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Establish mathematics goalsto focus learning.
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Establish mathematics goalsto focus learning.
Effective teaching of mathematics establishesclear goals for the mathematics that students
are learning, situates goal within learningprogressions, and uses the goals to guideinstructional decisions.
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What mathematics is being
learned?
Why is it important?
How does it relate to what has
already been learned?
Where are these mathematical
ideas going?
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Implement tasks that promotereasoning and problem solving.
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Levels of Demand
Memorization
Procedures Without Connections
Procedures With Connections
Doing Mathematics
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Phil Daros Thoughts
Answer Getting: How can I teachmy kids to get the answer to this
problem?
Mathematics Getting: Whats the
mathematics my kids are supposed
to learn working on this problem?How can I get them to learn this
mathematics?
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Phil Daros Thoughts
American Teacher: How can Iteach my kids to get the answer to
this problem?
Japanese Teacher: Whats the
mathematics my kids are supposed
to learn working on this problem?How can I get them to learn this
mathematics?
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Use and connect mathematicalrepresentations.
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Use and connect mathematicalrepresentations.
Effective teaching of mathematics engages
students in making connections among
mathematical representations to deepenunderstanding of mathematics concepts and
procedures and as tools for problem solving.
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Facilitate meaningfulmathematical discourse.
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Facilitate meaningfulmathematical discourse.
Effective teaching of mathematics facilitates
discourse among students to build shared
understanding of mathematical ideas by
analyzing and comparing student approaches
and arguments.
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5 Practices (Smith and Stein, 2011)1.Anticipatingstudent responses prior to
the lesson.
2. Monitoringstudents work on and
engagement with the tasks.
3. Selectingparticular students to presenttheir mathematical work.
4. Sequencingstudents responses in a
specific order for discussion.5. Connectingdifferent students responses
and connecting the responses to key
mathematical ideas.
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Pose purposeful questions.
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Pose purposeful questions.
Effective teaching of mathematics uses
purposeful questions to assess and advance
students reasoning and sense making about
important mathematical ideas and
relationships.
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Question Types Gathering Information: recall facts,
definitions, or procedures
Probing Thinking: explain, elaborate, orclarify their thinking
Making the Mathematics Visible: discussmathematical structures and make
connections among mathematical ideas
and relationships Encouraging Reflection andJustification: reveal deeper
understanding of reasoning and actions
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What do you NOTICEand WONDER?
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Build procedural fluency fromconceptual understanding.
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Build procedural fluency fromconceptual understanding.
Effective teaching of mathematics builds fluency
with procedures on a foundation of conceptual
understanding so that students, over time, become
skillful in using procedures flexibly as they solve
contextual and mathematical problems.
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Standard algorithms are to be understoodand explained and related to visual models
before there is any focus on fluency.
Fuson and Beckmann (2012/2013)28
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Support productive struggle inlearning mathematics.
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Support productive struggle inlearning mathematics.
Effective teaching of mathematics consistently
provides students, individually and collectively,
with opportunities and supports to engage in
productive struggle as they grapple with
mathematical ideas and relationships.
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T h A ti t Cl b d
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Expectations for Students Teacher Actions toSupport StudentsClassroom-based
Indicators of Success
Most tasks that promotereasoning and problem solving
take time to solve, and frustrationmay occur, but perseverance in
the face of initial difficulty isimportant.
Use tasks that promotereasoning and problem solving;explicitly encourage students topersevere; find ways to support
students without removing all thechallenges in a task.
Students are engaged in thetasks and do not give up. The
teacher supports students whenthey are stuck but does so in a
way that keeps the thinking andreasoning at a high level.
Correct solutions are important,but so is being able to explainand discuss how one thoughtabout and solved particular
tasks.
Ask students to explain andjustify how they solved a task.
Value the quality of theexplanation as much as the final
solution.
Students explain how they solveda task and provide mathematicaljustifications for their reasoning.
Everyone has a responsibility andan obligation to make sense of
mathematics by asking questionsof peers and the teacher whenhe or she does not understand.
Give students the opportunity todiscuss and determine the
validity and appropriateness ofstrategies and solutions.
Students question and critiquethe reasoning of their peers and
reflect on their ownunderstanding.
Diagrams, sketches, and hands-on materials are important toolsto use in making sense of tasks.
Give students access to tools thatwill support their thinking
processes.
Students are able to use tools tosolve tasks that they cannot solve
without them.
Communicating about onesthinking during a task makes itpossible for others to help thatperson make progress on the
task.
Ask students to explain theirthinking and pose questions that
are based on studentsreasoning, rather than on the waythat the teacher is thinking about
the task.
Students explain their thinkingabout a task to their peers andthe teacher. The teacher asks
probing questions based on thestudents thinking.
Redefining student and teacher success. Adapted from Smith (2000, p. 382)31
Teacher Actions to Classroom based
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Expectations for Students Teacher Actions toSupport StudentsClassroom-based
Indicators of Success
Most tasks that promotereasoning and problem solving
take time to solve, and frustrationmay occur, but perseverance in
the face of initial difficulty isimportant.
Use tasks that promotereasoning and problem solving;explicitly encourage students topersevere; find ways to support
students without removing all thechallenges in a task.
Students are engaged in thetasks and do not give up. The
teacher supports students whenthey are stuck but does so in a
way that keeps the thinking andreasoning at a high level.
Correct solutions are important,but so is being able to explainand discuss how one thoughtabout and solved particular
tasks.
Ask students to explain andjustify how they solved a task.
Value the quality of theexplanation as much as the final
solution.
Students explain how they solveda task and provide mathematicaljustifications for their reasoning.
Everyone has a responsibility andan obligation to make sense of
mathematics by asking questionsof peers and the teacher whenhe or she does not understand.
Give students the opportunity todiscuss and determine the
validity and appropriateness ofstrategies and solutions.
Students question and critiquethe reasoning of their peers and
reflect on their ownunderstanding.
Diagrams, sketches, and hands-on materials are important toolsto use in making sense of tasks.
Give students access to tools thatwill support their thinking
processes.
Students are able to use tools tosolve tasks that they cannot solve
without them.
Communicating about onesthinking during a task makes itpossible for others to help thatperson make progress on the
task.
Ask students to explain theirthinking and pose questions that
are based on studentsreasoning, rather than on the waythat the teacher is thinking about
the task.
Students explain their thinkingabout a task to their peers andthe teacher. The teacher asks
probing questions based on thestudents thinking.
Redefining student and teacher success. Adapted from Smith (2000, p. 382)32
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Elicit and use evidence ofstudent thinking.
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Elicit and use evidence ofstudent thinking.
Effective teaching of mathematics uses
evidence of student thinking to assess progress
toward mathematical understanding and to
adjust instruction continually in ways that
support and extend learning.
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OKMathTeachers.com
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[email protected] | @_levi_ | 405-522-3525
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