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Alaska English_Language Arts _ Mathematics Standards Introduction

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					A Look at the Math
Practices in Action
    m Alignment Institute
    12
Session Goals

• Build understanding of the Standards for
  Mathematical Practice
• Enhance skills in identifying the extent to which
  students exhibit the Standards for Mathematical
  Practice
• Consider the implications of the Standards for
  Mathematical Practice on the classroom.
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           012
Standards for Mathematical Practice

The Standards for Mathematical Practice describe
varieties of expertise that mathematics educators
at all levels should seek to develop in their students.
These practices rest on important “processes and
proficiencies” with longstanding importance in
mathematics education.

•   National Council of Teachers of Mathematics’ Process Standards
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•   National Research Council’s Strands of Mathematical Proficiency
               012
Standards for Mathematical Practice
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning
   of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
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7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
              12
Structuring the Math Practices


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         12
Pairs of Practices
   Reasoning and Explaining
   2. Reason abstractly and quantitatively
   3. Construct viable arguments and critique the reasoning of others

   Modeling and Using Tools
   4. Model with mathematics
   5. Use appropriate tools strategically

   Seeing Structure and Generalizing
   7. Look for and make use of structure
   8. Look for and express regularity in repeated reasoning

   Overarching Habits of Mind of a Productive Mathematical Thinker
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   1. Make sense of problems and persevere in solving them
   6. Attend to precision
                                            Adapted from (McCallum, 2011)
               012
    Examine a Pair of Practices
   1. With a partner, choose one of
      the two pairs of practices:
      Reasoning and Explaining or
      Modeling and Using Tools.

   2. Review the practice description
      and grade span descriptors for
      one of the two practices. Share
      an insight you had into the
      practices with your partner.


2012-13 Curriculum Alignment Institute
November 8-9, 2012
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2012-13 Curriculum Alignment Institute
November 8-9, 2012
 Classroom Vignette
    In our session, we will examine
    Standards for Mathematical Practice
    through a classroom vignette.

    Consider:

        What is the nature of mathematical tasks in
        the classroom?

        What do you hear or see in a mathematics
        classroom that is working to build the
        Standards for Mathematical Practice?


2012-13 Curriculum Alignment Institute
November 8-9, 2012
    Video Rental Task
                                          Online Flix          Mail Flix
        Create verbal                                       $18 per month
        and tabular                      $12 per month
                                                             regardless of
        representations                    plus $1 per
        of the 3 DVD                      movie rented
                                                            the number of
        rental plans                                        movies rented
        shown.
        Do the three                               Movie Buster
        plans ever cost
        the same?                                   $3 per movie
                                                       rented




2012-13 Curriculum Alignment Institute
November 8-9, 2012
     Opportunities in Tasks
     for both Content and Practice

      1. Individually, complete the task.
      2. Then work with a partner to compare your
         work and discuss the following questions:
           a) What mathematics content is needed to
              compete the task?
           b) What aspects of the explaining and
              modeling Standards of Practice might
              students need to complete the task?



2012-13 Curriculum Alignment Institute
November 8-9, 2012
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2012-13 Curriculum Alignment Institute
November 8-9, 2012
   Video Rental Task: Student H Sample
                                         Movies
                    1       2        3   4        5    6      7
     Movie
     Buster        $3      $6       $9   $12 $15      $18    $21
                                         Money

                    1       2        3   4        5    6      7
     Online
     Flix          $13 $14         $15   $16 $17      $18    $19


                    1       2        3   4        5    6      7
      Mail
      Flix         $18 $36         $54   $72 $90      $108   $126


2012-13 Curriculum Alignment Institute
November 8-9, 2012
   Using Student Work to Develop
   Standards for Mathematical Practice
     Use the questions posed by
     the teacher to analyze the
     tables generated by Student H.
        • Do the tables make
          mathematical sense, and
          do they match the plans?
        • Would these tables help
          us tell if the three plans
          will ever cost the same?




2012-13 Curriculum Alignment Institute
November 8-9, 2012
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2012-13 Curriculum Alignment Institute
November 8-9, 2012
     Math Practices in Action

     As you watch the video consider:
      • What evidence do you see
         that suggests students are
         developing competency with
         explaining and modeling?
      • In what ways did interactions
         between students support
         their ability to develop
         competency with explaining
         and modeling?


2012-13 Curriculum Alignment Institute
November 8-9, 2012
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2012-13 Curriculum Alignment Institute
November 8-9, 2012
   Video Rental Task: Student A Sample
                                          # of    MB OF MF
    Use the questions posed              Movies
    by the teacher to analyze
    the table generated by                 0       0   12   18
    Student A.
                                           1       3   25   18
      • Does the table make
        mathematical sense,                2       6   38   18
        and does it match the
        plans?                             3       9   51   18
      • Would this table help              4      12   64   18
        us tell if the three               5      15   77   18
        plans will ever cost
        the same?                          6      18   90   18

2012-13 Curriculum Alignment Institute
November 8-9, 2012
    Math Practices in Action

      As you watch the video consider:
        • What evidence do you see
          that suggests students are
          developing competency with
          explaining and modeling?
        • In what ways did interactions
          between students support
          their ability to develop
          competency explaining and
          modeling?



2012-13 Curriculum Alignment Institute
November 8-9, 2012
    Next Steps and Resources

       Consider what implications
       might the Standards for
       Mathematical Practice have
       on the classroom.
       What next steps might you
       need to take as a district,
       school, and teacher.




2012-13 Curriculum Alignment Institute
November 8-9, 2012
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2012-13 Curriculum Alignment Institute
November 8-9, 2012
www.mathedleadership.org

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      012
www.InsideMathematics.org

       m Alignment Institute
      012
 Contact Information

   Cecilia Miller
   Math Content Specialist
   Cecilia.miller@alaska.gov
   907-465-8703


2012-13 Curriculum Alignment Institute
November 8-9, 2012

				
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