Implementing the NYS P-12 Common Core Learning Standards for Mathematics

1. Implementing the NYS P-12 Common Core Learning Standards for Mathematics Please visit www.engageNY.org for additional information regarding the Common Core Learning Standards New York State Education Department. (2011). EngageNY. Retrieved from http://engageny.org/ 1

2. The Common Core State Standards Initiative Beginning in the spring of 2009, Governors and State Commissioners of Education from 48 states, 2 territories and the District of Columbia committed to developing a common core of state K-12 English language arts (ELA) and mathematics standards. The Common Core State Standards Initiative (CCSSI) is a state-led effort coordinated by the National Governors Association (NGA) and the Council of Chief State School Officers (CCSSO). www.corestandards.org Common Core State Standards Initiative. (2011). Common Core State Standards.      Retrieved from http://www.corestandards.org/ 2

3. Why Common Core State Standards? 3

4. Why Common Core State Standards? • Preparation: The standards are college- and career-ready. They will help prepare students with the knowledge and skills they need to succeed in education and training after high school. • Competition: The standards are internationally benchmarked. Common standards will help ensure our students are globally competitive. • Equity: Expectations are consistent for all – and not dependent on a student’s zip code. • Clarity: The standards are focused, coherent, and clear. Clearer standards help students (and parents and teachers) understand what is expected of them. • Collaboration: The standards create a foundation to work collaboratively across states and districts, pooling resources and expertise, to create curricular tools, professional development, common assessments and other materials. 4

5. The Mathematics Standards: How They Were Developed and Who Was Involved Key Points from Video • General discussion of mathematics standards • Aspirations for mathematics instruction at higher levels • Greater mastery through focus and coherence • Review of groups involved • General discussion of mathematics progressions • What is and is not included at the elementary level • What happens at middle school • Discussion of migration away from strands and into domains of mathematics McCallum, W. (2011). Mathematic Standards: How They Were Developed and Who Was      Involved [Video file]. Retrieved from http://www.youtube.com/watch?v=dnjbwJdcPjE 5

6. Underlying Frameworks Conceptual Understanding Productive Disposition Strands of Mathematical Proficiency Strategic Competence Procedural Fluency Adaptive Reasoning NRC (2001). Adding It Up. Washington, D.C.: National Academies Press. Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding it Up: Helping Children Learn Mathematics. Washington, DC: National Academies      Press. 6

7. Improving K-12 Mathematics is an URGENT Matter! 7

8. Key Questions What is the current state of mathematics performance… • In the United States compared to other nations? • In the United States? • In New York State compared to other states? • In your school/district compared to other districts in New York State? 8

9. What is TIMSS? The Trends in International Mathematics and Science Study (TIMSS) compares math and science achievement of 4th and 8th graders internationally. TIMSS is closely linked to the curricula of the participating countries, providing an indication of the degree to which students have learned concepts in mathematics and science they have encountered in school To date, more than 50 countries have participated. Trends in International Mathematics and Science Study(TIMSS). (n.d.). Retrieved      from Institute of Educational Science website: http://nces.ed.gov/timss/ 9

10. TIMSS 2007 Assessment 8th Grade Math Gonzales, P. (2009). Highlights From TIMSS 2007:Mathematics and Science Achievement of U.S. Fourth and Eighth-Grade Students in an International Context. Retrieved from National Center for Education Statistics      website: http://nces.ed.gov/pubs2009/2009001.pdf 10

11. TIMSS: Countries Behind U.S. Armenia, Australia, Sweden, Malta, Scotland, Serbia, Italy, Malaysia, Norway, Cyprus, Bulgaria, Israel, Ukraine, Romania, Bosnia and Herzegovina, Lebanon, Thailand, Turkey, Jordan, Tunisia, Georgia, Iran, Islamic Rep of, Bahrain, Indonesia, Syrian Arab Republic, Egypt, Algeria, Colombia, Oman, Palestinian Nat'l Auth., Botswana, Kuwait, El Salvador, Saudi Arabia, Ghana, Qatar, Morocco 11

12. What is PISA PISA (Programme for International Student Assessment) is an international study which began in the year 2000. It aims to evaluate education systems worldwide by testing the skills and knowledge of 15-year-old students in participating countries/economies. Since the year 2000 over 70 countries and economies have participated in PISA. Programme for International Student Assessment (PISA). (n.d.). Retrieved from      Organisation for Economic Co-operation and Development website: http://www.oecd.org/document/61/      0,3746,en_32252351_32235731_46567613_1_1_1_1,00.html 12

13. PISA PISA assesses how far students near the end of compulsory education have acquired some of the knowledge and skills that are essential for full participation in society. In all cycles, the domains of reading, mathematical and scientific literacy are covered not merely in terms of mastery of the school curriculum, but in terms of important knowledge and skills needed in adult life. In the PISA 2003 cycle,an additional domain of problem solving was introduced to continue the examination ofcross-curriculum competencies. Take the Test 13

14. PISA 2003 Programme for International Student Assessment. (n.d.). First Results from PISA 2003 [Executive Summary]. Retrieved from Organisation for Economic      Co-operation and Development website: http://www.oecd.org/dataoecd/1/63/      34002454.pdf 14

15. PISA 2006 15

16. The “Thin Elite Layer” 16

17. NAEP 2011 NY State National Center for Education Statistics. (n.d.). National Assessment of Educational Progress (NAEP). Retrieved from U.S. Department of Education      website: http://nces.ed.gov/nationsreportcard/ 17

18. NAEP 4th Grade Math National Center for Education Statistics. (n.d.). National Assessment of Educational Progress (NAEP). Retrieved from U.S. Department of Education      website: http://nces.ed.gov/nationsreportcard/ 18

19. NAEP 8th Grade Math National Center for Education Statistics. (n.d.). National Assessment of Educational Progress (NAEP). Retrieved from U.S. Department of Education      website: http://nces.ed.gov/nationsreportcard/ 19

20. NYS P-12 Common Core Learning Standards for Mathematics New York State Education Department. (2011). Common Core in Mathematics: Overview. Retrieved from http://engageny.org/resource/      common-core-in-mathematics-overview/ 20

21. Common Core Learning Standards 21

22. Instructional Shifts . . . 22

23. Shift 1 Focus Teachers use the power of the eraser and significantly narrow and deepen the scope of how time and energy is spent in the math classroom. They do so in order to focus deeply on only the concepts that are prioritized in the standards so that students reach strong foundational knowledge and deep conceptual understanding and are able to transfer mathematical skills and understanding across concepts and grades. 23

24. Reflection Read the “Shift” What does the “Shift” mean to you? What does it look like in mathematics classrooms (provide specific examples)? 24

25. Trends in International Mathematics and Science Study (TIMSS) Test your mathematics and science knowledge by completing test items in the Dare to Compare challenge! NCES Kids' Zone. (n.d.). Dare to Compare. Retrieved from U.S. Department of      Education website: http://nces.ed.gov/nceskids/eyk/?flash=true 25

26. The Importance of Focus in Mathematics • First-year college remediation challenges • Mismatch between higher education and K-12 -- more mastery of fewer topics vs. covering more • Focus as it relates to teachers' needs to build a solid foundation in early grades • Solid early foundation enables greater success later Zimba, J., & McCallum, W. (n.d.). The Importance of Focus in Mathematics [Motion      picture]. Retrieved from http://www.youtube.com/      watch?v=2rje1NOgHWs&list=UUF0pa3nE3aZAfBMT8pqM5PA&index=18&feature=plcp 26

27. Shift 2 Coherence Principals and teachers carefully connect the learning within and across grades so that, for example, fractions or multiplication spiral across grade levels and students can build new understanding onto foundations built in previous years. Teachers can begin to count on deep conceptual understanding of core content and build on it. Each standard is not a new event, but an extension of previous learning. 27

28. Reflection Read the “Shift” What does the “Shift” mean to you? What does it look like in mathematics classrooms (provide specific examples)? 28

29. The Importance of Coherence in Mathematics • Mathematics consists of pieces that make sense; they are not just independent manipulation/skills to be practiced and memorized – as perceived by many students. • These individual pieces progress through different grades (in organized structures we called “flows”) and can/should be unified together into a coherent whole. • Algebra as an example Zimba, J., & McCallum, W. (n.d.). The Importance of Coherence In Mathematics      [Motion picture]. Retrieved from http://www.youtube.com/      watch?v=2rje1NOgHWs&feature=autoplay&list=UUF0pa3nE3aZAfBMT8pqM5PA&playnext=1 29

30. The Structure is the Standardsby Phil Daro, Bill McCallum, Jason Zimba A Grecian Urn You have just purchased an expensive Grecian urn and asked the dealer to ship it to your house. He picks up a hammer, shatters it into pieces, and explains that he will send one piece a day in an envelope for the next year. You object; he says “don’t worry, I’ll make sure that you get every single piece, and the markings are clear, so you’ll be able to glue them all back together. I’ve got it covered.” Absurd, no? But this is the way many school systems require teachers to deliver mathematics to their students; one piece (i.e. one standard) at a time. They promise their customers (the taxpayers) that by the end of the year they will have “covered” the standards… 30

31. The Structure is the Standardsby Phil Daro, Bill McCallum, Jason Zimba Once you have read the article, please answer the questions below with an elbow partner. • How do the authors describe the standards? Provide evidence in the text. • How were the Common Core State Standards developed? Point to evidence in the text. • Why did they use the word “structure” in the title? Discuss with your elbow partner. Daro, P., McCallum, B., & Zimba, J. (2012, February 16). The Structure is the      Standards [Web log post]. Retrieved from http://commoncoretools.me/2012/02/      16/the-structure-is-the-standards/ 31

32. Dividing Fractions Imagine you are beginning to teach students division with fractions. What would you do to introduce this concept to students? 32

33. Dividing Fractions How would you present the following problem: 1 ¾ ÷ ½ ? 33

34. Knowing and Teaching Elementary Mathematics – Liping Ma What is the common phrase we hear teachers say when teaching students to divide fractions? Ma, L. (2010). Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States (Studies in Mathematical Thinking and Learning Series) (2nd ed.).      Routledge. 34

35. Knowing and Teaching Elementary Mathematics – Liping Ma Most of the Chinese teachers use the phrase “dividing by a number is equivalent to multiplying by its reciprocal” instead of what many U.S. teachers say “invert and multiply.” 35

36. Knowing and Teaching Elementary Mathematics – Liping Ma Dividing by 2 is the same as multiplying by ½, therefore dividing by ½ is the same as multiplying by 2. 36

37. Knowing and Teaching Elementary Mathematics – Liping Ma How many different ways can we solve the problem 1 ¾ ÷ ½ ? Let’s share and record all the various ways. 37

38. Knowing and Teaching Elementary Mathematics – Liping Ma Measurement Model – “How many ½s in 1 ¾?” (e.g., apples, graham crackers, piece of wood) Partitive Model – “Finding a number such that ½ of it is 1 ¾” (e.g., box of candy, cake, pizza, distance) Factors and Product – “Find a factor that when multiplied by ½ will make 1 ¾” (e.g., area of a rectangle) 38

39. The meaning of division by fractions Meaning of division with whole numbers The concept of inverse operations Meaning of multiplication with whole numbers Meaning of multiplication with fractions Concept of fraction Concept of unit Meaning of addition Knowing and Teaching Elementary Mathematics – Liping Ma 39

40. Shift 3 Fluency Students are expected to have speed and accuracy with simple calculations; teachers structure class time and/or homework time for students to memorize, through repetition, core functions such as multiplication tables so that they are more able to understand and manipulate more complex concepts. 40

41. Reflection Read the “Shift” What does the “Shift” mean to you? What does it look like in mathematics classrooms (provide specific examples)? 41

42. Granny Prix Oliver, N. (n.d.). Granny Prix [Math Game]. Retrieved from multiplication.com      website: http://www.multiplication.com/flashgames/GrannyPrix.htm 42

43. Key Fluencies 43

44. Mathematical Fluency: A Balanced Approach Balanced between procedural fluency and conceptual understanding, with examples Building on required fluencies McCallum, B., & Zimba, J. (n.d.). Mathematics Fluency A Balance Approach [Video      file]. Retrieved from http://www.youtube.com/watch?v=ZFUAV00bTwA. 44

45. Shift 4 Deep Understanding Teachers teach more than “how to get the answer” and instead support students’ ability to access concepts from a number of perspectives so that students are able to see math as more than a set of mnemonics or discrete procedures. Students demonstrate deep conceptual understanding of core math concepts by applying them to new situations. as well as writing and speaking about their understanding. 45

46. Reflection Read the “Shift” What does the “Shift” mean to you? What does it look like in mathematics classrooms (provide specific examples)? 46

47. Deep Conceptual Understanding McDonald’s Claim Wikipedia reports that 8% of all Americans eat at McDonalds every day. In the U.S., there are approximately 310 million people and 12,800 McDonalds. Do you believe the Wikipedia report to be true? Create a mathematical argument to justify your position. 47

48. Shift 5 Applications Students are expected to use math and choose the appropriate concept for application even when they are not prompted to do so. Teachers provide opportunities at all grade levels for students to apply math concepts in “real world” situations. Teachers in content areas outside of math, particularly science, ensure that students are using math – at all grade levels – to make meaning of and access content. 48

49. Reflection Read the “Shift” What does the “Shift” mean to you? What does it look like in mathematics classrooms (provide specific examples)? 49

50. Shift 6 Dual Intensity Students are practicing and understanding. There is more than a balance between these two things in the classroom – both are occurring with intensity. Teachers create opportunities for students to participate in “drills” and make use of those skills through extended application of math concepts. The amount of time and energy spent practicing and understanding learning environments is driven by the specific mathematical concept and therefore, varies throughout the given school year. 50