1. Overview Dr Kwaku Adu-Gyamfi Stefanie Smith

2. 2

3.  Work with your group  Who did you work with?  What did you learn about them?  Their knowledge of mathematics  Their problem solving techniques  Their mathematical preferences?  Present your Solutions 3

4. 4

5. 5

6. 6

7.  Mathematics involved in the task  Pedagogy experienced  Connecting task to CCSSM and the mathematical Practices  Adjusting the task for your class needs 7

8. 8

9.  Goal  Identify the domains, clusters and concept categories included in the standards  Identify and connect the standards for mathematical practice to the National Council of Teachers of Mathematics process standards 9

10.  Aligned with college and work expectations  Maintains focus on what matters most for readiness  Include rigorous content and application of knowledge through high-order skills  Build upon strengths and lessons of current state standards  Internationally benchmarked so that all students are prepared to succeed in our global economy and society  State led

11.  Focus and coherence Focus on key topics at each grade level. Coherent progressions across grade levels.  Balance of concepts and skills Content standards require both conceptual understanding and procedural fluency.  Mathematical practices Foster reasoning and sense-making in mathematics.  College and career readiness Level is ambitious but achievable.

12.  How teachers should teach  All that can or should be taught  The nature of advanced work beyond the core  The interventions needed for students well below grade level  The full range of support for learners and students with special needs  Everything needed to be college and career ready

13.  To be effective in improving education and getting all students ready for college, workforce training, and life, the Standards must be partnered with a content- rich curriculum and robust assessments, both aligned to the Standards.  NC Curriculum  MATH1 /MATH2  Algebra1/Algebra2  Integrated  NC Themes  Algebra Theme  Geometry Theme  Functions Theme  Statistics Theme

14. STANDARDS FOR HIGH SCHOOL MATHEMATICS 9-12

15. Part 1 15

16. Standards for Mathematical Content  Defines what students should understand and be able to do (conceptual categories) Standards for Mathematical Practice  Describes habits of mind of a mathematically proficient student CCSS= Math content + Math practices

17.  Organized by conceptual categories  The big ideas that connect mathematics across high school Number and Quantity Algebra Functions Modeling Geometry Statistics and Probability  Elaborated through domains, clusters and standards 17

18. CollegeHigh School  Linear Algebra  Calculus  Abstract Algebra  Introduction to proof  Geometry  Statistics and Probability  Number and Quantity  Algebra  Functions  Modeling  Geometry  Statistics and Probability 18

19. 19 Content standard Domain Cluster

20. 20 Domains: are larger groups that progress across grades (Big Idea) Content standards: defines what students should understand and be able to do with the big idea (Objectives) Clusters are groups of related standards (content needed to be covered for the said objective)

21. Domain Content Clusters 21

22.  Work with your partner (from the race track activity)  Go to the function section of the common core (CCSSM) document  Pick out a domain, identify the standards and clusters associated with the domain  Create a chart/visual or concept map that helps address the connection between Domain Content Clusters  Color code your chart…  Post your Chart Paper  Gallery Walk… 22

23. Part 2 23

24.  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  Use appropriate tools strategically  Attend to precision  Look for and make use of structure  Look for an express regularity in repeated reasoning 24

25.  Describes varieties of expertise that proficient mathematics students naturally have  Practices that all teachers should develop in their students  Practices rests on important processes and proficiencies of importance in mathematics education  Process standards  Mathematical proficiency strands 25

26.  Process Standards Problem Solving Reasoning and Proof Communication Connections Representations 26

27. 27

28. 28

29.  Conceptual Understanding-  comprehension of mathematical concepts, operations and relations  Procedural Fluency-  skill in carrying out procedures flexibly, accurately, efficiently and appropriately  Strategic Competence-  ability to formulate, represent and solve mathematical problems  Adaptive Reasoning-  capacity for logical thought, reflection, explanation and justification  Productive disposition-  inclination to see mathematics as sensible useful and worthwhile, coupled with a belief in diligence and one’s own efficacy 29

30.  Take a moment to examine the first three words of each of the 8 mathematical practices..what do you notice?  What are the verbs that illustrate the student actions for an identified mathematical practice?  Circle, highlight or underline them for your assigned practice  Discuss with a partner, what jumps out at you? 30

31. 31

32.  Stay in the same groups as for the previous activity  Each group is assigned 1-3 mathematical practices to review  Each group construct tasks that reflect their assigned practices  Write tasks on chart paper  Discuss challenges with regard to developing tasks 32

33. 33 What I Know about the CCSSM What I want to Know about the CCSSM What I learned about the CCSM

34. A function or not a function activity 34

35. 35

36. 36

37. Overview of Mathematics Task Types PARCC mathematics assessments will include three types of tasks. 37 Task TypeDescription of Task Type I. Tasks assessing concepts, skills and procedures Balance of conceptual understanding, fluency, and application Can involve any or all mathematical practice standards Machine scorable including innovative, computer-based formats Will appear on the End of Year and Performance Based Assessment components II. Tasks assessing expressing mathematical reasoning Each task calls for written arguments / justifications, critique of reasoning, or precision in mathematical statements (MP.3, 6). Can involve other mathematical practice standards May include a mix of machine scored and hand scored responses Included on the Performance Based Assessment component III. Tasks assessing modeling / applications Each task calls for modeling/application in a real-world context or scenario (MP.4) Can involve other mathematical practice standards. May include a mix of machine scored and hand scored responses Included on the Performance Based Assessment component For more information see PARCC Item Development ITN Appendix D.