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“Common Core State Standards for Mathematics 9-12 Administrator’s Academy 1169”

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“Common Core State Standards for Mathematics 9-12 Administrator’s Academy 1169”

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  1. “Common Core State Standards for Mathematics 9-12 Administrator’s Academy 1169” Pippen Consulting Randy and Sue Pippen 2011-12

  2. Warm-Up You have three playing cards lying face up, side by side. A five is just to the right of a two, a five is just to the left of a two, a spade is just to the left of a club, and a spade is just to the right of a spade. What are two possibilities for the three cards? Be ready to discuss your thinking!

  3. Introductions • Find a shoulder partner that is not in your school or district – move if you have to. • Introduce yourselves to each other: • Name, position, what you hope to learn today. • On a signal, tell the group what your partner told you.

  4. What does the traditional math lesson look like? Turn to partner and discuss • Does it look different at elementary, middle and high school? • Is this design effective? What is our evidence that it is? What is our evidence that it is not? • How long have we used this model?

  5. Rate Your Knowledge • Signal your familiarity with the new Illinois State Standards for Mathematics (Common Core State Standards) by showing a signal of 1 to 5 with 1 being the lowest.

  6. I D E A M O C

  7. Participants will be able to: • - understand that the Common Core Math State Standards are the new Illinois State Math Standards and will be the basis for the Math State Assessments for grades 9-12; • -learn for evaluation purposes that the new Common Core Math State Standards involve content and practice standards - what mathematics is to be taught and assessed, and what instructional practices are expected to be used for grades 9-12; • -examine how grades 9-12 math instruction and assessment must change in order to teach and assess for understanding, making sense, and what to monitor through evaluation; and • -analyze the differences between the grades 9-12 scope and sequence of the old Illinois Learning Standards

  8. Workshop Goals • Relate the New Common Core State Standards to the Illinois Standards and the upcoming change in State testing. • Relate the new Mathematics Practice Standards to the way instruction should look with the CCSSM. • Familiarize administrators with the instructional changes required for students to learn with depth, understanding and making sense of the mathematics. • Relate the differences in the old Illinois Math Standards and the new Illinois Math Standards (CCSSM). • Develop a plan to update staff on the key components of the Content and Practice Standards and how they will be assessed.

  9. Major Ideas of the CCSSM Fewer, higher, more focused Benchmarked Internationally Equal emphasis of understanding and skills Much more specific than old Illinois Learning Standards Emphasis on number early on, learning trajectories develop through the grades Highly visual and connected with multiple representations of functions: graphs/verbal/symbolic/numeric

  10. Major Content Differences • Emphasis on arithmetic and number patterns translating to algebra • Congruence and similarity based on transformations • Resurgence of constructions, but in a variety of ways • Algebra 1, Geometry, and Algebra 2 for all students • Modeling, modeling, modeling or “What’s it good for?” • Precalculus only for students who will take calculus • Not all students should take calculus – STEM standards (+) • A variety of fourth year courses • No longer push for more students in the 8th grade taking high school algebra

  11. 8th Grade Algebra • Currently sending too many underprepared students to algebra at the 8th grade • Program may not be equivalent to high school due to time constraints of middle school, may not have a secondary-math- certified teacher • There cannot be any skipping in CCSSM • There are other ways to accelerate (p. 81 Appendix A) • Not all students need calculus, therefore do not need to accelerate at all.

  12. Eighth Grade Expressions and Equations • Understand the connections between proportional relationships, lines, and linear equations. 5. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. 6. Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

  13. Eighth Grade Expressions and Equations • Analyze and solve linear equations and pairs of simultaneous linear equations. 7. Solve linear equations in one variable. a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

  14. New Assessment Design • No ISAT or PSAE after 2013-2014. • May be pilot items in ISAT in 2012-2014. • Some areas tested by current state tests will no longer be tested in new design. • NCLB has not been reauthorized nor made any adjustments for CCSS. Many states are refusing to continue with NCLB. • A waiver is to be available to states who meet the be released in September

  15. The PARCC System – Initial Design English Language Arts and Mathematics, Grades 3 - 11 25% 50% 75% 90% PARTNERSHIP RESOURCE CENTER: Digital library of released items, formative assessments, model curriculum frameworks, curriculum resources, student and educator tutorials and practice tests, scoring training modules, and professional development materials • Focused • ASSESSMENT 1 • ELA • Math • Focused • ASSESSMENT 2 • ELA • Math • Focused • ASSESSMENT 3 • ELA • Math END OF YEAR COMPREHENSIVE ASSESSMENT • Focused • ASSESSMENT4 • Speaking • Listening Summative assessment for accountability Required, but not used tor accountability

  16. Partnership for Assessment of Readiness for College and Careers (PARCC) Governing Board States Participating States

  17. The PARCC Goals • Create high-quality assessments • Build a pathway to college and career readiness for all students • Support educators in the classroom • Develop 21st century, technology-based assessments • Advance accountability at all levels

  18. Priority Purposes of PARCC Assessments: • Determine whether students are college- and career-readyor on track • Assess the full range of the Common Core Standards, including standards that are difficult to measure • Measure the full range of student performance, including the performance high and low performing students • Provide data during the academic year to inform instruction, interventions and professional development • Provide data for accountability, including measures of growth • Incorporate innovative approaches throughout the system

  19. Goal #1: Create High Quality Assessments • Summative Assessment Components: • Performance-Based Assessment (PBA) administered as close to the end of the school year as possible. The ELA/literacy PBA will focus on writing effectively when analyzing text. The mathematics PBA will focus on applying skills, concepts, and understandings to solve multi-step problems requiring abstract reasoning, precision, perseverance, and strategic use of tools. • End-of-Year Assessment (EOY) administered after approx. 90% of the school year. The ELA/literacy EOY will focus on reading comprehension The math EOY will be comprised of innovative, machine-scorable items • Formative Assessment Components: • Early Assessment designed to be an indicator of student knowledge and skills so that instruction, supports and professional development can be tailored to meet student needs • Mid-Year Assessment comprised of performance-based items and tasks, with an emphasis on hard-to-measure standards. After study, individual states may consider including as a summative component

  20. Goal #1: Create High Quality Assessments The PARCC assessments will allow us to make important claims about students’ knowledge and skills. • In English Language Arts/Literacy, whether students: • Can Read and Comprehend Complex Literary and Informational Text • Can Write Effectively When Analyzing Text • Have attained overall proficiency in ELA/literacy • In Mathematics, whether students: • Have mastered knowledge and skills in highlighted domains (e.g. domain of highest importance for a particular grade level – number/ fractions in grade 4; proportional reasoning and ratios in grade 6) • Have attained overall proficiency in mathematics

  21. Goal #1: Create High-Quality Assessments – New Design Flexible • End-of-Year • Assessment • Innovative, computer-based items • Mid-Year Assessment • Performance-based • Emphasis on hard to measure standards • Potentially summative • Performance-Based • Assessment (PBA) • Extended tasks • Applications of concepts and skills • Early Assessment • Early indicator of student knowledge and skills to inform instruction, supports, and PD • ELA/Literacy • Speaking • Listening Summative assessment for accountability Formative assessment

  22. Goal #2: Build a Pathway to College and Career Readiness for All Students K-2 formative assessment being developed, aligned to the PARCC system • Targeted interventions & supports: • 12th-grade bridge courses • PD for educators Timely student achievement data showing students, parents and educators whether ALL students are on-track to college and career readiness College readiness score to identify who is ready for college-level coursework SUCCESS IN FIRST-YEAR, CREDIT-BEARING, POSTSECONDARY COURSEWORK ONGOING STUDENT SUPPORTS/INTERVENTIONS


  24. Goal #4: Develop 21st Century, Technology-Based Assessments PARCC’s assessment will be computer-based and leverage technology in a range of ways to: • Item Development • Develop innovative tasks that engage students in the assessment process • Administration • Reduce paperwork, increase security, reduce shipping/receiving & storage • Increase access to and provision of accommodations for SWDs and ELLs • Scoring • Make scoring more efficient by combining human and automated approaches • Reporting • Produce timely reports of students performance throughout the year to inform instructional, interventions, and professional development

  25. Goal #4: Develop 21st Century, Technology-Based Assessments • PARCC assessments will be purposefully designed to generate valid, reliable and timely data, including measures of growth,for various accountability uses including: • School and district effectiveness • Educator effectiveness • Student placement into college-credit bearing courses • Comparisons with other state and international benchmarks • PARCC assessments will be designed for other accountability uses as states deem appropriate

  26. Sept. 2012 First year field testing and related research and data collection begins Sept. 2013 Second year field testing begins and related research and data collection continues Sept. 2014 Full administration of PARCC assessments begins Summer 2015 Set achievement levels, including college-ready performance levels Oct. 2010 Launch and design phase begins Sept. 2011 Development phase begins PARCC Timeline

  27. Implementation Challenges Estimating costs over time, including long-term budgetary planning Transitioning to the new assessments at the classroom level Ensuring long-term sustainability Policy Challenges Student supports and interventions Accountability High school course requirements College admissions/ placement Perceptions about what these assessments can do Technical Challenges Developing an interoperable technology platform Transitioning to a computer-based assessment system Developing and implementing automated scoring systems and processes Identifying effective, innovative item types Key Challenges for PARCC

  28. Reason for New Assessment Design Change • Cost effectiveness in a difficult economy • The three summative through-course assessments could dictate the scope and sequence of the curriculum limiting local flexibility (not federal government right) • The potential that the required three through-course assessments would disrupt the instructional program on, and in preparation for, testing days

  29. Intended to ensure results will be reported in categories consistent with the CCSS. • Separate scores in ELA for reading and writing as well as an overall score indicating on track to college and career readiness. • Separate score in a “highlighted domain” that reflects the CCSS’s emphasis at each grade level (e.g., fractions in grade 4, rations and proportional relationships at grade 6), as well as an overall math score indicating on track to college readiness. • Measures student growth over a full academic year or course • Provides data during the academic year to inform instruction, interventions and professional development activities. • Accessible to all students including disabled and ELL • Must be approved by the US Department of Education

  30. Highlighted Domains - PARCC

  31. Brain Break! • Listen to directions • See what it looks like • Stand up and try it

  32. Comparison of Content Standards

  33. Comparison of Process Standards

  34. Progressions

  35. Number Goal – ILS (Old)

  36. Reason quantitatively and use units to solve problems. • N.Q.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. • N.Q.2 Define appropriate quantities for the purpose of descriptive modeling. • N.Q.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

  37. Explain to your partner… 1a. How do you solve 3x + 1 = -14 ? 1b. Why did you do it the way you did? • Switch roles 2a. How do you graph y = ½ x -3? 2b. Why did you do it the way you did?

  38. Algebra Goal - OLD ILS

  39. Understand solving equations as aprocess of reasoning and explain the reasoning. (CCSSM Algebra) • A.REI.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

  40. Geometry Goal – Old ILS

  41. Geometry - CCSSM • G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. • G.CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). • G.CO.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. • G.CO.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. • G.CO.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

  42. Why is Change Needed? • There is a train. It leaves a station an hour later than a plane flying overhead, flying in the opposite direction. • The number of the train is a 3-digit number whose tens digit is 3 more than its units digit. • The conductor of the train is half as old as the train was when the conductor was a third as old, just a third as old. •  The conductor’s niece and nephew are on the train. They head toward the club car at the back of the train to buy mixed nuts; some of the nuts are $1.79 a pound and some are $2.25 a pound. •  They have quarters, dimes and nickels in their pockets to pay for the nuts. •  The niece starts first and walks at 2 miles per hour and the nephew starts later and walks at 3 miles per hour. •  How long will it take them to get to the back of the train if they walk together? Enuf said?

  43. No Numbers Warm-up • If you know the width of a lawn mower in inches, how can you find how many square yards of lawn it cuts in running a certain number of feet? • Problems Without Figures • Gillan, 1909

  44. High School – Appendix A • Traditional Path or Integrated Path • Same fifteen units – distributed by course • Illinois will have to choose one or the other to determine testing • Challenges: Materials for either path • Texts: May say they are aligned, probably not

  45. Mathematics I Common Core State Standards • Unit 1 – Relationships Between Quantities • Unit 2 – Linear and Exponential Relationships • Unit 3 – Reasoning with Equations • Unit 4 – Descriptive Statistics • Unit 5 – Congruence, Proof and Constructions • Unit 6 – Connecting Algebra and Geometry through Coordinates Algebra I Unit 1 – Relationships Between Quantities and Reasoning with Equations Unit 2 – Linear and Exponential Relationships Unit 3 – Descriptive Statistics Unit 4 - Expressions and Equations Unit 5 – Quadratic Functions and Modeling

  46. Mathematics II Common Core State Standards • Unit 1 – Extending the Number System • Unit 2 - Quadratic Functions and Modeling • Unit 3 – Expressions and Equations • Unit 4 – Applications of Probability • Unit 5 – Similarity, Right Triangle Trigonometry and Proof • Unit 6 – Circles With and Without Coordinates Geometry Unit 1 - Congruence, Proof, and Constructions Unit 2 - Similarity, Proof and Trigonometry Unit 3 - Extending to Three Dimensions Unit 4 - Connecting Algebra and Geometry through Coordinates Unit 5 - Circles with and Without Coordinates Unit 6 - Applications of Probability

  47. Mathematics III Common Core State Standards • Unit 1 – Inferences and Conclusions from Data • Unit 2 – Polynomial, Rational and Radical Relationships • Unit 3 – Trigonometry of (+)General Triangles and Trigonometric Functions • Unit 4 – Mathematical Modeling Algebra II Unit 1 – Polynomial, Rational and Radical Relationships Unit 2 – Trigonometric Functions Unit 3 – Modeling with Functions Unit 4 – Inferences and Conclusions from Data

  48. Major Changes at the High School • More algebra at the eighth grade means a different algebra in high school, more technology for both • Geometry must be built upon grade school transformations – most books are not written that way • More Probability and Stats in all high school courses • Advanced Algebra has less content but more depth than previous courses, more technology

  49. Discussion – Partner Talk • Turn to your shoulder partner and talk about what you see regarding the new and old ILS – specifically, talk about implications for instruction • Signal to start, signal to stop (about 2 minutes). • Whole Group Sharing

  50. Brain Break! • Listen to directions • See what it looks like • Stand up and try it