Transcript Mathematics Progressions – Common Core

Mathematics Progressions –
Common Core
Elizabeth Gamino, Fresno Unified Public Schools
Denise Walston, Council of the Great City Schools
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Purpose
S Review and take a closer look at the Mathematics
Progressions
S Focus, Coherence, and Rigor
S Instructional implications
S Scaffolding
S Explain their thinking; critique the reasoning of others
S Developing mathematical arguments
S Reading and interpreting real-world problems
S Technical language of the discipline
Instructional Shifts
Mathematics
A Look Back
S
Mathematics Instructional
Shifts
S Focus
S Coherence
S Rigor
S Conceptual understanding
S Procedural skill and fluency
S Applications
Focus
S Significantly narrow and deepen the way that time and
energy is spent in the math classroom
S Communicate focus so that it is manageable in instruction; it is more
than merely writing a standard a day
S Focus deeply on those concepts emphasized in the standards
S Provide the time for students to transfer mathematical
skills and understanding across concepts and grade levels
S Deep conceptual understanding
S Connect conceptual and procedural understanding
S Transitions from concrete↔pictorial↔language↔abstract
Coherence
S Coherence provides the opportunity for students to make
connections between mathematical ideas and across content areas
S Connects the learning both within a grade and across grades
S Thinking across grades
S Each standard is not a new event, but an extension of previous learning
S Allows students to see mathematics as inter-connected ideas
S Mathematics instruction cannot be relegated to merely a checklist of
topics to cover, but instead must be centered around a set of
interrelated and powerful ideas, rather than a series of disconnected
topics
Rigor
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Conceptual Understanding
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Involves more than getting the right answer
Access concepts from multiple perspectives
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Transitions from concrete↔pictorial↔language↔abstract
Procedural Skill and Fluency
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Study algorithms as a way to see the structure of mathematics (organization, patterns, predictability)
or apply a variety of appropriate procedure flexibly to solve problems
Students are expected to achieve speed and accuracy with simple calculations (at specific grade levels)
Fluent is used in the Standards to mean “efficient and accurate”
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With equal intensity
Class time and/or homework should be structured for students to practice core functions such as singledigit multiplications
Application
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Expectation that students apply math and choose the appropriate concept for application, even when
not prompted to do so
Apply math concepts in real-world situations
Mathematical modeling
Common Core State
Standards
Mathematics
Closer Look at Fractions
S
Fraction Concepts
S Grade One:
Partition circles and rectangles into two
and four equal shares, describe the
shares using the words halves, fourths,
and quarters, and use the phrase half of,
fourth of, and quarter of. Describe the
whole as two of or four of the shares.
Understand for these examples that
decomposing into more equal shares
creates smaller shares.
Fraction Concepts
S Grade Two
same
Partition circles and rectangles into two,
three, or four equal shares, describe the
shares using the words halves, thirds,
half of, a third of, etc., and describe the
whole as two halves, three thirds, four
fourths. Recognize that equal shares of
identical wholes need not have the
shape.
Coherence – strengthens
foundations
S Progression involving fractional concepts (conceptual understanding) and
operations (multiplication and division of fractions):
S Grade Three:
Develop understanding of fractions as numbers
Develop understanding of fractions as part of a
whole and as a number on the number line
Explain equivalence of fractions in special cases, and
compare fractions by reasoning about their size
S Grade Four:
Extend understanding of fraction equivalence and
ordering
Build fractions from unit fractions by applying and
extending previous understandings on whole numbers
(decompose a fraction into a sum of fractions with the
same denominator)
Coherence: Number and
Operations - Fractions
S Grade Four:
Multiply a fraction by a whole number
S Grade Five:
Multiply a fraction by a fraction
Divide unit fractions by a whole number; and whole
numbers by unit fractions
S Grade Six:
Interpret and compute quotients of
fractions and solve word problems
The Mathematics
Progressions
Developing a deep
understanding of focus,
coherence, and rigor
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• Mathematics Progressions
• Common Core State Standards in Mathematics
• Informed by research on children’s cognitive
development and the logical structure of
mathematics
• Narrative documents
• Progression of concepts across several grade bands
Closer Look – Fraction Progression
Fraction as number
Linking content to the
Mathematical Practices
and
District Perspective
S Read and analyze the progressions (book study, close read)
S Through the lens of focus, coherence and rigor
S Need to look at the standards in their entirety K-12
S Determine what happens prior to students entering your door
and where they need to go - beyond the grade level below and
above.
Problems for
consideration
Exploring the Fraction Progression using
illustrative tasks
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Questions to consider
S What are some things that you had to attend to?
S What are some things that ELLs need to be aware of ?
S What are the implications for planning for instruction?
S How might you assess student understanding specifically
related to ELLs?
S What are the implications for professional development?
Online Resources
Fraction Professional Development Module
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Fraction Progression Online
Module
S Goals/Purpose:
S Deepen educators content knowledge, specifically around the
mathematics “Fractions” progression;
S Engage practicing educators in the development of CCSS-aligned
professional development; and
S Provide consistent, high-quality professional development that can
be used at large scale and online across PARCC states to inform
elementary teachers and instructional leaders
S Partnership with CGCS, Institute for Mathematics & Education,
University of Arizona, and Achieve
Design within Edmodo
S Features of the module
S Online and interactive
S Based on a framework developed collaboratively with CGCS
S Illustrative of the Fractions Progression in the CCSSM
S Seven units anchored by a 3-5 minute video
S Three to four illustrative tasks associated with the progression
S Built-in, interactive checks for understanding
S Interactive-check for understandings – Quiz – linked to the
commentary
Online Professional
Development Module
S http://commoncoreworks.org/domain/121