Agenda CCSS math shifts – digging in deep for high school Smarter Balanced Assessment Resources and professional learning opportunities 2 CCSS Math Webinar Part 4: 5/28/13 OSPI CCSS Quarterly Webinar Series http://www.k12.wa.us/CoreStandards/UpdatesEvents.aspx#Webinar Year 2 Topics: 2012-13 CCSS Systems for District and Building Leaders 1. September 2012: Recap / State Context / Resources / Where to Start / Professional Learning Systems 2. December 2012: The Basics for School Boards 3. March 2013: Focus on Instructional Materials / Principal Leadership 4. May 2013: Focus on Communications and Smarter Balanced Digital Library CCSS-M Content for Leaders 1. September 2012: Recap / Math Shifts and Resources and Cross-Content Teams 2. December 2012: Diving into the Math Shifts for Elementary 3. March 2013: Diving into the Math Shifts for Middle School 4. May 2013: Diving into the Math Shifts for High School CCSS-ELA for Leaders and Cross-Content Teams 3 1. September 2012: Recap / ELA Shifts and Resources 2. December 2012: Diving into ELA and Text Selection / Implications for ELA in History/Social Studies 3. March 2013: Diving into the ELA: A Focus on Evidence in Reading/Writing/Speaking & Listening 4. May 2013: Diving into ELA: Academic Vocabulary and ELA across the Part Subjects (Science, the Arts, etc.) CCSS Math Webinar 4: 5/28/13 Before we begin…About You We’d like to know a little about who is out there. Time for a poll (one more time…) 4 CCSS Math Webinar Part 4: 5/28/13 ESEA Flexibility CAREER AND COLLEGE READY LEARNING STANDARDS FOR K-12 Vision Every Washington Student and Educator Purpose Core Values All students leave high school college and career ready Our Purpose: To develop a statewide system with resources that support partners at all levels in their preparation of ALL educators and ALL students to implement the CCSS. 5 Washington’s State Learning Goals are the Foundation (HB 1209+; RCW 28A.150.210) 1. Read with comprehension, write effectively, and communicate successfully in a variety of ways and settings and with a variety of audiences; 2. Know and apply the core concepts and principles of mathematics; social, physical, and life sciences; civics and history, including different cultures and participation in representative government; geography; arts; and health and fitness; 3. Think analytically, logically, and creatively, and to integrate technology literacy and fluency as well as different experiences and knowledge to form reasoned judgments and solve problems; and 4. Understand the importance of work and finance and how performance, effort, and decisions directly affect future career and educational opportunities. 5. Updated in 2011: SSB 5392) 6 CCSS Math Webinar Part 4: 5/28/13 CCSS Implementation Timeline Phase 1: CCSS Exploration Phase 2: Build Awareness & Begin Building Capacity Phase 3: Build State & District Capacity and Classroom Transitions Phase 4: Statewide Application and Assessment Ongoing: Statewide Coordination and Collaboration to Support Implementation 7 CCSS Math Webinar Part 4: 5/28/13 Our guiding beliefs and approach for CCSS Implementation in WA 2-Prongs: 1. The What: Content Shifts (for students and educators) The How: System “Remodeling” 2. 8 Belief that past standards implementation efforts have provided a strong foundation on which to build for CCSS; HOWEVER there are shifts that need to be attended to in the content. Belief that successful CCSS implementation will not take place top down or bottom up – it must be “both, and…” Belief that districts across the state have the conditions and commitment present to engage wholly in this work. Professional learning systems are critical CCSS Math Webinar Part 4: 5/28/13 Ongoing: Statewide Coordination and Collaboration to Support Implementation Washington Including: • School Districts (CCSS District Implementation Network) • Higher Education • Education and Educator Content Associations • Business Partners 9 CCSS Math Webinar Part 4: 5/28/13 “These standards are not intended to be new names for old ways of doing business.” CCSSM, page 5 10 CCSS Math Webinar Part 4: 5/28/13 The 3 Shifts in CCSSM Focus strongly where the standards focus Coherence: Think across grades and link to major topics within grades Rigor: In major topics, pursue with equal intensity: 11 Conceptual understanding Procedural skill and fluency Application CCSS Math Webinar Part 4: 5/28/13 Shift One: Focus strongly where the Standards focus • Move away from "mile wide, inch deep" curricula identified in TIMSS. • Learn from international comparisons. • Teach less, learn more. “Less topic coverage can be associated with higher scores on those topics covered because students have more time to master the content that is taught.” – Ginsburg et al., 2005 12 CCSS Math Webinar Part 4: 5/28/13 Focus in International Comparisons TIMSS and other international comparisons suggest that the U.S. curriculum is ‘a mile wide and an inch deep.’ “…On average, the U.S. curriculum omits only 17 percent of the TIMSS grade 4 topics compared with an average omission rate of 40 percent for the 11 comparison countries. The United States covers all but 2 percent of the TIMSS topics through grade 8 compared with a 25 percent noncoverage rate in the other countries. High-scoring Hong Kong’s curriculum omits 48 percent of the TIMSS items through grade 4, and 18 percent through grade 8.” 13 CCSS Math Webinar Part 4: 5/28/13– Ginsburg et al., 2005 Focus in Early Grades Materials do not assess any of the following topics before the grade level indicated. Grade Introduced Topic Probability, including chance, likely outcomes, probability models. 7 Statistical distributions, including center, variation, clumping, outliers, mean, median, mode, range, quartiles, and statistical association or trends, including two-way tables, bivariate measurement data, scatter plots, trend line, line of best fit, correlation. 6 Similarity, congruence, or geometric transformations. 8 Symmetry of shapes, including line/reflection symmetry, rotational symmetry. 4 Additionally, materials do not assess pattern problems in K-5 that do not support the focus on arithmetic, such as “find the CCSS Math Webinar Part 4: 5/28/13 next one” problems. 14 Shift Two: Coherence Think across grades, and link to major topics within grades Carefully connect the learning within and across grades so that students can build new understanding onto foundations built in previous years. Begin to count on solid conceptual understanding of core content and build on it. Each standard is not a new event, but an extension of previous learning. 15 CCSS Math Webinar Part 4: 5/28/13 How do students perceive mathematics? • Doing mathematics means following the rules laid down by the teacher. • Knowing mathematics means remembering and applying the correct rule when the teacher asks a question. • Mathematical truth is determined when the answer is ratified by the teacher. -Mathematical Education of Teachers report (2012) 16 CCSS Math Webinar Part 4: 5/28/13 How do students perceive mathematics? Students who have understood the mathematics they have studied will be able to solve any assigned problem in five minutes or less. Ordinary students cannot expect to understand mathematics: they expect simply to memorize it and apply what they have learned mechanically and without understanding. 17 CCSS Math Webinar Part 4: 5/28/13 -Mathematical Education of Teachers report (2012) Coherence with Functions Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. 3.OA.D.9 3rd Grade Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. 6.EE.C.9 6th Grade Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. 8.F.B.4 8th Grade Write a function that describes a relationship between two quantities. Combine standard function types using arithmetic operations. F-BF.A.b F-BF.A HS Functions Coherence Within A Grade Functions – Connections to Expressions, Equations, Modeling and Coordinates Determining an output value for a particular input involves evaluating a an expression; finding inputs that yield a given output involves solving an equation. Questions about when two functions have the same value for the same input lead to equations, whose solutions can be visualized from the intersection of their graphs. Because functions describe relationship between quantities, they are frequently used in modeling. Sometimes functions are defined by a recursive process, which can be displayed effectively using a spreadsheet or other technology. Shift Three: Rigor Equal intensity in conceptual understanding, procedural skill/fluency, and application The CCSSM require: Solid conceptual understanding Procedural skill and fluency Application of skills in problem solving situations In the major work of the grade, this requires equal intensity in time, activities, and resources in pursuit of all three 20 CCSS Math Webinar Part 4: 5/28/13 It starts with Focus The current U.S. curriculum is ‘a mile wide and an inch deep.’ Focus is necessary in order to achieve the rigor set forth in the standards More in-depth mastery of a smaller set of things pays off 21 CCSS Math Webinar Part 4: 5/28/13 22 CCSS Math Webinar Part 4: 5/28/13 The Structure is the Standards A Grecian urn You have just purchased an expensive Grecian urn and asked the dealer to ship it to your house. He picks up a hammer, shatters it into pieces, and explains that he will send one piece a day in an envelope for the next year.You object; he says “don’t worry, I’ll make sure that you get every single piece, and the markings are clear, so you’ll be able to glue them all back together. I’ve got it covered.” Absurd, no? But this is the way many school systems require teachers to deliver mathematics to their students; one piece (i.e. one standard) at a time.” Adapted from “The Structure is the Standards” by Bill McCullum, Phil Daro and Jason Zimba 23 CCSS Math Webinar Part 4: 5/28/13 Standards for Mathematical Practice 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 and express regularity in repeated reasoning CCSS Math Webinar Part 4: 5/28/13 Standards for Mathematical Practices Graphic 25 CCSS Math Webinar Part 4: 5/28/13 Some Old Ways of Doing Business • A different topic every day • Every topic treated as equally important • Elementary students dipping into advanced topics at the expense of mastering fundamentals • Infinitesimal advance in each grade; endless review • Incoherence and illogic – bizarre associations, or lacking a thread CCSS Math Webinar Part 4: 5/28/13 26 Traditional Ways of Doing Business Finding Intercepts by Substitution Find the intercepts of the line y = 13 – x Solution The first intercept is easy to find. The y-intercept occurs when x = 0. Substituting gives us y = 13-0 = 13, so the y-intercept is (0, 13). Similarly, the x-intercept occurs when y = 0. Plugging in 0 for y gives us 0 = 13 - x, and adding x to both sides gives us x = 13. So (13, 0) is the x-intercept. 27 CCSS Math Webinar Part 4: 5/28/13 Traditional Ways of Doing Business Finding Intercepts for Standard Form Equations Using the Cover- Up Method Find the intercepts of 7x - 3y = 21 28 CCSS Math Webinar Part 4: 5/28/13 Traditional Ways of Doing Business Factoring Methods Factoring out a monomial Factoring by grouping Factoring x2 + bx + c Factoring ax2 + bx + c When c is postivie When c is negative When a is negative Factoring Special cases 29 When c is positive When c is negative Difference of two squares Perfect square trinomials CCSS Math Webinar Part 4: 5/28/13 New Ways of Doing Business Teacher: To avoid mile wide factoring, I’m thinking CCSS intends for us to narrow down the toolbox but I need to know what to cut. I taught factoring monomials from bi, then grouping, then turning trinomials into four factors for grouping and relating special cases to grouping, all the while motivating toward guess and check for shortcuts. The CCSS do not seem to include grouping which wipes out the rest of my sequence. Can someone please clarify what factoring tools will be used, particularly if don’t factor by grouping? Is there a connected sequence? Bill McCallum: I would say that CCSS is not so much narrowing down the toolbox, as encouraging students to see that all the different tools work on the same principle, so that you don’t have to remember so many different tools.Your progression is fine, and can be understood as progressively more sophisticated applications of the distributive property. I don’t know exactly what you mean when you say that the “CCSS does not seem to include grouping.” If I understand correctly what you mean by grouping, it is an instance of the distributive property, which is fundamental from early grades (even if it does not go by that name). 30 CCSS Math Webinar Part 4: 5/28/13 Some New Ways of Doing Business A.SEE Interpret the structure of expressions. Suppose P and Q give the sizes of two different animal populations, where Q>P. In (a)–(d), say which of the given pair of expressions is larger. Briefly explain your reasoning in terms of the two populations. 31 CCSS Math Webinar Part 4: 5/28/13 A Look at Assessment 32 CCSS Math Webinar Part 4: 5/28/13 CCSS Assessment System Transitions Our change to Common Core is at the heart of assessment changes for ELA and Math NCLB requires states to assess state standards We’ve changed standards so we need to change assessments What we change to is our choice Smarter Balanced is where we are headed for ELA and Math Graduation requirements are a state’s choice 33 IMPT: There are currently no assessment consortia established for Science Supt Dorn is proposing reduced graduation requirements ESEA Waiver changes expectation that all students are proficient next year (2014) – it gives us more time and more individualized school-based goals CCSS Math Webinar Part 4: 5/28/13 Smarter Balanced Assessment System Components Common Core State Standards specify K-12 expectations for college and career readiness Summative assessments Benchmarked to college and career readiness Teachers and schools have information and tools they need to improve teaching and learning Teacher resources for formative assessment practices to improve instruction 34 All students leave high school college and career ready Interim assessments Flexible, open, used for actionable feedback CCSS Math Webinar Part 4: 5/28/13 A Balanced Assessment System English Language Arts/Literacy and Mathematics, Grades 3-8 and High School School Year Last 12 weeks of the year* DIGITAL CLEARINGHOUSE of formative tools, processes and exemplars; released items and tasks; model curriculum units; educator training; professional development tools and resources; scorer training modules; and teacher collaboration tools. Optional Interim Assessment Computer Adaptive Assessment and Performance Tasks Optional Interim Assessment Computer Adaptive Assessment and Performance Tasks PERFORMANCE TASKS • ELA/Literacy • Mathematics Scope, sequence, number and timing of interim assessments locally determined COMPUTER ADAPTIVE TESTS • ELA/Literacy • Mathematics Re-take option *Time windows may be adjusted based on results from the research agenda and final implementation decisions. 35 Claims for the Mathematics Summative Assessment Overall Claim for Grades 3-8 Overall Claim for Grade 11 “Students can demonstrate progress toward college and career readiness in mathematics.” “Students can demonstrate college and career readiness in mathematics.” Claim #1 - Concepts & Procedures “Students can explain and apply mathematical concepts and interpret and carry out mathematical procedures with precision and fluency.” Claim #2 - Problem Solving “Students can solve a range of complex well-posed problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies.” Claim #3 - Communicating Reasoning “Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others.” Claim #4 - Modeling and Data Analysis “Students can analyze complex, real-world scenarios and can construct and use mathematical models to interpret and solve problems.” CCSS Math Webinar Part 4: 5/28/13 36 Smarter Balanced Timeline – Washington’s Involvement (http://www.k12.wa.us/SMARTER/default.aspx) OSPI staff involved in workgroups 2010-2014 Teachers involved in item writing Summer/Fall 2012 Sample Released Items and Performance Tasks – October 2012 (view the OSPI webinar!) Small Scale Trials in Oct/Nov 2012 Pilot in Spring 2013 Practice Test widely available May 29 Comprehensive field test in 2013-14 Operational use in 2014-15 The Digital Library… Work begins late spring 2013 State Network of Educators to be recruited in May 2013 to populate the digital library CCSS Math Webinar Part 4: 5/28/13 37 Smarter’s Vision for the Digital Library Provide an online, interactive clearinghouse with all the formative tools and resources necessary to transform classroom practices to support student success. Prior to summative assessment, primary focus professional development. With the summative, data from summative and interim score reports integrated into resources for teachers, students, and parents. 38 CCSS Math Webinar Part 4: 5/28/13 Digital Library Features One Stop: The Digital Library will have links to all test engine systems through a single sign-on with user permission levels so teachers, parents, and students have access to all of the curriculum and professional learning resources. Assessment literacy Formative assessment resources Links to other resources and other components of the Smarter online system Interactive Teacher Space Opportunities to keep journals of practices Key words or phrases in the journals will generate suggested lists of resources. Record resources consulted and suggest others. Teachers can request resources matched to student assessment results. 39 CCSS Math Webinar Part 4: 5/28/13 Digital Library Deliverables Teaching and Learning Resources for Educators Modules for Grades K-2, 3-5, 6-8, 9-12 Assessment Literacy Modules 144 Assessment Literacy professional learning modules that include: 40 how to build, administer, score, evaluate, interpret, and use data from formative, interim, and summative assessments Includes resources for each grade band that address English Language Learners and Students With Disabilities CCSS Math Webinar Part 4: 5/28/13 Digital Library Deliverables Exemplar Instruction Modules 50 instructional modules for each grade band (Grades K-2, 3-5, 6-8, 9-12) ELA/Literacy – Proposed Modules Mathematics – Proposed Modules Balance of Inf. and Literary Text Focus Literary in the Content Areas Coherence Increased complexity of text Fluency Text-Based questions and answers Duel Intensity Academic Vocabulary Deep Understanding Writing using evidence Math Practices across various standards Writing using evidence (Wireless Generation Response pg. 97) Page 41 CCSS Math Webinar Part 4: 5/28/13 Deliverables – Exemplar Instruction Modules …each instructional module will: Start by identifying the learning targets for the lesson, which align with the CCSS in ELA or Math. Begin lesson with a formative pre-assessment to determine the level of knowledge students have about the learning target. (ASSESS) Use formative assessment data/information to plan the lesson so that the teacher knows individual students’ needs related to the learning targets. (PLAN) Provide examples of instruction that can teach the learning target and also meet the needs of diverse learners.(TEACH) Conclude the lesson with a formative post- assessment whose data will determine the plan for the next lesson (ASSESS) Contain embedded links to the Digital Library resources, Assessment Literacy modules and glossary, and additional resources as available. Page 42 (Wireless Generation Response pg. 108 ) CCSS Math Webinar Part 4: 5/28/13 Deliverables – Exemplar Instruction Each module will show video clips on: Classroom instruction of the learning targets Formative assessment (pre and post instruction) of the learning targets Teacher and student reflections following the lesson The length of each video will be between 1–3 minutes, with the final length of each module no longer than 15–25 minutes. Each module will include a Teacher Resource Guide with: Graphic/visual and text versions of the full cycle of instruction using formative assessment practices; and key CCSS-M/ELA instructional shifts Student work samples (by grade band) from diverse student groups Examples of the writing required in each grade level Evidence gathering tools and techniques (by content and grade band) including preassessments (prior to lesson), post-assessments(following the lesson) Links to resources on CCSS, formative assessments, appropriate accommodations for CCSS content and meeting needs of diverse learners. Page 43 (Wireless Generation Response pg. 109) CCSS Math Webinar Part 4: 5/28/13 State Network of Educators (SNE) http://www.k12.wa.us/SMARTER/EducatorInvolvement.aspx Overview: 70-100 members per state and a minimum of 2700+ across all governing states (WA will have 92) Participate in web-based review and feedback cycles to develop (2 year commitment) Digital Library Application Quality Criteria Policies Inventory of Currently Available Resources Smarter Balanced Professional Learning Resources Educator Training Materials Identify and recommend additional resources for the Digital Library Disseminate web-based educator training to state professional learning networks Receive stipends from Contractor Timeline: Statewide recruitment process in May 2013 – APPLY TODAY! Notifications in early July 2013 Work begins in Summer 2013 44 CCSS Math Webinar Part 4: 5/28/13 Tools and Supports What’s new and what’s next 45 CCSS Math Webinar Part 4: 5/28/13 Washington State Common Core State Standards Year 2 Professional Learning Opportunities In partnership with OSPI, Regional Math and English Language Arts Coordinators from each ESD across the state, have created consistent, equitable professional development opportunities to support implementation of the Common Core State Standards. These workshops align with the transition plans set out by the collective group. Mathematics Grades 46 CCSS Focus Domain: K-2 Counting and Cardinality Numbers and Operations in Base Ten and Algebraic Thinking 3-5 Numbers and Operations - Fractions 6-8 Ratio and Proportional Relationships HS Linear Relationships and Functions Description Teachers across all grade bands will deepen their understanding of the major shifts to the Common Core State Standards (CCSS): Embed Standards for Mathematical Practices with grade specific content Analyze, adapt and implement tasks with the intended rigor of the CCSS Understand the Smarter Balanced Assessment System Analyze student work to identify next steps for learning CCSS Math Webinar Part 4: 5/28/13 Top Resources for Math Educators Inside Mathematics Video excerpts of mathematics lessons correlated with the practice standards, resources on content standards alignment, and videos of exemplary lessons in both elementary and secondary settings. Illustrative Mathematics Guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students experience in a faithful implementation of the Common Core State Standards. Progressions Documents for the Common Core Math Standards Narrative documents describing the progression of a topic across a number of grade levels. Publishers Criteria Provides criteria for aligned materials to CCSS. Based on the two major evidence-based design principles of the CCSSM, focus and coherence, the document intends to guide the work of publishers and curriculum developers, as well as states and school districts, as they design, evaluate, and select materials or revise existing materials. Achieve The Core Guidance and templates on how to begin implementing the shifts, assembled by the nonprofit Student Achievement Partners. 47 CCSS Math Webinar Part 4: 5/28/13 Algebra Progression Document Seeing Structure in Expressions Seeing structure in expressions entails a dynamic view of an algebraic expression, in which potential rearrangements and manipulations are ever present.A-SSE.2 An important skill for college readiness is the ability to try out possible manipulations mentally without having to carry them out, and to see which ones might be fruitful and which not. CCSS Math Webinar Part 4: 5/28/13 Algebra Progression Document Reasoning with Equations and Inequalities The danger in learning algebra is that students emerge with nothing but the moves, which may make it difficult to detect incorrect or made-up moves later on. Thus the first requirement in the standards in this domain is that students understand that solving equations is a process of reasoning. A-REI. It is traditional for students to spend a lot of time on various techniques of solving quadratic equations, which are often presented as if they are completely unrelated (factoring, completing the square, the quadratic formula). In fact, as we have seen, the key step in completing the square, going from 𝑥 2 = 2 𝑡𝑜 𝑥 = ± 𝑞 , involves at its heart factoring. And the quadratic formula is nothing more than an encapsulation of the method of completing the square. Rather than long drills on techniques of dubious value, students with an understanding of the underlying reasoning behind all these methods are opportunistic in their application, choosing the method that bests suits the situation at hand. A-REI.4b http://commoncoretools.me/wpcontent/uploads/2012/12/ccss_progression_algebra_2012_12_04.pdf CCSS Math Webinar Part 4: 5/28/13 Resources for Considering Instructional Materials OSPI Instructional Materials Web Site: http://www.k12.wa.us/CurriculumInstruct/InstructionalMaterialsReview.aspx OSPI’s Open Educational Resources Project: http://digitallearning.k12.wa.us/oer/ From CCSS Developers… CCSS Publisher’s Criteria – ELA and Math (http://engageny.org/resource/publishers-criteria-for-elaliteracy-and-math/) CCSS Evidence Guides: Common Core-aligned practice made clear (from Achieve the Core) These tools provide specific guidance for what the CCSS for ELA / literacy and math looks like in planning and practice. They are designed as developmental tools for teachers and those who support teachers. http://www.achievethecore.org/leadership-tools-common-core/instructional-practice/ Going deeper with other states… EQuip Review Rubrics and Process (http://engageny.org/resource/tri-state-quality-review-rubric-and-rating-process/) 50 CCSS Math Webinar Part 4: 5/28/13 2012-13 CCSS Implementation Resources & Activities Opportunities and Resources CCSS Awareness and Professional Learning Opportunities and Materials (http://www.k12.wa.us/CoreStandards/Resources.aspx) OSPI CCSS Webinar Series PD Offered through all 9 ESDs CCSS District Implementation Network Collaborations Instructional Materials Quality Considerations & Supports Assessment System Resources Smarter Balanced Released Sample Items / Perf. Tasks Dynamic Learning Map Assessment Literacy Supports Teacher-Leader Capacity Building Opportunities Math and ELA “Fellows” build capacity around common learning (Spring 2013) 51 CCSS Math Webinar Part 4: 5/28/13 Thank YOU! Common Core Supports: OSPI Lead Team: General Support / Overall CCSS Leadership: - General email: corestandards@k12.wa.us - Jessica Vavrus, jessica.vavrus@k12.wa.us Math Support / CCSS Coordination Lead: - Greta Bornemann, Greta.Bornemann@k12.wa.us ELA Support: - Liisa Moilanen Potts, Liisa.moilanenpotts@k12.wa.us 52 CCSS Math Webinar Part 4: 5/28/13