21 st Century Mathematics & Common Core Standards

1. 21st Century Mathematics & Common Core Standards An Opportunity for South Carolina & Beaufort School District Ed Dickey College of Education University of South Carolina

2. Mathematics Tools for the 21st Century Classroom • U.S. Secretary of Education Arne Duncan at NCTM Annual Meeting, 15 April 2011 • “Curricular materials cover so much ground too superficially, failing to provide students with an understanding of the concepts that are essential for success.” • “Tests don’t always measure what’s important, or provide information back to you to help you improve.”

3. Mathematics for the 21st Century Societal Need for • Competitiveness (Knowledge-based global economy) • Fulfillment (sustainability in diverse society)

4. Competitiveness in the 21st Century • Technology • New tools for understanding and visualizing numerical ideas • Web-based, hand-held, ubiquitous • Hans Rosling • “The Joy of Stats”

5. Competitiveness in the 21st Century • Technology • New tools for understanding and visualizing numerical ideas • Computer Algebra Systems • On iPads and Smartphones • Wolfram Alpha

6. Wolfram Alpha

7. Competitiveness in the 21st Century • Computer Algebra Systems • Handheld Calculators • Equation of a line ( y = mx + b) with sliders using TI Nspire Calculator

8. Fulfillment in the 21st Century • Teaching IS a gratifying profession…

9. Fulfillment the 21st Century • Cultural Diversity Understanding mathematical content in a manner that ENGAGES the learners who populate our classrooms

10. Cultural Diversity

11. Cultural Diversity • Vedic Multiplication 21 x 13 video

12. Subtraction in Mexico 963 -369 1 7 4 1 4 9 5

13. NCTM Affiliated Groups • TODOS advocating for equitable, high quality mathematics education for all, in particular, Hispanic/Latino students • www.todos-math.org

14. NCTM Affiliated Groups • Benjamin Banneker Association, advocating for the mathematics education of African-American students • www.bannekermath.org

15. NCTM Affiliated Groups • South Carolina Council of Teachers of Mathematics • www.scctm.org

16. Mathematics for the 21st Century • Common Core State Standards for Mathematics • An opportunity to address… • Competitiveness • Fulfillment

17. Common Core Standards • Sponsored by the Council of Chief State School Officers (CCSS) and the National Governors Association (NGA) • First significant attempt to systematically align K-12 standards across the U.S. • Building on NCTM’s standards documents from 1980, 1989, 2000, 2006, and 2009 • NCTM among groups providing feedback

18. Common Core Standards • Different from most current state standards • Based on most recent research regarding students’ learning trajectories related to mathematics content • Includes detailed description of the way mathematics is learned and used by students (Mathematical Practice)

19. Common Core Development • Initially 48 states and three territories signed on • As of April 1, 2011, 41 states have officially adopted (plus DC and US VI) • Final Standards released June 2, 2010, at www.corestandards.org • Adoption required for Race to the Top funds

20. Common Core Development • Each state adopting the common core either directly or by fully aligning its state standards may do so in accordance with current state timelines for standards adoption not to exceed three (3) years. • States that choose to align their standards to the common core standards accept 100% of the core. States may add additional standards.

22. Benefits for States and Districts • Allows collaborative professional development based on best practices • Allows development of common assessments and other tools (SC in SMARTER Balanced and PARCC) • Enables comparison of policies and achievement across states and districts • Creates potential for collaborative groups to get more economical mileage for: • Curriculum development, assessment, and professional development

23. CCSSM CCSSM stands for Common Core State Standards for Mathematics

24. Arne Duncan at NCTM • “... today’s tests don’t measure higher-order thinking skills or deep understanding of subject material. American students deserve better than the fill-in-the-bubble tests that are now common across states.” • New assessments “… are the ones that you’ve longed for. They will measure critical thinking skills and complex student learning.”

25. Characteristics • Fewer and more rigorous • Aligned with college and career expectations • Internationally benchmarked • Rigorous content and application of higher-order skills. • Builds on strengths and lessons of current state standards. • Research based

26. Intent of the Common Core • The same goals for all students • Coherence • Focus • Clarity and Specificity

27. Coherence • Articulated progressions of topics and performances that are developmental and connected to other progressions • Conceptual understanding AND procedural skills stressed equally NCTM states coherence also means that instruction, assessment, and curriculum are aligned

28. Focus • Key ideas, understandings, and skills are identified • Deep learning of concepts is emphasized • That is, time is spent on a topic and on learning the topic well. This counters the “mile wide, inch deep” criticism leveled at most current U.S. standards.

29. Clarity and Specificity • Skills and concepts are clearly defined • Being able to apply concepts and skills to new situations is expected

30. CCSSM • Word Cloud

31. CCSSM Mathematical Practices • Common Core includes a set of Standards of Mathematical Practices that all teachers should develop in their students. • Similar to NCTM’s Mathematical Processes from the Principles and Standards for School Mathematics. • Practices MUST be assessed

32. 8 CCSSM Mathematical Practices • Make sense of problems and persevere in solving them. • Reason abstractly and quantitatively. • Construct viable arguments and critique the reasoning of others. • Model with mathematics.

33. Geometry Lesson from Japan

34. 5 m 8 m 2 m 8 m 10 m 3 m 2m Make Sense / Critique Reasoning Find the area of the shaded region:

35. 5 m 8 m 2 m 8 m 10 m 3 m 2m Reasoning

36. Learning Trajectories • Area is invariant under transformations

37. 8 CCSSM Mathematical Practices 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.

38. Look for and make use of structure • What is the result when you add… • Even + Even ? • Odd + Odd ?

39. Mod 2 Arithmetic • Modular arithmetic used in encryption codes..

40. Vi Hart’s Binary Hand Dance

41. Mathematical Structures Vi Hart Blog at vihart.com • Base 2 • Modular arithmetic • Mathematical food • And other engaging ideas about mathematics • … BUT now back to the Common Core

42. Common Core Format Domains are large groups of related standards. Standards from different domains may sometimes be closely related. Look for the name with the code number on it for a Domain.

43. Common Core Format Clusters are groups of related standards.Standards from different clusters may sometimes be closely related, because mathematics is a connected subject. Clusters appear inside domains.

44. Common Core Format Standards define what students should be able to understand and be able to do – part of a cluster.

45. Common Core Format K-8 Grade Domain Cluster Standards (There are no preK Common Core Standards) High School Conceptual Category Domain Cluster Standards Domains are NOT courses  Clusters are NOT units 

46. Grade Level Overview

47. Grade Level Overview Critical Areas – similar to NCTM’s Curriculum Focal Points

48. Grade Level Format of K-8 Standards Domain

49. Standard Format of K-8 Standards Cluster Standard Cluster

50. Domain Format of High School Standard Cluster