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Deep Dive into Math Shift 3 RIGOR

Deep Dive into Math Shift 3 RIGOR. Understanding Rigor in the Common Core State Standards for Mathematics Using the 2013-2014 Course Descriptions. Shift #3: Rigor. What is meant by rigor? The CCSSM require a balance of: Solid conceptual understanding Procedural skill and fluency

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Deep Dive into Math Shift 3 RIGOR

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  1. Deep Dive into Math Shift 3RIGOR Understanding Rigor in the Common Core State Standards for Mathematics Using the 2013-2014 Course Descriptions

  2. Shift #3: Rigor What is meant by rigor? The CCSSM require a balance of: • Solid conceptual understanding • Procedural skill and fluency • Application of skills in problem solving situations Pursuit of all three requires equal intensity in time, activities, and resources. RIGOR Fluency Application Conceptual Understanding

  3. Today’s AgendaRigor in the CCSSM • Discuss Rigor and Find evidence of it within the 2013-2014 Florida Math Course Descriptions • Look specifically at PARCC fluency recommendations for High School • Determine what instructional shifts must occur as we increase the rigor

  4. Building Fluency Mathematics Fluency: A Balanced Approach (1:56) • http://www.youtube.com/watch?v=ZFUAV00bTwA&list=PLD7F4C7DE7CB3D2E6&index=13&feature=plpp_video • http://youtu.be/ZFUAV00bTwA

  5. FluencyWhat is it? Skill in carrying out proceduresflexibly, accurately, efficiently and appropriately

  6. Deep UnderstandingWhat is it? Comprehension of Mathematical Concepts

  7. ApplicationWhat is it? Bringing mathematical skill and understanding together and applying it to real-world situations and in new contexts

  8. Rigorous Group Discussion • Share examples of relevant real-world experiences you use to make important connections to the concepts you teach. • How do these applications relate back to both fluency and conceptual understanding?

  9. Florida 2013-2014 Math Instruction • Blended Instruction between the CCSS and a subset of NGSSS (assessed by State EOC). • Algebra I and Geometry assessed by the Florida EOC Exams. Transitional Shifts • Increased rigor • Classroom assessment to include PARCC-like tasks

  10. Rigor Addressed in the Standards • Conceptual Understanding: 912.N-VM.3.9 Understandthat, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties. • Application: 912.G-MG.1.2 Apply concepts of density based on area and volume in modeling • Procedural Skill and Fluency: 7.EE.2.4a …..Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently…

  11. Rigor Requires Balance Conceptual Understanding + Procedural Skill and Fluency + Application = RIGOR

  12. Key Fluencies

  13. HS Fluency • The words fluently and fluencyare not found in the HS Standards • Fluencies are indicated by culminating standards which mark the end of learning progressions • Recommended fluencies are identified in the PARCC Model Content Frameworks

  14. Evidence of Rigor in the Standards key words within the standards Conceptual Understanding Understand Recognize Interpret Describe Explain Use Relate Represent Identify Justify Solve Application Solve Word Problem Real World Problem Apply Mathematical Problem Model(ing)

  15. Fluency Progression Culminating in Algebra 1 • As early as grades 6 and 7, students begin to use the properties of operations to generate equivalent expressions (6.EE.3, 7.EE.1). • By grade 7, they begin to recognize that rewriting expressions in different forms could be useful in problem solving (7.EE.2). • In Algebra I, these aspects of algebra carry forward as students continue to use properties of operations to rewrite expressions, gaining fluencyand engaging in what has been called “mindful manipulation.”

  16. Locating Evidence of Rigor in the Standards Activity • Read each standard in your course description • Look for and underline or highlight key words or phrases indicating RIGOR • Understand • Solve Real World problems or word problems • Locate an indicated fluency by finding at least one progression and culminating standard • Post your questions and comments to the Parking Lot

  17. HS Fluency Recommendations http://www.parcconline.org/sites/parcc/files/PARCCMCFMathematicsNovember2012V3_FINAL.pdf

  18. RIGOR is a Balancing Act Conceptual Understanding RIGOR Application Fluency

  19. Rigor in the Standards for Mathematical Practice http://www.insidemathematics.org/index.php/classroom-video-visits/public-lessons-properties-of-quadrilaterals/300-properties-of-quadrilaterals-tuesday-group-work-part-a?

  20. Group Discussion Which of the 8 Standards for Mathematical Practice are evidenced? Where was the rigor? What shifts need to occur in your classroom?

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