Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom?

1. Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom? Bay District Schools Panama City, Florida January 22 & 23, 2013 Presenter: Elaine Watson, Ed.D.

2. Introductions Share What grade levels do you supervise? On a scale of 1 – 5, how comfortable are you observing math classrooms?

3. Volunteers for Breaks I need volunteers to remind me when we need breaks! Every 20 minutes, we need a 2-minute “movement break” to help our blood circulate to our brains. Bathroom Breaks: Take when you need them.

4. Formative Assessment How familiar are you with the Common Core Standards for Mathematical Practice?

5. Goals for this Workshop You will leave with a deeper understanding of: The 8 Common Core Practice Standards Recognizing the Practice Standards in action by the STUDENTS in a math class. Recognizing TEACHER MOVES that elicit the Practice Standards being used by students.

6. Goals for this Workshop You will leave with a deeper understanding of: The TYPES of TASKS that help to build students’ ability to “practice” the Practice Standards

7. We will accomplish these goals by: Using the SMP Template to look for “teacher moves” and “evidence of students using the practice” Looking at other resources for observation tools – CCL4 ipad app rich mathematical tasks

8. CCSSM Equally Focuses on… Standards for Mathematical Content Standards for Mathematical Practice Same for All Grade Levels Specific to Grade Level

9. Video Bill McCallum & Jason Zimba on Math Practice Standards

10. 1. Make sense of problems and persevere in solving them What does SMP # 1 look like in your school’s classrooms? What are students doing? What are teachers doing?

11. 1. Make Sense of Problems and Persevere in Solving Mathematically proficient students: Explainto self the meaningof a problem and look for entrypointsto a solution Analyzegivens, constraints, relationships and goals Make conjectures about the form and meaning of the solution

12. 1. Make Sense of Problems and Persevere in Solving Mathematically proficient students: Monitorandevaluatetheir progress and change course if necessary… “Does this approach make sense?”

13. 1. Make Sense of Problems and Persevere in Solving Mathematically proficient students: Perseverein Solving by: Transformingalgebraic expressions Changingthe viewing window on a graphing calculator Movingbetween the multiple representations of: Equations, verbal descriptions, tables, graphs, diagrams

14. 1. Make Sense of Problems and Persevere in Solving Mathematically proficient students: Check their answers “Does this answer make sense?” Does it include correct labels? Are the magnitudesof the numbers in the solution in thegeneral ballpark tomake sensein the real world?

15. 1. Make Sense of Problems and Persevere in Solving Mathematically proficient students: Check their answers Verify solution using adifferent method Compareapproach with others: How does their approach compare with mine? Similarities Differences

16. 2. Reason Abstractly and Quantitatively What does SMP # 2 look like in your school’s classrooms? What are students doing? What are teachers doing?

17. 2. Reason Abstractly and Quantitatively Mathematically proficient students: Make sense of quantities and their relationships in a problem situation Bring two complementary abilities to bear on problems involving quantitative relationships: The ability to… decontextualize to abstract a given situation, represent it symbolically, manipulate the symbols as if they have a life of their own contextualize to pause as needed during the symbolic manipulation in order to look back at the referent values in the problem

18. 2. Reason Abstractly and Quantitatively Mathematically proficient students: Reason Quantitatively, which entails habits of: Creating acoherent representation of the problem at hand considering the unitsinvolved Attending to the meaning of quantities, not just how to compute them Knowing andflexibly using different properties of operations and objects

19. 3.Construct viable arguments and critique the reasoning of others Mathematically proficient students: Understand and use… stated assumptions, definitions, and previously established results… when constructing arguments

20. 3.Construct viable arguments and critique the reasoning of others Mathematically proficient students: Understand and use… stated assumptions, definitions, and previously established results… when constructing arguments

21. 4. Model with Mathematics Modeling is both a K - 12 Practice Standard and a 9 – 12 Content Standard.

22. 4. Model with Mathematics What does SMP # 4 look like in your school’s classrooms? What are students doing? What are teachers doing?

23. 4. Model with Mathematics Mathematically proficient students: Use powerful tools for modeling: Diagrams or graphs Spreadsheets Algebraic Equations

24. 4. Model with Mathematics Mathematically proficient students: Models we devise depend upon a number of factors: Howprecisedo we need to be? What aspects do we most need to undertand, control, or optimize? Whatresourcesof time and tools do we have?

25. 4. Model with Mathematics Mathematically proficient students: Models we devise are also constrained by: Limitations of our mathematical, statistical, and technical skills Limitations of our ability to recognize significant variablesand relationships among them

26. Modeling Cycle The word “modeling” in this context is used as a verb that describes the process of transforming a real situation into an abstract mathematical model.

27. Modeling Cycle Problem Formulate Validate Report Compute Interpret

28. Modeling Cycle Problem Identify variables in the situation Select those that represent essential features

29. Modeling Cycle Formulate Select or create a geometrical, tabular, algebraic, or statistical representation that describes the relationships between the variables

30. Modeling Cycle Compute Analyze and perform operations on these relationships to draw conclusions

31. Modeling Cycle Interpret Interpret the result of the mathematics in terms of the original situation

32. Modeling Cycle Validate Validate the conclusions by comparing them with the situation…

33. Modeling Cycle Validate Re - Formulate Report on conclusions and reasoning behind them

34. Modeling Cycle Problem Formulate Validate Report Compute Interpret

35. 5. Use appropriate tools strategically What does SMP # 5look like in your school’s classrooms? What are students doing? What are teachers doing?

36. 5. Use appropriate tools strategically Tools can be physical: Measurement tools (ruler, meter stick, tape measure, protractor) Calculating tools (calculator, computer) Drawing tools (straight edge, compass, graph paper)

37. 5. Use appropriate tools strategically Tools can be mathematical: Equations Graphs Tables Matrices Facts tables

38. 6. Attend to precision What does SMP # 6 look like in your school’s classrooms? What are students doing? What are teachers doing?

39. 6. Attend to precision Mathematically proficient students: Try to communicate precisely to others: Use clear definitions State the meaning of symbols they use Use the equal sign consistently and appropriately Specify units of measure Label axes

40. 6. Attend to precision Mathematically proficient students: Try to communicate precisely to others Calculate accurately and efficiently Express numerical answers with a degree of precision appropriate for the problem context Give carefully formulated explanations to each other Can examine claims and make explicit use of definitions

41. Use the Standards for Mathematical Practice Lesson Alignment Template.What SMPs do you see? http://ummedia04.rs.itd.umich.edu/~dams/umgeneral/seannumbers-ofala-xy_subtitled_59110_QuickTimeLarge.mov

42. 7. Look for and make use of structure What does SMP # 7 look like in your school’s classrooms? What are students doing? What are teachers doing?

43. 7. Look for and make use of structure Mathematically proficient students: Look closely to discern a pattern or structure In x2 + 9x + 14, can see the14as2 x 7 and the9as2 + 7 Can see complicated algebraic expressions as being composed of several objects: 5 – 3 (x – y)2 is seen as 5 minus a positive number times a square, so its value can’t be more than 5 for any real numbers x and y

44. 8. Look for and express regularity in repeated reasoning. What does SMP # 8 look like in your school’s classrooms? What are students doing? What are teachers doing?

45. 8. Look for and express regularity in repeated reasoning. Mathematically proficient students: Notice if calculations are repeated Look for both general methods and for shortcuts Maintain oversight of the process while attending to the details.

46. Observe SMPs 1 – 8 in Action While you watch the video,use the SMP template to record to teacher moves and the student moves that you see for SMPs 1 – 8. High School Geometry lesson

47. Do All 8 Practice Standards Need to be Used in Every Lesson? There are some rich problems that elicit all 8 of the Practice Standards. However, these types of problems can’t be done on a daily basis. Instructional time still needs to be balanced between building the students’ technical skills and No…but the teacher should plan so that over the span of a few days, the students are given learning opportunities to of the practicing standards

48. A Balanced Approach math facts how to approach and a novel situation procedures mathematically

49. Math Facts and Procedures Memorizing Math Facts and Naked Number Exercises are Important! Practice Standards that apply: #2 Reason Quantitatively #6 Attend to Precision #7 Look for and Use Structure #8 Use Repeated Reasoning

50. What SMPs Do You Observe Maya Practicing? http://www.livescribe.com/cgi-bin/WebObjects/LDApp.woa/wa/MLSOverviewPage?sid=r6Hkjn0xzFPB