Download Standards for Mathematical Practice

Common Core State
Standards—Mathematics
Introduction/Overview
Cathy Carroll
[email protected]
1
Characteristics of CCSS–M
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Fewer and more rigorous standards
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Rigorous content and application of higher-order
skills
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Aligned with college and career expectations
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Research-based
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Build on strengths and lessons of current state
standards
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Internationally benchmarked
2
Principles Underlying the
Common Core State Standards

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Focus
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Identify key ideas, understandings and skills for each
grade or course
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Stress deep learning, which means applying concepts
and skills within the same grade or course
Coherence
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Articulate a progression of topics across grades and
connect to other topics
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Vertical growth that reflects the nature of the discipline
3
Shifts in Mathematics
Shift 1
Focus
Teachers significantly narrow and deepen the scope of how time
and energy is spent in the math classroom. They do so in order
to focus deeply on only the concepts that are prioritized in the
standards.
Shift 2
Coherence
Principals and teachers carefully connect the learning within and
across grades so that students can build new understanding
onto foundations built in previous years.
Shift 3
Fluency
Students are expected to have speed and accuracy with simple
calculations; teachers structure class time and/or homework
time for students to memorize, through repetition, core functions.
Shift 4
Deep
Understanding
Students deeply understand and can operate easily within a
math concept before moving on. They learn more than the trick
to get the answer right. They learn the math.
Shift 5
Application
Students are expected to use math and choose the appropriate
concept for application even when they are not prompted to do
so.
Shift 6
Dual Intensity
Students are practicing and understanding. There is more than
a balance between these two things in the classroom – both are
occurring with intensity.
SOURCE: Engage NY
Design and Organization
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Standards For Mathematical Practice
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Describe habits of mind of a mathematically expert
student, and are expected to be implemented at all
levels
Mathematical Content Standards
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K-8 standards presented by grade level
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Organized into domains that progress over several grades.
High school standards presented by conceptual
themes
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Number & Quantity, Algebra, Functions, Modeling, Geometry,
Statistics & Probability
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 Governors Association Center for Best Practices
and Council of Chief State School Officers (2010)
Common Core State Standards for Mathematics
6
Underlying Frameworks
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Adding It Up—National Research Council
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Strands of Mathematical Proficiency
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Conceptual understanding
Procedural fluency
Strategic competence
Adaptive reasoning
Productive disposition
Principles and Standards for School Mathematics—NCTM
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Process Standards
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Problem Solving
Reasoning and Proof
Communication
Connections
Representation
Standards for Mathematical
Practice
1. Make sense of problems and persevere in
solving them
6. Attend to precision
Overarching Habits of Mind
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
8
Standards for Mathematical
Practice

On one hand, the Standards for Mathematical
Practice describe mathematical content students
need to learn.
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SP1. Make sense of problems

“… students can explain correspondences between
equations, verbal descriptions, tables, and graphs or draw
diagrams of important features and relationships, graph data,
and search for regularity or trends.”
9
Standards for Mathematical
Practice

On the other hand, they describe the nature of
the learning experiences, thinking processes,
habits of mind, and dispositions that students
need to develop a deep, flexible, and enduring
understanding of mathematics.

SP1. Make sense of problems

“….they [students] analyze givens, constraints, relationships
and goals. ….they monitor and evaluate their progress and
change course if necessary. …. and they continually ask
themselves “Does this make sense?”
10
Mathematics Content
Standards
Modeling
Content Overviews
Critical
Areas of
Focus
Description of
Critical Area
Format of Content Standards
Domain
Grade Level or
Conceptual
Category
Cluster
Standards
High School Conceptual
Categories
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Rather than list HS content by course or by
grade level, CCSSM identifies “Conceptual
Categories.” These categories represent:

The big ideas that connect mathematics across high
school
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Such as Functions or Probability and Statistics
A progression of increasing complexity
Description of mathematical content to be learned
elaborated through domains, clusters, and standards
High School Pathways
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The CCSSM Model Pathways are two models
that organize the CCSSM into coherent, rigorous
courses
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Pathway A—two algebra courses and geometry
Pathway B—three integrated courses
The CCSSM Model Pathways are NOT required.
The two sequences are examples, not mandates
A variety of year 4 courses can follow either
pathway
Articulating the Challenge

The Common Core State Standards are not
intended to be new names for old ways of doing
business. They are a call to take the next step. It
is time…to work together to build on lessons
learned from two decades of standards-based
reforms. It is time to recognize that standards are
not just promises to our children, but promises we
intend to keep.
— CCSS (2010, p.5)