# Alaska English_Language Arts _ Mathematics Standards Introduction

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```					A Look at the Math
Practices in Action
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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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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
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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.
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Structuring the Math Practices

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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
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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
one of the two practices. Share
an insight you had into the

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
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
for both Content and Practice

2. Then work with a partner to compare your
work and discuss the following questions:
a) What mathematics content is needed to
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

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www.InsideMathematics.org

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Contact Information

Cecilia Miller
Math Content Specialist
907-465-8703

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

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