Dr. DeAnn HuinkerUniversity of Wisconsin-Milwaukee
Journey to the Core
This material was developed for use by participants in the Common Core Leadership in Mathematics (CCLM^2) 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.
Dr. DeAnn HuinkerUniversity of Wisconsin-Milwaukee
Shared, the
same for everyone
Essential, fundamental knowledge and skills
necessary for student success
Adopted and
maintained by States;
not a federal policy
Benchmarks of what
students are expected to learn in a
content area
Dr. DeAnn HuinkerUniversity of Wisconsin-Milwaukee
45 states, D.C., & 3 territories
Dr. DeAnn HuinkerUniversity of Wisconsin-Milwaukee
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
Dr. DeAnn HuinkerUniversity of Wisconsin-Milwaukee
Dr. DeAnn HuinkerUniversity of Wisconsin-Milwaukee
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 we’ve 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
Dr. DeAnn HuinkerUniversity of Wisconsin-Milwaukee
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.
Dr. DeAnn HuinkerUniversity of Wisconsin-Milwaukee
Focus: Unifying themes and guidance on “ways of knowing” the mathematics.
Coherence: Progressions across grades based on discipline of mathematics and on student learning.
Understanding (Rigor): Deep, genuine understanding of mathematics and ability to use that knowledge in real-world situations.
Dr. DeAnn HuinkerUniversity of Wisconsin-Milwaukee
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
Standards for Mathematical Practice
Standards for Mathematics Content
Standards
Domains
Clusters
Dr. DeAnn HuinkerUniversity of Wisconsin-Milwaukee
Dr. DeAnn HuinkerUniversity of Wisconsin-Milwaukee
Mathematics content Teaching of mathematics Student “knowing” of mathematics
Digging in…
Begin to unearth some discoveries:
Dr. DeAnn HuinkerUniversity of Wisconsin-Milwaukee
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.
Reflecting…
Dr. DeAnn HuinkerUniversity of Wisconsin-Milwaukee
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 >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
Reflecting…
Dr. DeAnn HuinkerUniversity of Wisconsin-Milwaukee
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 >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
Reflecting…
Dr. DeAnn HuinkerUniversity of Wisconsin-Milwaukee
Which is larger?
or34
67
Find a common
numerator!
68
67
Rename
or
Dr. DeAnn HuinkerUniversity of Wisconsin-Milwaukee
Focus and
Coherence
Dr. DeAnn HuinkerUniversity of Wisconsin-Milwaukee
CCSS “design principles”
Focus Coherence
Dr. DeAnn HuinkerUniversity of Wisconsin-Milwaukee
The Hunt Institute Video SeriesCommon Core State Standards: A New Foundation for Student Success
www.youtube.com/user/TheHuntInstitute#p
Helping Teachers: Coherence and Focus
Dr. William McCallum
Professor of Mathematics, University of Arizona
Lead Writer, Common Core Standards for Mathematics
Dr. DeAnn HuinkerUniversity of Wisconsin-Milwaukee
Features of Focus and Coherence
“Give more detail than teachers were used to seeing in standards.”
Fewer Topics
Progressions
More Detail
Show how ideas fit with subsequent or previous grade levels.
“Free up time” to do fewer things more deeply.
Dr. DeAnn HuinkerUniversity of Wisconsin-Milwaukee
Unifying Themes Details
Domains Clusters Standards
Dr. DeAnn HuinkerUniversity of Wisconsin-Milwaukee
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
Unifying Themes Details
Grade Domains Clusters Standards
Dr. DeAnn HuinkerUniversity of Wisconsin-Milwaukee
Conceptual Category
Domains Clusters StandardsAll
StandardsAdvanced
Number & Quantity
Algebra
Functions
Geometry
Statistics & Probability
Modeling
Unifying Themes Details
Dr. DeAnn HuinkerUniversity of Wisconsin-Milwaukee
Conceptual Category
Domains Clusters StandardsAll
StandardsAdvanced
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 * * * *
Unifying Themes Details
Dr. DeAnn HuinkerUniversity of Wisconsin-Milwaukee
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).
Discipline of mathematics
Research on students’ mathematics learning
Coherence
Dr. DeAnn HuinkerUniversity of Wisconsin-Milwaukee
CCSSM Progression Documents (draft)
by The Common Core Standards Writing Team
ime.math.arizona.edu/progressions
Comprehensive discussions on:
• Intent of specific standards.
• Development within and across grades.
• Connections across domains.
• Suggested instructional approaches.
Dr. DeAnn HuinkerUniversity of Wisconsin-Milwaukee
Dr. DeAnn HuinkerUniversity of Wisconsin-Milwaukee
Domains and Clusters as unifying themes
within & across grades.
Domains and Clusters as unifying themes
within & across grades.
Detail in the standards give guidance on
“ways of knowing” the mathematics
Detail in the standards give guidance on
“ways of knowing” the mathematics
Focus and Coherence
Embedded progressions of
mathematical ideas.
Embedded progressions of
mathematical ideas.
Dr. DeAnn HuinkerUniversity of Wisconsin-Milwaukee
Understandingthe Mathematics
“Rigor”
Dr. DeAnn HuinkerUniversity of Wisconsin-Milwaukee
Understanding in CCSSM…
Word Number of instances
Understand(s) 147
Understanding 92
Understandings 21
Understood 3
TOTAL 263
Dr. DeAnn HuinkerUniversity of Wisconsin-Milwaukee
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 student’s mathematical maturity, why a particular mathematical statement is true or where a mathematical rule comes from.
CCSSM, p. 4
Dr. DeAnn HuinkerUniversity of Wisconsin-Milwaukee
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.
Dr. DeAnn HuinkerUniversity of Wisconsin-Milwaukee
Mathematical understanding and
procedural skill are equally important, and
both are assessable using mathematical
tasks of sufficient richness.
CCSSM, p. 4
Dr. DeAnn HuinkerUniversity of Wisconsin-Milwaukee
SBAC States…
Dr. DeAnn HuinkerUniversity of Wisconsin-Milwaukee
PARCC States…
Dr. DeAnn HuinkerUniversity of Wisconsin-Milwaukee
And so the journey begins…
Dr. DeAnn HuinkerUniversity of Wisconsin-Milwaukee
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
Dr. DeAnn HuinkerUniversity of Wisconsin-Milwaukee
CCSSM
Progression
Progressio
n
Progressio
n
Understanding
Focus
Coherence
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