Principles to Actions - CareerTech Presentation

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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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    http://okmathteachers.com/http://okmathteachers.com/
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    [email protected] | @_levi_ | 405-522-3525