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From NECAP to the Common Core Mathematics and New Assessments

From NECAP to the Common Core Mathematics and New Assessments. April 26, 2011. AGENDA From NECAP to the Common Core Mathematics and New Assessments. Introduction and background information Transition Timeline (NECAP to the Common Core and New assessments) Overview of Mathematics CCSS

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From NECAP to the Common Core Mathematics and New Assessments

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  1. From NECAP to the Common Core Mathematics and New Assessments April 26, 2011

  2. AGENDAFrom NECAP to the Common Core Mathematics and New Assessments • Introduction and background information • Transition Timeline (NECAP to the Common Core and New assessments) • Overview of Mathematics CCSS • Design and Organization • Similarities/Differences between CCSS & GLEs/GSEs • Time for Questions and Answers • Next Steps

  3. Introduction and Background Information State-led and developed common core standards for K-12 in English/language arts and mathematics Focus on learning expectations for students, not how students get there.

  4. Why Now? Disparate standards across states Student mobility Global competition Today’s jobs require different skills

  5. Why Important? Prepares students with the knowledge and skills they need to succeed in college and work Ensures consistent expectations regardless of a student’s zip code Provides educators, parents, and students with clear, focused guideposts

  6. From NECAP to the Next Generation Assessment Systems Transition / Timeline

  7. So what?Implications & Impact in NH • Adoption • State Board adopted the CCSS “in principle” and is committed to a thoughtful, orderly transition process for implementation and assessment • Alignment • Process began this summer to look at gaps and matches and grade differentials • DOE putting together a broad view to post & distribute • Focus groups currently meeting to review analysis • Implementation • TAKE IT SLOW! • NECAP in place for at least three years • Toolkit for administrators & curriculum leaders in development

  8. Now what?Transition Timeline 2010-2011– NECAP as usual Begin review of standards-Use Toolkit NECAP Management Team releases plan to principals in April 2011 2011-2012 – NECAP as usual 2012 2013 – NECAP (with transitional items) 2013 2014 – final NECAP (best possible transitional test) 2014-2015 – no fall NECAP test NECAP Science remains New assessments based CCSS

  9. Curriculum and Assessment Timeline for New Hampshire (adjusted format) *NH Curriculum Standards in all other content areas remain in place http://www.education.nh.gov/spotlight/k12_ccss.htm A place to start:

  10. 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 Mathematics Common Core Standards

  11. Review of Major Components of the Mathematics CCSS Presentation for the NH Department of Education

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

  13. Key Features: Mathematics Learning progressions that follow how students learn concepts Understanding the mathematics AND procedural skill are equally important “processes and proficiencies” from the NCTM process standards & Adding It Up 8 mathematical practices are the same throughout the grades Standards for content vary by grade Mastery of standards through grade 7 prepares students for algebra in grade 8 Appendix: Designing HS Mathematics Courses [http://www.corestandards.org/assets/CCSSI_Mathematics_Appendix_A.pdf ] 16

  14. Common Core State Standards • Introduction • Application of CCSS for ELLs • Application to Students with Special Needs • Mathematics Standards • Standards for Mathematical Practice • Grade levels/strand introductions • Domains, Clusters and Standards • Appendix A: Model Pathways for High School Courses [http://www.corestandards.org/assets/CCSSI_Mathematics_Appendix_A.pdf ]

  15. Standards for Mathematical Practice [Explain and make conjectures…] [Make sense of ...] [Understand and use…] [Apply and interpret…] [Consider and Detect] [Communicate precisely to others…] [Discern and recognize…] [Notice and pay attention to….] • 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 and express regularity in repeated reasoning

  16. Key Advances • Properties of operations: Their role in arithmetic and algebra • Mental math and “algebra” vs. algorithms • Operations and the problems they solve • Units and unitizing • Unit fractions • Unit rates • Quantities-variables-functions-modeling • Number-expression-equation-function • Modeling • Practices

  17. Common Core Format High School Conceptual Category Domain Cluster Standards K-8 Grade Domain Cluster Standards (There are no preK Common Core Standards)

  18. Mathematics Standards:

  19. Mathematics K-8 : Design & Organization • Introduction Page • Highlights: 2-3 Critical Areas • Provides: Emphasis of Content • Overview Page • Provides: • Domains • Cluster Headings • Mathematical Practices

  20. Components: K-8 grade level Mathematics Standards

  21. High School Conceptual Categories Standards forMathematical Content Grade Level Domains K – 5 Counting and Cardinality Operations and Algebraic Thinking Number and Operations in Base Ten Number and Operations – Fractions Measurement and Data Geometry 6-8 Ratios and Proportional Relationships The Number System Expressions and Equations Functions Geometry Statistics and Probability Number and Quantity Algebra Functions Modeling Geometry Statistics and Probability

  22. Distribution of the Domains (K-8)

  23. Overview: Mathematics Grades K - 5 Introduction at earlier grade • Addition, subtraction, multiplication, and division of whole numbers and other rational numbers Introduction at later grade • Statistics & probability is introduced as a domain in Grade 6 • Expressions & Equations is introduced as a domain in Grade 6 More specificity • Focus on operations with whole numbers, fractions, and decimals as the foundation for more demanding math concepts and procedures

  24. Overview: Mathematics Grades 6 – 8 Introduction at earlier grade • Percent increase and decrease and interest rate • Histograms, box plots, quartiles and inter-quartile range Introduction at later grade • Functions as a domain is introduced in grade 8 More specificity • Grades 6 & 7 standards: ramp up to algebraic concepts in Gr. 8 • Grade 8 standards focus is on linear equations and functions

  25. High School Conceptual Categories Standards forMathematical Content Grade Level Domains K – 5 Counting and Cardinality Operations and Algebraic Thinking Number and Operations in Base Ten Number and Operations – Fractions Measurement and Data Geometry 6-8 Ratios and Proportional Relationships The Number System Expressions and Equations Functions Geometry Statistics and Probability Number and Quantity (N) Algebra (A) Functions (F) Modeling (*) Geometry (G) Statistics and Probability (S)

  26. High School Standards • Conceptual Categories • Cross course boundaries • Span high school years • Standards • “Core” for common mathematics curriculum for all students to be college and career ready • “College Ready” for entry level credit bearing course • (+) Additional mathematics that students should learn in order to take courses such as calculus, discrete mathematics, or advanced statistics.

  27. Components: High School Mathematics Standard

  28. Conceptual Categories: Domains • Number and Quantity • The Real Number System • Quantities • The Complex Number System • Vector and Matrix • Algebra • Seeing Structure in Expressions • Arithmetic with Polynomials & Rational Functions • Creating Equations • Reasoning with Equations and Inequalities • Functions • Interpreting Functions • Building Functions • Linear, Quadratic, & Exponential Models • Trigonometric Functions

  29. Conceptual Categories: Domains (continued) • Modeling • Geometry • Congruence • Similarity, Right Triangles, and Trigonometry • Circles • Expressing Geometric Properties with Equations • Geometric Measurement & Dimension • Modeling with Geometry • Statistics and Probability • Interpreting Categorical and Quantitative Data • Making Inferences and Justifying Conclusion • Conditional Probability and Rules of Probability • Using Probability to Make Decisions

  30. Overview: Mathematics High School Introduction at earlier grade • Complex numbers • Quadratic, logarithmic, & trigonometric functions • Logarithmic identities Specificity • Reflects four years of instruction • 1st three years prepare students for college or career • 4th year allows for course of choice • STEM standards (+) • Modeling is integrated throughout all the domains (*)

  31. Integrated Model Course Pathways in Mathematics Traditional ALGEBRA I GEOMETRY ALGEBRA II 4th Year Mathematics Course MATHEMATICS I MATHEMATICS II MATHEMATICS III 4th Year Mathematics Course

  32. Cracking the High School Mathematics “Code” High School • Number and Quantity • The Real Number System N-RN • Quantities N-Q • The Complex Number System N-CN • Vector and Matrix N-VM • Algebra • Seeing Structure in Expressions A-SSE • Arithmetic with Polynomials & Rational Functions A-APR • Creating Equations A-CED • Reasoning with Equations and Inequalities A-REI

  33. Cracking the High School Mathematics “Code” (continued) • Functions • Interpreting Functions F-IF • Building Functions F-BF • Linear, Quadratic, & Exponential Models F-LE • Trigonometric Functions F-TF • Modeling * • Geometry • Congruence G-CO • Similarity, Right Triangles, and Trigonometry G-SRT • Circles G-C • Expressing Geometric Properties with Equations G-GPE • Geometric Measurement and Dimension G-GMD • Modeling with Geometry G-MG

  34. How to read a Common Core High SchoolMathematics Standard A-SSE.1b Letter & Number indicating the Standard within the Cluster Conceptual Category Domain

  35. How to read a Common Core High School PATHWAYS Mathematics Standard (+)N.CN.4,5,6 Indicates: STEM standard Numbers indicating the Standards within the Cluster Heading Conceptual Category Domain

  36. For grades preK-8, a model of implementation can be found in NCTM’sCurriculum Focal Points For the secondary level, please see NCTM’sFocus in High School Mathematics: Reasoning and Sense Making See Handout w/additional resources Additional Information www.nctm.org/cfp www.nctm.org/FHSM

  37. Reflections: Now What? What actions will you take based upon what we worked on today? • What do you need to learn? • Who will you work with? • What do you need to integrate into your practice? • Who will support you?

  38. Want to know more? NH DOE Website: http://www.education.nh.gov/spotlight/k12_ccss.htm Maine Department of Education http://www.maine.gov/education/lres/math/standards.html NCSM November 30 2010 Webinar on CCSShttp://www.carnegielearning.com/webinars/getting-started-with-the-common-core-state-standards-first-steps-for-mathematics-education-leaders/ Rhode Island Department of Education http://www.ride.ri.gov/Instruction/CommonCoreMaterials.aspx#HowToReadPPT

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