1. Dr. DeAnn Huinker University 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.

2. Dr. DeAnn Huinker University 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

3. Dr. DeAnn Huinker University of Wisconsin-Milwaukee 45 states, D.C., & 3 territories

4. Dr. DeAnn Huinker University 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

5. Dr. DeAnn Huinker University of Wisconsin-Milwaukee

6. Dr. DeAnn Huinker University 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

7. Dr. DeAnn Huinker University 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.

8. Dr. DeAnn Huinker University 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.

9. Dr. DeAnn Huinker University 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

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11. Dr. DeAnn Huinker University of Wisconsin-Milwaukee  Mathematics content  Teaching of mathematics  Student “knowing” of mathematics Digging in… Begin to unearth some discoveries:

12. Dr. DeAnn Huinker University 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…

13. Dr. DeAnn Huinker University 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…

14. Dr. DeAnn Huinker University 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…

15. Dr. DeAnn Huinker University of Wisconsin-Milwaukee Which is larger? or 3434 6767 Find a common numerator! 6868 6767 Rename or

16. Dr. DeAnn Huinker University of Wisconsin-Milwaukee Focus and Coherence

17. Dr. DeAnn Huinker University of Wisconsin-Milwaukee CCSS “design principles” Focus Coherence

18. Dr. DeAnn Huinker University of Wisconsin-Milwaukee The Hunt Institute Video Series Common 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

19. Dr. DeAnn Huinker University 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.

20. Dr. DeAnn Huinker University of Wisconsin-Milwaukee Unifying ThemesDetails DomainsClustersStandards

21. Dr. DeAnn Huinker University of Wisconsin-Milwaukee GradeDomainsClustersStandards K5922 141121 241026 351125 451228 551126 651029 75924 851028 Unifying ThemesDetails GradeDomainsClustersStandards

22. Dr. DeAnn Huinker University of Wisconsin-Milwaukee Conceptual Category DomainsClustersStandards All Standards Advanced Number & Quantity Algebra Functions Geometry Statistics & Probability Modeling Unifying ThemesDetails

23. Dr. DeAnn Huinker University of Wisconsin-Milwaukee Conceptual Category DomainsClustersStandards All Standards Advanced Number & Quantity 49918 Algebra 411234 Functions 410226 Geometry 615376 Statistics & Probability 49229 Modeling **** Unifying ThemesDetails

24. Dr. DeAnn Huinker University 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

25. Dr. DeAnn Huinker University 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.

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27. Dr. DeAnn Huinker University of Wisconsin-Milwaukee Domains and Clusters as unifying themes within & across grades. Detail in the standards give guidance on “ways of knowing” the mathematics Focus and Coherence Embedded progressions of mathematical ideas.

28. Dr. DeAnn Huinker University of Wisconsin-Milwaukee Understanding the Mathematics “Rigor”

29. Dr. DeAnn Huinker University of Wisconsin-Milwaukee Understanding in CCSSM… WordNumber of instances Understand(s)147 Understanding 92 Understandings 21 Understood 3 TOTAL263

30. Dr. DeAnn Huinker University 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

31. Dr. DeAnn Huinker University 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.

32. Dr. DeAnn Huinker University of Wisconsin-Milwaukee Mathematical understanding and procedural skill are equally important, and both are assessable using mathematical tasks of sufficient richness. CCSSM, p. 4

33. Dr. DeAnn Huinker University of Wisconsin-Milwaukee SBAC States…

34. Dr. DeAnn Huinker University of Wisconsin-Milwaukee PARCC States…

35. Dr. DeAnn Huinker University of Wisconsin-Milwaukee And so the journey begins…

36. Dr. DeAnn Huinker University 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

37. Dr. DeAnn Huinker University of Wisconsin-Milwaukee CCSSM Progression Understanding Focus Coherence