Journey%20to%20the%20Core

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Journey to the Core
This material was developed for use by
participants in the Common Core Leadership in
Mathematics (CCLM2) project through the
University of Wisconsin-Milwaukee. Use by school
district personnel to support learning of its
teachers and staff is permitted provided
appropriate acknowledgement of its source. Use by
others is prohibited except by prior written
permission.
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Common Core State Standards
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45 states, D.C., 3 territories
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A Long Overdue Shifting of the Foundation

• For as long as most of us can remember, the K-12
  mathematics program in the U.S. has been aptly
  characterized in many rather uncomplimentary
  ways underperforming, incoherent, fragmented,
  poorly aligned, narrow in focus, skill-based,
  and, of course, a mile wide and an inch deep.

---Steve Leinwand, Principal Research Analyst
American Institutes for Research in Washington,
D.C
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• But hope and change have arrived!
• Like the long awaited cavalry, the new Common
  Core State Standards for Mathematics (CCSS)
  presents us a once in a lifetime opportunity to
  rescue ourselves and our students from the myriad
  curriculum problems weve faced for years.
• ---Steve Leinwand, Principal Research Analyst
  American Institutes for Research in Washington,
  D.C

Make no mistake, for K-12 math in the United
States, this IS a brave new world. --Steve
Leinwand
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• For over a decade, research of mathematics
  education in high-performing countries have
  pointed to the conclusion that the math
  curriculum in the United States must become
  substantially more focused and coherent in order
  to improve mathematics achievement in this
  country.

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• Focus Unifying themes and guidance on ways of
  knowing the mathematics.

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• Standards for Mathematical Practice

• Standards for Mathematics Content

• Make sense of problems
• Reason quantitatively
• Viable arguments critique
• Model with mathematics
• Strategic use of tools
• Attend to precision
• Look for and use structure
• Look for regularity in reasoning

• K-8 Grade Levels
• HS Conceptual Categories

Domains
Standards
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Digging in
Begin to unearth some discoveries

• Mathematics content
• Teaching of mathematics
• Student knowing of mathematics

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Reflecting
2NBT9. Explain why addition and subtraction
strategies work, using place value and the
properties of operations. 3OA3. Use
multiplication and division within 100 to solve
word problems in situations involving equal
groups, arrays, and measurement quantities, e.g.,
by using drawings and equations with a symbol for
the unknown number to represent the problem.
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Reflecting
4NF2. Compare two fractions with different
numerators and different denominators, e.g., by
creating common denominators or numerators, or by
comparing to a benchmark fraction such as 1/2.
Recognize that comparisons are valid only when
the two fractions refer to the same whole. Record
the results of comparisons with symbols gt, , or
lt, and justify the conclusions, e.g., by using a
visual fraction model.
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Reflecting
4NF2. Compare two fractions with different
numerators and different denominators, e.g., by
creating common denominators or numerators, or by
comparing to a benchmark fraction such as 1/2.
Recognize that comparisons are valid only when
the two fractions refer to the same whole. Record
the results of comparisons with symbols gt, , or
lt, and justify the conclusions, e.g., by using a
visual fraction model.
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Which is larger?
Find a common numerator!
or
Rename
or
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• Focus and
• Coherence

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• CCSS design principles

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The Hunt Institute Video SeriesCommon Core State
Standards A New Foundation for Student
Successwww.youtube.com/user/TheHuntInstitutep

• Helping Teachers Coherence and Focus
• Dr. William McCallum
• Professor of Mathematics, University of Arizona
• Lead Writer, Common Core Standards for Mathematics

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Features of Focus and Coherence
Fewer Topics
Free up time to do fewer things more deeply.
Progressions
Show how ideas fit with subsequent or previous
grade levels.

• Give more detail than teachers were used to
  seeing in standards.

More Detail
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Unifying Themes
Details
Domains Clusters Standards
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Unifying Themes
Details
Grade Domains Clusters Standards
K 5 9 22
1 4 11 21
2 4 10 26
3 5 11 25
4 5 12 28
5 5 11 26
6 5 10 29
7 5 9 24
8 5 10 28
Grade Domains Clusters Standards
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Unifying Themes
Details
Conceptual Category Domains Clusters Standards All Standards Advanced
Number Quantity
Algebra
Functions
Geometry
Statistics Probability
Modeling
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Unifying Themes
Details
Conceptual Category Domains Clusters Standards All Standards Advanced
Number Quantity 4 9 9 18
Algebra 4 11 23 4
Functions 4 10 22 6
Geometry 6 15 37 6
Statistics Probability 4 9 22 9
Modeling
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Coherence

• Research on students mathematics learning

• Discipline of mathematics

• Content Standards Reflect hierarchical nature
  structure of the discipline.
• Progressions
• Ways of Knowing
• Practice Standards Reflect how knowledge is
  generated within the discipline.

• Reflects what we know about how students develop
  mathematical knowledge.
• Reflects the needs of learners to organize and
  connect ideas in their minds (e.g., brain
  research).

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• CCSSM Progression Documents (draft)
• by The Common Core Standards Writing Team

Comprehensive discussions on Intent of
specific standards. Development within and
across grades. Connections across domains.
Suggested instructional approaches.
ime.math.arizona.edu/progressions
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Focus and Coherence
Domains and Clusters as unifying themes within
across grades.
Detail in the standards give guidance on ways of
knowing the mathematics
Embedded progressions of mathematical ideas.
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• Understanding
• the Mathematics
• Rigor

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Understanding in CCSSM
Word Number of instances
Understand(s) 147
Understanding 92
Understandings 21
Understood 3
TOTAL 263
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• These Standards define what students should
  understand and be able to do in their study of
  mathematics...
• But what does mathematical understanding look
  like? One hallmark of mathematical understanding
  is the ability to justify, in a way appropriate
  to the students mathematical maturity, why a
  particular mathematical statement is true or
  where a mathematical rule comes from.
• CCSSM, p. 4

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Task

• Select a grade level.
• Find the list of Clusters in CCSSM.
• Read through the clusters and count the
  occurrences of understand.
• Highlight one example of particular significance.

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Mathematical understanding and procedural skill
are equally important, and both are assessable
using mathematical tasks of sufficient
richness. CCSSM, p. 4
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SBAC States
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PARCC States
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And so the journey begins
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• I really hope these standards will help teachers
  be more creative in the classroom, engender the
  mathematical practices, and free up time to
  really focus on teaching mathematics.
• --Bill McCallum

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CCSSM