Focus, Coherence, and Rigor

1. Mathematical Shifts of the Common Core State Standards May 2013 Common Core Training for Administrators Middle Grades Mathematics Division of Academics, Accountability, and School Improvement Focus, Coherence, and Rigor

2. Mathematical Shifts of the Common Core State Standards: Focus, Coherence and Rigor AGENDA Purpose and Vision of CCSSM Implementation Timeline Six Shifts in Mathematics Design and Organization Instructional Implications: Classroom Look-fors Expectations of Student Performance CCSSM Resources: Websites Reflections / Questions and Answers

3. Community Norms We are all learners today We are respectful of each other We welcome questions We share discussion time We turn off all electronic devices __________________

4. Purpose and Vision of the CCSSM

5. WhyCommon Standards? Consistency • Previously, every state had its own set of academic standards and different expectations of student performance. Equity • Common standards can help create more equal access to an excellent education. Opportunity • Students need the knowledge and skills that will prepare them for college and career in our global economy. Clarity • These new standards are clear and coherent in order to help students, parents, and teachers understand what is expected.

6. College and Career Readiness: Anchor for the Common Core The Common Core State Standards were back-mapped from the anchor of college and career readiness because governors and state school chiefs realized there was a significant gap between high school expectations for students and what students are expected to do in college/career. Among high school graduates, about only half are academically prepared for postsecondary education.

7. College Remediation and Graduation Rates • Remediation rates and costs are staggering • As much as 40% of all students entering 4-year colleges need remediation in one or more courses • As much as 63% in 2-year colleges • Degree attainment rates are disappointing • Fewer than 42% of adults aged 25-34 hold college degrees Source: The College Completion Agenda 2010 Progress Report, The College Board

8. Are We Mathematically Ready for College and Careers?

9. Common Core State Standards Mission • The Common Core State Standards provide a consistent, clear understanding of what students are expected to learn, so teachers and parents know what they need to do to help them. The standards are designed to be robust and relevant to the real world, reflecting the knowledge and skills that our young people need for success in college and careers. With American students fully prepared for the future, our communities will be best positioned to compete successfully in the global economy.

10. M-DCPS Florida’s Common Core State Standards Implementation Timeline F L F L • F – Full Implementation of CCSSM • L – Full implementation of content area literacy standards including: text complexity, quality and range in all grades (K-12) • B – Blended instruction of CCSS with NGSSS; last year of NGSSS assessed on FCAT 2.0 (Grades 3-8); 4th quarter will focus on NGSSS/CCSSM grade level content gaps

11. CCSSM CCSSM NGSSS CCSSM CCSSM CCSSM NGSSS NGSSS CCSSM NGSSS CCSSM NGSSS CCSSM CCSSM NGSSS

12. Six Shifts in Mathematics

13. Mathematical Shifts FOCUSdeeply on what is emphasized in the Standards COHERENCE: Think across grades, and link to major topics within grades RIGOR:Require- Fluency Deep Understanding Model/Apply Dual Intensity

15. Name that Shift… • At your tables, use the provided cards to place under the appropriate shift listed on the handout: focus, coherence, fluency, deep understanding, application, and dual intensity. • After this is complete, your table will receive one large card identifying what the student does and the teacher does for a particular shift. Discuss with your table the shift that the card describes and tape it to the corresponding chart paper. Be ready to explain your reasoning.

16. Shift 1: Focus Teachers use the power of the eraser and significantly narrow and deepen the scope of how time and energy is spent in the math classroom. They do so in order to focus deeply on only the concepts that are prioritized in the standards so that students reach strong foundational knowledge and deep conceptual understanding and are able to transfer mathematical skills and understanding across concepts and grades. Students are able to transfer mathematical skills and understanding across concepts and grades. – Spend more time on Fewer Concepts Achievethecore.org

17. Mathematics Shift 1: Focus Spend more time on Fewer Concepts http://www.fldoe.org/schools/ccc.asp

18. “Teach Less, Learn More…” - Ministry of Education, Singapore

19. K-8 Priorities in Math Priorities in Support of Rich Instruction and Expectations of Fluency and Conceptual Understanding K–2 Addition and subtraction, measurement using whole number quantities 3–5 Multiplication and division of whole numbers and fractions 6 Ratios and proportional reasoning; early expressions and equations 7 Ratios and proportional reasoning; arithmetic of rational numbers 8 Linear algebra Achievethecore.org

20. Shift 2: Coherence Principals and teachers carefully connect the learning within and across grades so that students can build new understanding onto foundations built in previous years. Teachers can begin to count on deep conceptual understanding of core content and build on it. Eachstandard is not a new event, but an extension of previous learning. A student’s understanding of learning progressions can help them recognize if they are on track. Keep Building on learning year after year Achievethecore.org

21. Mathematics Shift 2: Coherence Keep Building on learning year after year http://www.fldoe.org/schools/ccc.asp

22. Shift 3: Fluency Teachers help students to study algorithms as “general procedures” so they can gain insights to the structure of mathematics (e.g. organization, patterns, predictability). Students are expected to have speed and accuracy with simple calculations and procedures so that they are more able to understand and manipulate more complex concepts. Students are able to apply a variety of appropriateproceduresflexiblyas they solve problems. Spend time Practicing (First Component of Rigor) Achievethecore.org

23. Mathematics Shift 3: Fluency Spend time Practicing http://www.fldoe.org/schools/ccc.asp

24. K-8 Key Fluencies Achievethecore.org

25. Shift 4: Deep Conceptual Understanding Teachers teach more than “how to get the answer;” they support students’ ability to access concepts from a number of perspectives so that students are able to see math as more than a set of mnemonics or discrete procedures. Students demonstrate deep conceptual understanding of core math concepts by applying them to new situations as well as writing and speaking about their understanding. UnderstandMath, DoMath, andProveit (Second Component of Rigor) Achievethecore.org

26. Mathematics Shift 4: Deep Understanding UnderstandMath, DoMath, andProveit http://www.fldoe.org/schools/ccc.asp

27. Shift 5: Applications (Modeling) Teachers provide opportunities to apply math concepts in “real world” situations. Teachers in content areas outside of math ensure that students are using math to make meaning of and access content. Students are expected to use math and choose the appropriate concept for application even when they are not prompted to do so. Apply math in Real World situations (Third Component of Rigor)

28. Mathematics Shift 5: Application (Modeling) Apply math in Real World situations http://www.fldoe.org/schools/ccc.asp

29. Shift 6: Dual Intensity There is a balance between practice and understanding; both are occurring with intensity. Teachers create opportunities for students to participate in “drills” and make use of those skills through extended application of math concepts. Thinkfast and Solveproblems (Fourth Component of Rigor) Achievethecore.org

30. Mathematics Shift 6: Dual Intensity Thinkfast and Solveproblems http://www.fldoe.org/schools/ccc.asp

31. Design and Organization

32. Design and Organization Standards for Mathematical Content • K-8 standards presented by grade level • Organized into domains that progress over several grades • Grade introductions give 2–4 focal points at each grade level Standards for Mathematical Practice • Carry across all grade levels • Describe habits of mind of a mathematically expert student

33. Mathematical Practices • 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

34. Standards for Mathematical Practice How we teach is just as important as what we teach….

35. Learning Experiences It matters how students learn • Learning mathematics is more than just learning concepts and skills. Equally important are the cognitive and metacognitive process skills. These processes are learned through carefully constructed learning experiences. • For example, to encourage students to be inquisitive and have a deeper understanding of mathematics, the learning experiences must include carefully structured opportunities where students discover mathematical relationships and principles on their own.

36. What does mathematical understanding look like?

37. Overarching Habits of Mind of a Productive Mathematical Thinker 1. Make sense of problems and persevere in solving them 6. Attend to precision Modeling and Using Tools Reasoning and Explaining Seeing Structure and Generalizing 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 4. Model with mathematics 5. Use appropriate tools strategically 7.Look for and make use of structure 8.Look for and express regularity in repeated reasoning

38. Overarching Habits of Mind of a Productive Mathematical Thinker Gather Information Make a plan Anticipate possible solutions Continuously evaluate progress Check results Question sense of solutions MP 1: Make sense of problems and persevere in solving them. MP 6: Attend to precision Mathematically proficient students can… Mathematically proficient students can… use mathematical vocabulary to communicate reasoning and formulate precise explanations calculate accurately and efficiently and specify units of measure and labels within the context of the situation explain the meaning of the problem and look for entry points to its solution monitor and evaluate their progress and change course if necessary use a variety of strategies to solve problems

39. Reasoning and Explaining MP 2: Reason abstractly and quantitatively. MP 3: Construct viable arguments and critique the reasoning of others Mathematically proficient students can… Mathematically proficient students can… • have the ability to contextualize and decontextualize problems involving quantitative relationships: • decontextualize - to abstract a given situation and represent it symbolically and manipulate the representing symbols • contextualize - to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. make a mathematical statement (conjecture) and justify it listen, compare, and critique conjectures and statements

40. Modeling and Using Tools MP 4: Model with Mathematics. • In early grades, this might be as simple as writing an addition equation to describe a situation. • In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. MP 5: Use appropriate tools strategically Mathematically proficient students can… Mathematically proficient students can… apply mathematics to solve problems that arise in everyday life reflect and make revisions to improve their model as necessary map mathematical relationships using tools such as diagrams, two-way tables, graphs, flowcharts and formulas. consider the available tools when solving a problem (i.e. ruler, calculator, protractor, manipulatives, software) use technological tools to explore and deepen their understanding of concepts

41. Seeing Structure and Generalizing MP 7: Look for and make use of structure MP 8: Look for and express regularity in repeated reasoning Mathematically proficient students can… Mathematically proficient students can… look closely to determine possible patterns and structure (properties) within a problem analyze a complex problem by breaking it down into smaller parts notice repeating calculations and look for efficient methods/ representations to solve a problem generalize the process to create a shortcut which may lead to developing rules or creating a formula

42. GROUP ACTIVITY • Each group will receive: • An envelope containing 8 small cards and a handout of the listed mathematical practices. • Instructions: • Match each of the 8 small cards with its mathematical practice (using the handout of the listed mathematical practices).