Exploring Rigor in the
2011 MA Curriculum Framework
for Mathematics
Exploration Activity:
Connecting the
Standards for Mathematical Practice
to the Content Standards
April 2011
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Desired Outcomes
After this activity participants will:
• Be familiar with the format and terminology of
the Standards for Mathematical Practice.
• Understand how the practice standards bring
rigor to the grade level standards.
• Understand the difference and connection
between the Standards for Mathematical
Practice and the grade level content standards.
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Supporting changes in practice
• The new standards support improved
curriculum and instruction due to increased:
– FOCUS, via critical areas at each grade level
– COHERENCE, through carefully developed
connections within and across grades
– CLARITY, with precisely worded standards
that cannot be treated as a checklist
– RIGOR, including a focus on College and
Career Readiness and Standards for
Mathematical Practice throughout Pre-K-12
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Background Information:
Standards for Mathematical Practice
“These practices rest on important ‘processes and
proficiencies’ with longstanding importance in
mathematics education.”
(Massachusetts Curriculum Frameworks for Mathematics, 2011, p. 15)
•The NCTM process standards (2000)
•The National Research Council’s report Adding It
Up (2001)
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NCTM – Principles & Standards for
School Mathematics
Process Standards
The five standards address the processes of
•Problem solving
•Reasoning and proof
•Connections
•Communication
•Representation
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Intertwined Strands of Proficiency
p. 117
Adding It Up: Helping Children Learn Mathematics
By Jeremy Kilpatrick,
Jane Swafford, & Bob Findell (Editors). (2001).
Washington, DC: National Academy Press
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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.
7. Look for and make use of structure.
8. Look for and express regularity in repeated
reasoning.
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Grade Level Overview Page
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Standards for Mathematical Content
•
Content standards are a balanced combination of
procedure and understanding.
• Content standards that set an expectation of
understanding are potential “points of intersection”
between the content standards and the practice
standards (see p. 17 of the Math Framework).
− A lack of understanding of mathematical content
effectively prevents a student from engaging in the
mathematical practices.
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Session Overview
• Warm-up focusing on Standard for
Mathematical Practice #4: Modeling (10
minutes)
• Main activity matching a focus practice
standards to strongly connected content
standards, and examples to justify each
match (30 minutes)
• Whole group discussion about impacts on
teaching and learning (10 minutes)
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Warm-Up : Examining Standard 4
Model with Mathematics
 Read Practice Standard #4 – Model with
Mathematics (see p. 16 of the Math Framework)
• Underline important language (words and
phrases) that help you remember the essence
of this practice.
 How might students use this practice standard
at the grade level you teach?
 Share at least one of your ideas with your
grade-level group.
Time estimate: 10 minutes
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Main Activity: Connecting
Content and Practices Standards
1. Choose one Standard for Mathematical Practice
as a focus of this activity.
2. Underline important language (words and
phrases) that help you remember the essence of
this practice.
3. Look through the Content Standards for the
grade level you teach.
4. Identify 3-5 Content Standards that would
address your focus mathematical practice.
5. Justify each match with an example.
Time estimate: 20 minutes
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Main Activity: Small Group Share
Share with your group at least one of your
examples of a content standard aligned with
the standard for mathematical practice you
chose as a focus.
Time estimate: 10 minutes
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Wrap-up: Whole Group Discussion
• How will incorporating the Standards
for Mathematical Practice impact
teaching and learning, including:
– Planning for instruction?
– Rigor?
– Student learning as they progress
through the grades?
•How will you begin to integrate these
practices in your classroom?
Time estimate: 10 minutes
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Feedback and Information
• To provide feedback on this activity as a
facilitator or participant, or to find more
activities and resources, go to the ESE’s
Curriculum and Instruction page at:
http://www.doe.mass.edu/candi/commoncore/
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