanding comes from procedural fluency.

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Sometimes conceptual understanding comes from procedural fluency.

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Productive struggle.

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1. It's important to establish clear goals.

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1. It's important to establish clear goals.

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2. Engage students in solving problems and discussing outcome.
3. Connect and explain tools used.
4. Compare students approaches and arguments.
5. Teach how to use purposeful questions.
6. Build fluency
7. Support opportunities to engage in productive struggles.
8. Use evidence of student thinking

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4.Facilitate discourse among students by positioning them as authors of ideas, who explain and defend their approaches.

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4.Facilitate discourse among students by positioning them as authors of ideas, who explain and defend their approaches.

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1. What is the purpose of the lesson? Why am I learning this? Why should I care? How is this meaningful

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1. What is the purpose of the lesson? Why am I learning this? Why should I care? How is this meaningful

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2. Teacher can encourage students to use a varied approaches and strategies to make sense of and solve tasks. 

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2. Teacher can encourage students to use a varied approaches and strategies to make sense of and solve tasks. 

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3.  Teacher is asking students to make math drawings to justify their reasoning.  Students are sketching diagrams to solve problems.

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3.  Teacher is asking students to make math drawings to justify their reasoning.  Students are sketching diagrams to solve problems.

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Build from conceptual understanding to procedural fluency.

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2.Identify how the goal fits into the progression  of learning.
3. Ensure students are learning.
4. Encourage student's learning.
5.Use purposeful questioning.
6.Build fluency on foundational concepts
7.Provide opportunity to engage in the productive struggle of learning.
8.Use evidence of student thinking.

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TASKS

REPRESENTATIONS

MATHEMATICAL DISCOURSE

POSE PURPOSEFUL QUESTIONS

BUILD PURPOSEFUL FLUENCY

SUPPORT

USE EVIDENCE

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1. Using the mathematics goals for lesson planning and reflection

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1. Using the mathematics goals for lesson planning and reflection

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Posing questions that make sense of why to the students.

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Shared understanding

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2. Tasks that promote reasoning & problem solving

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2. Tasks that promote reasoning & problem solving

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Teacher encourages students to use a variety of strategies to make sense and solve task.
Students use tools and representations as needed to support thinking.

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2.  Teacher regularly poses tasks requiring high level of cognitive demand.  Students use tools and representations to support their problem solving.

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2.  Teacher regularly poses tasks requiring high level of cognitive demand.  Students use tools and representations to support their problem solving.

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Making connections

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2. Students take responsibility for making sense of tasks by drawing on and making connections with their prior understanding and ideas.

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2. Students take responsibility for making sense of tasks by drawing on and making connections with their prior understanding and ideas.

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3. Ask students to make math drawings or use other visual supports to explain reasoning.

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3. Ask students to make math drawings or use other visual supports to explain reasoning.

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2.  discussing and reasoning

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1. Teacher establishes clear goals of mathematics instruction.  Students assess and monitor their progress toward the goals.

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1. Teacher establishes clear goals of mathematics instruction.  Students assess and monitor their progress toward the goals.

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2. Posing tasks on a regular basis that require a high level of cognitive demand.

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2. Posing tasks on a regular basis that require a high level of cognitive demand.

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1. Clear learning goals focus the work of teaching and student learning.

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1. Clear learning goals focus the work of teaching and student learning.

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Teacher establishes clear math goals in a lesson, over series of lessons or a unit.
Students use the goals to stay focused and improve understanding of math content.

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1.Using mathematical goals to guide lesson planning.

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1.Using mathematical goals to guide lesson planning.

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1.  Establishing clear goals and using them to guide instruction.

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1.  Establishing clear goals and using them to guide instruction.

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2. Engaging students in tasks that promote mathematical reasoning.
3.Guiding students to help them make mathematical connections while solving problems.
4.Facilitating discourse among students.
5. Teacher poses questions to help students develop reasoning skills.
6. Teacher helps students to build a strong foundation of Mathematical problem solving skills.
7.Teacher allows for productive struggle time.
8. Teacher assesses students' progress in order to identify the next steps for instruction.

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Engage in productive struggle

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3-Use and Connect Mathematical Representation 

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3-Use and Connect Mathematical Representation 

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-Important connections among contextual, visual, verbal, physical and symbolic representation...

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2. Motivating students
3. Proper Representation
4. Encouraging discourse
5. Going deeper
6. Independent exploration
7. Modeling
8. Differentiated instruction
9.Tieing up loose ends

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Goals: "Discussing and referring to the mathematical purpose and goal of a lesson during instruction to ensure that students understand how the current work contributes to their learning." I think mentioning the goal more than once is a waste of time. If it is necessary to mention it again, then the lesson is too convoluted and is straying too far away from the goal. Or the lesson sucks.

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Goals: "Discussing and referring to the mathematical purpose and goal of a lesson during instruction to ensure that students understand how the current work contributes to their learning." I think mentioning the goal more than once is a waste of time. If it is necessary to mention it again, then the lesson is too convoluted and is straying too far away from the goal. Or the lesson sucks.