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Common Core State Standards in Mathematics Overview Tere Hirsch Contract Consultant, Mathematics Division of Curriculum and Instructional Services Los Angeles County Office of Education [email protected] Objectives for today: EXAMINE ANALYZE FOCUS THINK “Math Class needs a Makeover” with Dan Meyer http://www.ted.com/talks/dan_meyer_math_curriculum_makeover.html CCSS Math Note Taking Guide Reflection #1: Т Math Class Needs a MakeoverУ Reflection #2 : Reflection #2: “Implications for the classroom teacher” Reflection #3: Standards of Mathematical Practice (SMP) Reflection #4: Grade Level Standards Reflection #5 : WhatХs Next? Reflection #1 What similarities or differences did you see in the video compared to your classroom or those that you have observed? Race To the Top 2009 Common Core State Standard (CCSS) Initiative sponsored by NGA and CCSSO Committee convened to develop… 1. CCSS 2. Nationwide assessment 3. Timeline for state adoption California Timeline Jan 2010: ACSC (Academic Content Standards Commission) is created and members are chosen June 2010 : ACSC studies CCSS July 2010 : ACSC recommends adoption with some additions August 2, 2010: SBE adopts ACSC’s recommendations Materials: Implementation Timeline 1 Milestone Math ELA Completed 1/2012 Field review of framework 9/2012 9/2013 SBE action on framework 5/2013 5/2014 2014–15 2014–15 Materials submission 3/2016 3/2018 SBE approves materials 11/2016 11/2018 Curriculum Commission approves plan, timeline and criteria committee application Common core assessments Assumes the passage of Assembly Bill 250 (Brownley), which partially lifts the suspension under EC Section 60200.7, and Curriculum Commission funding for 2011 and subsequent years. 8 Assessment SBAC (Smarter Balance Assessment Consortium) http://www.k12.wa.us/smarter/ Reflection #2 What are the implications for the classroom teacher? You can always count on Peter… Mathematical Proficiency As defined by the California Framework “WHERE” THE MATHEMATICS WORK Problem Solving Computational & Procedural Skills DOING MATH Conceptual Understanding “WHY” THE MATHEMATICS WORK “HOW” THE MATHEMATICS WORK Big Picture in Mathematics CCSS Standards of Mathematical Practice Grade Level Standards Grades K-5 Grades 6-8 High School Math 8th Grade Options Algebra 1 Core Standards to prepare for Algebra 1 How do we achieve understanding? How do we foster mathematically proficient students? The Standards for Mathematical Practice Standards for Mathematical Practice 1 Make sense of problems and persevere in solving them 4 Model with mathematics 6 Look for and make use of structure 2 Reason abstractly and quantitatively 3 Construct viable arguments and critique the reasoning of others 5 Standards for Mathematical Practice 7 Attend to precision Use appropriate tools strategically. 8 Look for and express regularity in repeated reasoning Grouping the Standards of Mathematical Practice 1. Make sense of problems and persevere in solving them. 6. Attend to precision. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. Overarching habits of mind of a productive mathematical thinker. Reasoning and explaining Modeling and using tools. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. William McCallum University of Arizona- April 1, 2011 Seeing structure and generalizing. 1. Make sense of problems and persevere in solving Do students: • EXPLAIN? • ANALYZE? • Make CONJECTURES? • PLAN a solution pathway? • MULTIPLE representations? • Use DIFFERENT METHODS to check? • Check that it all makes sense? • Understand other approaches? • See connections among different approaches? 2. Reason abstractly and quantitatively Do students: • Make sense of quantities & their relationships? • Decontextualize? • Contextualize? • Create a coherent representation? • Consider units involved? • Deal with the meaning of the quantities? 3. Construct viable arguments and critique the reasoning of others. Do students: • Understand & use stated assumptions, definitions, and previous results? • Analyze situations, recognize & use counterexamples? • Justify conclusions, communicate to others & respond to arguments? • Compare the effectiveness of 2 plausible arguments? • Distinguish correct logical reasoning from flawed & articulate the flaw? • Look at an argument, decide if it makes sense,& ask useful questions to clarify or improve it? • Make conjectures& build a logical progression? • Use mathematical induction as technique for proof? • Write geometric proofs, including proofs of contradiction? 4. Model with mathematics Do students: • Apply the mathematics they know everyday? • Analyze relationships mathematically to draw conclusions? • Initially use what they know to simplify the problem? • Identify important qualities in a practical situation? • Interpret results In the context of the situation? • Reflect on whether the results make sense? 5. Use appropriate tools strategically. Do students: • Consider available tools? • Know the tools appropriate for their grade or course? • Make sound decisions about when tools are helpful? • Identify & use relevant external math Sources? • Use technology tools to explore & deepen understanding of concepts? 6. Attend to precision. Do students: • Communicate precisely with others? • Use clear definitions? • Use the equal sign consistently & appropriately? • Calculate accurately & efficiently? 7. Look for and make use of structure. Do students: • Look closely to determine a pattern or structure? • Use properties? • Decompose & recombine numbers & expressions? • Have the facility to shift perspectives? 8. Look for and express regularity in repeated reasoning. Do students: • Notice if calculations are repeated? • Look for general methods & shortcuts? • Maintain process while attending to details? • Evaluate the reasonableness of intermediate results? Reflection #3 What is the intent of the SMPs – in the teacher’s case ? – in the student’s case? CA Common Core Grade Level Standards in Mathematics Focus of the Common Core State Standards Ratios & Proportional Relationships Counting & Cardinality The Number System Operations & Algebraic Thinking Number & Operations in Base Ten Expressions & Equations Fractions Functions Measurement and Data Geometry Geometry Statistics & Probability K 1 2 3 4 5 From Willi am McCallum, Arizona, (one of the writers of CCSS) 6 7 8 CCSS Domains K-5 Domain K 1 2 3 4 5 Counting and Cardinality (CC) Operations and Algebraic Thinking (OA) Number and Operations in Base Ten (NBT) Measurement and Data (MD) Geometry (G) Number and Operations – Fractions (NF) In grades K-5, students develop a solid foundation in whole numbers, addition, subtraction, multiplication, division, fractions, and decimals. CCSS Domains 6-8 6 7 Ratios and Proportional Relationships (RP) The Number System (NS) Expressions and Equations (EE) Geometry (G) Statistics and Probability (SP) Domain Functions (F) 8 With a strong foundation of content knowledge from grades K-5, middle school students are prepared for robust learning in geometry and statistics and probability California Grade 8 Options The goal for 8th grade students is Algebra 1 Two options for grade 8 that prepare students for college and career: • Algebra 1: Grade 8 Common Core and the high school Algebra content cluster • Grade 8 Common Core: goal of grade 8 Common Core is to finalize preparation for students to take Algebra I in high school. Grade Level Overviews Standards for Mathematical Content Content standards define what students should understand and be able to do. Clusters are groups of related content standards. Domains are larger groups of related content standards that progress across grade levels. Domain Code Standard from Grade 3 Standard Cluster Fractions, Grades 3-6 Gr. 3: Develop an understanding of fractions as numbers Gr. 4: Extend understanding of fraction equivalence and ordering Gr. 4: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers Gr. 4: Understand decimal notation for fractions, and compare decimal fractions Gr. 5: Use equivalent fractions as a strategy to add and subtract fractions Gr. 5: Apply and extend previous understandings of multiplication and division to multiply and divide fractions Gr. 6: Apply and extend previous understandings of multiplication and division to divide fractions by fractions Phil Daro High School Standards: Conceptual Categories Are arranged by conceptual cluster, not by course. • number and quantity • algebra • functions • Modeling* • Geometry • Statistics and Probability Eighth grade Algebra 1 standards are organized around these themes as well. *Modeling Standard for Mathematical Practice is emphasized at the high school level. Students are expected to use mathematics to analyze situations, understand them more fully, and make decisions related to their everyday lives. (pp.60-61) Theme Domain Cluster of Standards High School Conceptual Theme Notation Reflection #4 At first glance, how are the CCSS grade level standards different from or similar to our current standards? Next Steps What will we do? Remember: – Testing begins in 2014/15 Some ideas – websites & resources Reflection #5 What else do you need to know about CCSS? What are your next steps in this learning process? REMEMBER….. DEEP DOWN INSIDE, WE ALL LOVE MATH