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Focus, Coherence, and Rigor

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  1. Mathematical Shifts of the Common Core State Standards May 2013 Common Core Training for Administrators Elementary 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 Expectations of Student Performance Instructional Implications: Engaging in Mathematical Practices’ Look-fors 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. How do you know?

  5. Good Mathematics is NOT how many answers you know… but how you behave when you don’t know.


  6. 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

  7. CCSSM • CCSSM • CCSSM NGSSS • CCSSM • CCSSM NGSSS • CCSSM NGSSS NGSSS • CCSSM NGSSS • CCSSM • CCSSM NGSSS

  8. Purpose and Vision of the CCSSM

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

  11. Mathematical Shifts of the Common Core State Standards Focus, Coherence, and Rigor Fluency, Deep Understanding, Application, Dual Intensity

  12. Six Mathematical Shifts 1. FOCUSdeeply on what is emphasized in the Standards 2. COHERENCE: Think across grades, and link to major topics within grades RIGOR:Requires 3. Fluency 4. Deep Understanding 5. Model/Apply 6. Dual Intensity

  13. 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

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

  15. 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

  16. Pair-share Activity Describe what is and what is not FOCUS

  17. 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

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

  19. Pair-share Activity Describe what is and what is not COHERENCE

  20. 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

  21. K-8 Key Fluencies Achievethecore.org

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

  23. Pair-share Activity Describe what is and what is not FLUENCY

  24. 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

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

  26. Pair-share Activity Describe what is and what is not DEEP CONCEPTUAL UNDERSTANDING

  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) Achievethecore.org

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

  29. Pair-share Activity Describe what is and what is not APPLICATION/MODELING

  30. 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

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

  32. Pair-share Activity Describe what is and what is not DUAL INTENSITY

  33. Design and Organization

  34. Design and Organization • Standards for Mathematical Practice • Carry across all grade levels • Connect with content standards in each grade • Describe “habits of mind” of a mathematically expert student Standards for Mathematical Content • K - 8 grade-by-grade standards organized by domains that progress over several grades. • 9 – 12 high school standards organized by conceptual categories

  35. Standards for Mathematical Practice

  36. Standards for Mathematical Practices “The Standards for Mathematical Practice are unique in that theydescribe how teachers need to teach to ensure their students become mathematically proficient. We were purposeful in calling them standards because then they won’t be ignored.” ~ Bill McCallum

  37. 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

  38. 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

  39. 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 clear definitions and mathematical vocabulary to communicate reasoning careful about specifying units of measure and labels to clarify the correspondence with quantities in a problem explain the meaning of the problem monitor and evaluate their progress “Does this make sense?” use a variety of strategies to solve problems

  40. 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 (navigate between the concrete and the abstract). understand and explain the computation methods they use. make a mathematical statement (conjecture) and justify it listen, compare, and critique conjectures and statements manipulatives pictures symbols

  41. Modeling and Using Tools MP 4: Model with Mathematics. MP 5: Use appropriate tools strategically Mathematically proficient students can… Mathematically proficient students can… 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 apply mathematics to solve problems that arise in everyday life reflect on their attempt to solve problems and make revisions to improve their model as necessary

  42. 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 patterns and apply them in appropriate mathematical context notice repeating calculations and look for efficient methods/ representations to solve a problem evaluate the reasonableness of their results throughout the problem solving process.

  43. Mathematical Practices Indicators a second look . . .

  44. A second look . . . #. Mathematical Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Match each given set of student indicators to a Mathematical Practice Match each given set of teacher indicators to a Mathematical Practice Find another group so you can complete a set of Mathematical Practice Indicators Post your conclusions on chart paper for sharing out

  45. 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

  46. Focal Points at Each Grade LevelEach grade level addresses specific “critical areas”

  47. Mathematics | Grade 4 In Grade 4, instructional time should focus on three critical areas: 1) developing understanding and procedural fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends; 2) developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers; 3) understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry. Note:  listed above are excerpts from the original critical areas delineated on the CCSS document..

  48. Clustersare groups of related standards.Standards from different clusters may sometimes be closely related, because mathematics is a connected subject. Standardsdefine what students should be able to understand and be able to do - part of a cluster Domainsare large groups of related standards. Standards from different domains may sometimes be closely related. Look for the name with the code number on it for a Domain. standard cluster

  49. Grade Level Overview (not all domains are shown below)

  50. New Florida Coding for CCSSM MACC.4.NF.1.1 Domain Common Core Math Standard Cluster Grade Level