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Journey to the Core

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

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Journey to the Core

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  1. 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. Common CoreState Standards Adopted and maintained by States; not a federal policy Shared, thesame for everyone Benchmarks of what students are expected to learn in a content area Essential, fundamental knowledge and skills necessary for student success

  3. 45 states, D.C., & 3 territories

  4. 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. 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

  6. 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.

  7. 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.

  8. 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 Standards for Mathematical Practice Standards for Mathematics Content • K-8 Grade Levels • HS Conceptual Categories Domains Clusters Standards

  9. Digging in… Begin to unearth some discoveries: • Mathematics content • Teaching of mathematics • Student “knowing” of mathematics

  10. 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.

  11. 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 >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

  12. 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 >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

  13. Find a common numerator! Which is larger? 3 4 6 8 6 7 6 7 or Rename or

  14. Focus and Coherence

  15. CCSS “design principles” Focus Coherence

  16. The Hunt Institute Video SeriesCommon Core State Standards: A New Foundation for Student Successwww.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

  17. Features of Focus and Coherence Fewer Topics “Free up time” to do fewer things more deeply. “Give more detail than teachers were used to seeing in standards.” Progressions Show how ideas fit with subsequent or previous grade levels. More Detail

  18. Unifying Themes Details

  19. Unifying Themes Details

  20. Unifying Themes Details

  21. Unifying Themes Details

  22. Content Standards: Reflect hierarchical nature & structure of the discipline. – Progressions – Ways of Knowing Practice Standards: Reflect how knowledge is generated within the discipline. Discipline of mathematics Research on students’ mathematics learning Coherence 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).

  23. 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

  24. 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 progressionsof mathematical ideas.

  25. Understanding the Mathematics “Rigor”

  26. Understanding in CCSSM…

  27. 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

  28. 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.

  29. Mathematical understanding and procedural skill are equally important, and both are assessable using mathematical tasks of sufficient richness. CCSSM, p. 4

  30. SBAC States…

  31. PARCC States…

  32. And so the journey begins…

  33. 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

  34. CCSSM Progression Focus Coherence Understanding Progression Progression

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