Vermont’s Transition to the Common Core State Standards: Going Deeper into the Standards for Mathematics

1. Vermont’s Transition to the Common Core State Standards: Going Deeper into the Standards for Mathematics Kathy Renfrew Elementary Math & Science Coordinator and Julie Conrad Middle & High School Mathematics Coordinator

2. A Special Thanks to our partner: Champlain Valley Educator Development Center (CVEDC)

3. Introductions: • Research Standards and Assessment Team Gail Taylor -- Director Marty Gephart -- CCSS Program Coordinator Pat Fitzsimmons -- Assistant Director • Vermont Math Advisory Team • Beth Hulbert

4. Vermont’s Transition to the Common Core State Standards: Going Deeper into the Standards for Mathematics Written by Vermont Mathematics Advisory Team. Published in August 2011 Partnered with 5 ESAs for Fall Meetings (Today)

5. Vermont’s Professional Learning Implementation Timeline Professional Learning on significant shifts in instruction SY2010-2011 SY 2011-2012 SY 2012-2013 SY2013-2014 SY2014-2015 VT is here!

6. Statewide Implementation Plan Goal Each Vermont educator will have an equitable opportunity over time to develop an understanding, appropriate to his or her educational responsibilities, of the Common Core State Standards (CC) and their application to curriculum, instruction and assessment.

7. You are here!

8. Today’s Agenda 8:00-8:30 Registration 8:30 Welcome/Intro/Overview 8:45 Overview of the Mathematical Practices: Why Start here? 9:00 Mathematical Practice #6: Attend to precision 10:00 Break 10:15 Mathematical Practice #3: Construct viable arguments and critique the reasoning of others. 11:15 Planning for your implementation Administrative break-out 12:00 Lunch 1:00 Break out groups: K-5: Algebraic and Operational Thinking 6-8: Expression, Equations, and Functions 9-12: High School Modeling 2:30 District team sharing and planning: Prioritizing where to start and planning your next steps.

9. Brain Research proves, If you want to remember, take notes! “The one who is doing – is the one who learns!” ~C. Jernstedt

10. Why Start with the Mathematical Practices?

11. It is the recommendation of the committee that all professional development for the Standards of Mathematical Practices should: • Develop an awareness of the Standards of Mathematical Practices • Model Standards of Mathematical Practices during all PD opportunities always integrating into mathematical topics • Provide opportunities for teachers to construct an understanding and deepen their own knowledge and experience of the Standards of Mathematical Practices through multiple mathematical domains. • Provide collaborative opportunities for teachers to reflect and improve their practices in integrating the Standards of Mathematical Practices in instruction of all mathematical content • Define and design ways to collect evidence to ensure that students are meeting these standards

12. “The Mathematical Practices are unique in that it describes how teachers need to teach to ensure their students become mathematically proficient.” “We were purposeful in calling them standards because then they won’t be ignored.” Bill McCallum

13. “The single greatest determinant of learning is not socio-economic factors or funding levels, it is instruction… Instruction itself has the largest influence on achievement.” Mike Schmoker, Results NOW

14. The Mathematical Practices are enhanced when teachers have: • A deep understanding of the practices and how they relate to each other and support mathematical proficiency • An understanding of how mathematical practices and mathematical topics interact and how they can be integrated into instruction and assessment in increasing the rigor of the content • An understanding of how and why mathematical practices must be integrated into instruction and assessment

16. MATHEMATICAL PRECISION THINK PAIR SHARE

17. Why is language soimportant? • Mathematical knowledge and reasoning depends on and is supported by mathematical language. • Teaching and learning mathematics depends on and is supported by language. • Mathematical language is both mathematical content to be learned and medium for learning mathematical content. Deborah Ball University of Michigan October 2011

18. Mathematical Practice #6:Attend to precision Mathematically proficient students: • communicate precisely to others. • use clear definitions in discussion with others and in their own reasoning. • state the meaning of the symbols they choose, • use the equal sign consistently and appropriately.

19. Mathematical Practice #6:Attend to precision Mathematically proficient students: • specify units of measure, and label axes to clarify the correspondence with quantities in a problem • calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context.

20. An Opportunity for a Close Look • Underline words that demonstrate the essence of this practice. • Choose one grade level and look at the CCSS Mathematics and identify standards that are connected to the Attending to Precision Mathematical Practice. • How do you see this information being used in your classroom?

21. How Might Teachers Support Students Becoming Precise Mathematicians ?

22. Attend to Precision • Attention to task and instructional wording • Support acquisition of academic language • Non-confrontational language correction

23. Attend to Precision • Attention to task and instructional wording • Support acquisition of academic language • Non-confrontational language correction

24. ATTENDING TO WORDING • POSSIBLE PROBLEM: If I pull out two coins, what amounts of money might I have? Deborah Ball University of Michigan Oct., 2011

25. Reasoning about different wording If I pull out two coins, what amounts of money might I have? 2. I have pennies, nickels, and dimes in my pocket. If I pull out two coins, what amount of money might I have? 3. I have pennies, nickels, and dimes in my pocket. If I pull out two coins, how many combinations are possible? 4. I have pennies, nickels, and dimes in my pocket. If I pull out two coins, how many different amounts of money are possible? Prove that you have found all the amounts that are possible. What are the differences among these questions?

26. Vocabulary Instruction

27. 1. Teacher or other students provide description, explanation, examples/non-examples 2. Students restate word and explanation in own words, verbally and in writing 3. Students create non-linguistic representations 4. Students do periodic activities to refine knowledge of vocabulary terms (compare, classify, analogize, revise, explain, study roots and suffixes) 5. Students describe/discuss terms with each other 6. Students play games to practice the use of word Building Background Knowledge (2004), Marzano identifies Six Steps to Effective Vocabulary

28. Academic Vocabulary Beck, I., McKeown, & Kucan. Bringing Words to Life. New York: the Guildford Press. 2002

29. Academic Vocabulary 1. Specific mathematical concepts (e.g., outcome, even number, , rectangle , = ) 2. Terms for knowledge or knowing (e.g., prove, conjecture)

30. Precise Definitions Eliminates Misconceptions • You ask your learners to explain what a rectangle is. One child offers a definition:. A rectangle is a flat shape. It has four square corners, and it is closed all the way around.

31. What Should the Teacher Do? A rectangle is a flat shape. It has four square corners, and it is closed all the way around. • See what is missing. • Decide what to do or say. 3. Offer a counterexample.

32. DEFINITION . A rectangle is a flat shape with straight sides that are connected at exactly four square corners. It is closed all the way around.

33. Dilemmas of using language 1. Learners necessarily use imprecise language. 2. We expect students to express themselves precisely. 3. Informal language can serve as a bridge or a support. 4. Attending to the needs of English language learners.

34. Language correction How do you balance ensuring students remain engaged in classroom discussions but still promote precision of language?

35. What are some tools to help Teachers? • Frayer Model Diagram • Venn Diagrams • Word Maps • Vocabulary Tier Table

36. You’ve been working hard, take a minute break.

38. Bugs, Giraffes, Elephants and More Images are not to scale CellNo Plan Problem

39. Why is argumentation an essential mathematical practice? THINK PAIR SHARE

40. “Argumentation ensures that we pay attention to the reasoning processes of students, not just analyze their procedures.” Jason Zimba

41. Learning really occurs as we examine questions in our mind... Growth Time B.Rich and G.C. Jernstedt

42. So what’s the problem? A Farmer has cows and chickens in his field. There is a total of 18 legs. How many cows and chickens does the farmer have? Answer: “There are multiple solutions.”

43. What does student argumentation look like?

44. Intro into Sean’s Numbers Class is studying the definitions of even and odd. Sean has claimed that 6 is special because it can be both even and odd. “Six can be divided into 3 groups of twos and 3 is odd. So it’s even and odd.”

45. Sean’s Numbers Watch Sean’s classmates argument. Write down the important moments in her argumentation process! http://ummedia04.rs.itd.umich.edu/~dams/umgeneral/seannumbers-ofala-xy_subtitled_59110_QuickTimeLarge.mov

46. What are the ingredients to an argument?

47. Toulmin-style Argument

48. Toulmin-style Argument: Mathematized! Assumptions Logic Data/ Evidence Argument Agreement Parameters

49. Critique: to judge or discuss the merits and faults of

50. How do we critique the reasoning of others? • Listen to their argument and ask clarifying questions. • Check their assumptions against yours. • Check their logic for missing assumptions. • Restate your opponents case. • Try to find a counterexample. (Close examples) • Question if there are constraints that won’t make their claim true.