CMI2012 CCSS for Mathematics
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CMI 2012 Presentation By Janet Hale

CMI 2012 Presentation By Janet Hale

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CMI2012 CCSS for Mathematics Presentation Transcript

  • 1. Designing  Common  Core  State  Standards   Systemic  Mathema4cs  Curriculum   Presented  By  Janet  Hale        www.CurriculumMapping101.com  
  • 2. Backchannel: todaysmeet.com/ccssm
  • 3. Architects Contractors design. build. LEARN TEACH
  • 4. Aspen Grove MentalitySystemic Design - Interdependent 1 Grove…1 Root System
  • 5. Designing Systemic K-12 CCSS Math Collaborative MapsHow long will it take for the K-12 Task Force to complete Stage 1?
  • 6. Part 1 Design / Part 2 Design Vertical Alignment Horizontal Alignment Design units that represent Design units of study that K-12 learning continuum integrate learning within and/(e.g., Geometry, Measurement/Data) or among strands by single/mixed domains in one grade level across grade levels (e.g., intradisciplinary, program-based, interdisciplinary)
  • 7. Part 1 – Phase I•  Unit Names•  Enduring Understandings/ Essential Questions•  Standards for Mathematical Practice•  Vocabulary
  • 8. Designing UNIT NAMES Quickly locating learningby reading electronic (Pre-­‐K)  K  through  12   “binder” spine.
  • 9. Arizona http://www.azed.gov/standards-practices/ mathematics-standards/ Ohiohttp://education.ohio.gov/GD/Templates/Pages/ODE/ODEDetail.aspxPage=3&TopicRelationID=1704&Content=123507 (Transitional Tools)
  • 10.    High School Course Design Determine Desired Pathway Math CCSS Appendix A
  • 11.    Math CCSS Courses – Suggested Starting Points K-8 Math (K-8) GEOMETRY (K-2, 6-8) GEOMETRY/MEASURMENT (3-5) DATA: MEASUREMENT/DATA (K-5) DATA: STATISTICS/PROBABILITY (6-8) NUMBER/QUANTITATIVE: COUNTING/CARDINALITY (K) NUMBER/ALGEBRAIC: NUMBER BASE 10/OPERATIONS (K-5) NUMBER: NUMBER SYSTEM/EXPRESSIONS/EQUATIONS (6-8) QUANTITATIVE: RATIOS/PROPORTIONAL RELATIONSHIPS (6-8) Coordinate Algebra (9) (Integrated Pathway) EXPRESSIONS/EQUATIONS LINEAR FUNCTIONS EXPOTENTIAL FUNCTIONS DATA ANALYSIS COORDINATE PLANE INEQUALITIES Analytic Geometry (10) Advanced Algebra (11) (Above examples based on work in Muscogee CSD, Columbus, GA)
  • 12. Part 1 – Phase I•  Unit Names•  Enduring Understandings/ Essential Questions•  Standards for Mathematical Practice•  Vocabulary
  • 13. K-12 CCSS Aligned/DesignedEnduring Understandings/ Essential QuestionsCreate CCSS-based EUs/EQs prior to Part 1 or… Create CCSS-based EUs/EQs prior to Part 2
  • 14. Enduring Understandings/ Essential Questions It usually takes a task force two full days (including initial training: “What are EUs/EQs/SQs?”) to create K-12 CCSS-based Math EUs/EQs.
  • 15. Part 1 – Phase I•  Unit Names•  Understandings/ Essential Questions•  Standards for Mathematical Practice•  Vocabulary
  • 16.    Domains, Cluster, Standard Statements (CCSS,  p.  5)  
  • 17. Page  7-­‐8,  CCSSM  1.  Make sense of problems and persevere in solving them.2.  Reason abstractly and quantitatively.3.  Construct viable arguments and critique the reasoning of others.4.  Model with mathematics.5.  Use appropriate tools strategically.6.  Attend to precision.7.  Look for and make use of structure.8.  Look for and express regularity in repeated reasoning. Standards for Mathematical Practice are the same K-12…
  • 18. http://www.azed.gov/standards-practices/mathematics-standards/
  • 19.    Standards for Mathematical Practice Choices… 1.  Embed SMP expectations as part of skill statements by asking for justifying reasoning and provide examples (e.g., ____) for teachers to gain insight into higher level of expectation (students “owning” the learning) 3. Construct viable arguments and critique the reasoning of others. 2.  Create SMP-based skill statements that represent the essence of the eight practices to be included as a part of Part 2’s units of study.
  • 20. Grade  1    GEOMETRY  Content  E.  Geometrical  Rela.onships:  Composi.on  -­‐-­‐2-­‐Dimensional  (Quarter  Circle,  Half  Circle,  Quarter  Circle,  Circle,  Square,  Rectangle,  Triangle,  Trapezoid,  Hexagon)  -­‐-­‐3-­‐Dimensional  (Cube)  Skill  E.  Compose  manipula.vely,  orally,  and  in  wri.ng  1  two-­‐dimensional  shape/figure  using  appropriate  2-­‐dimensional  shapes  (i.e.,  see  Possible  Composi/ons  reference)  and  jus.fy  reasoning  (e.g.,  Ami  has  a  cardstock  square  in  front  of  her.  She  has  various  cardstock  shapes  nearby.  Mr.  Mar/n  asks  her  to  show  him  3  ways  she  can  compose  a  square  with  the  various  shapes.  Ami  makes  1  square  first  using  4  smaller  squares;  next  using  2  rectangles;  and  then  using  4  triangles.  The  teachers  asks  her  to  explain  in  wri/ng  what  she  did  and  why.  Ami  shared,  “I  first  composed  1  large  square  using  4  small  squares…See  1,  2,  3,  4  equal  shares.  Then  I  took  them  off  and  used  2  equal  shares;  2  rectangles.  And  last,  I  took  off  the  rectangles  and  used  4  equal  shares,  but  this  /me  they  were  triangles  instead  of  squares,  but  the  s/ll  fit  just  right  on  the  large  square.”)  
  • 21. Design  Note  …  Use  of  parentheses  in  skill  statements        Reduce  complex  frac.on  (frac.on  over  frac.on)  by  mul.plying   by  common  denominator  (e.g.,  see  complex  frac/on  example)      Describe  orally  and  in  wri.ng  par..oned  shares  using                                         6  terms  (halves,  half  of,  thirds,  third  of,  quarters,  quarter  of)             (e.g.,  Carmen  par//ons  a  circle  into  2  equal  shares.  She  writes:  The  circle               has  2  equal  shares  or  2  halves.)  (e.g.,  _____________  )  =  (i.e.,  ______________)  =  (______________)    =  
  • 22. Algebra  “Connec4ons”  ….  Use  of  “Baby  a”  Content  S.  Addi.on/Subtrac.on:  Differen.a.on  Between        1-­‐Step/2-­‐Step  Word  Problems  Skills  Sa.  Differen.ate  orally  and  in  wri.ng  between  1-­‐step  word  problem  having  1-­‐event  equa.on  (1  sum/1  difference)  versus  2-­‐step  problem  where  sum/difference  of  1st-­‐event  equa.on  must  be  used  in  2nd-­‐event  equa.on  to  find  final  sum/difference  and  jus.fy  reasoning        (e.g.,  Mr.  Bryan  reads  2  displayed  word  problems  to  his  class,  "The  first  problem  says:  George  collects  coins.  He  has  32  coins.  His  uncle  brought  him  14  coins  from  Japan  to  add  to  the  his  collec/on.  How  many  coins  does  George  have  now?  The  second  problem  says:  A  cafeteria  has  a  basket  of  25  oranges.  The  basket  has  5  oranges  leY  in  it  at  the  end  of  lunch.  The  next  morning  a  cafeteria  worker  adds  10  more  oranges  to  the  basket.  How  many  oranges  will  be  available  for  lunch  today?"  Mr.  Bryan  asks,  "Which  problem  is  a  1-­‐step  problem  and  which  problem  is  a  2-­‐step  problem?"  Jeb  raises  his  hand.  Mr.  Bryan  asks  him  to  come  to  the  board.  Jeb  comes  up  and  shares  his  reasoning,  "The  problem  about  the  coins  is  a  1-­‐step  problem  because  all  you  have  to  do  is  add  the  2  sets  of  coins  together  so  it  is  1  event.”  He  writes  on  the  board:  32  +  14    =  46.  "The  second  problem  is  a  2-­‐step  problem  because  it  has  2  events.  For  the  1st  event  you  have  to  subtract  to  find  the  difference.  Then  you  have  to  add  10  to  the  difference  in  the  2nd  event."  He  writes:  25  –  20  =  5,  5  +  10  =  15).    
  • 23. Part 1 – Phase I•  Unit Names•  Enduring Understandings/ Essential Questions•  Standards for Mathematical Practice•  Vocabulary
  • 24.    Vocabulary Choices… Embed vocabulary terms and definitions within Content field? Skills field? Resources as an attachment? Format… Agree on visual format so vocabulary will be consistent for curriculum design not only for Math, but other disciplines as well. The more continuity among disciplines, the more accurate and useful the reporting features are within a mapping system.
  • 25. Grade  6        QUANTITATIVE:  RATIOS/PROPORTIONAL  RELATIONSHIPS   A.  Communicate  concepts/explana.ons  orally   and  in  wri.ng  using  3  terms:  
  • 26. Part 1 – Phase I•  Unit Names•  Enduring Understandings/ Essential Questions•  Standards forMathematical Practice•  Vocabulary
  • 27. Part 1 – Phase II•  Breaking Apart (Translating, Unpacking)Standards(Design Influences – Key Shifts, Depth of Knowledge)•  Systemic Content / Skills Development(Process: Format … Collaborative Agreement on Tight and Loose)•  PreK-12 Vertical Reviews(Internal Alignment – Content/Skills& External Alignment to CCSS)•  Horizontal Units of Study(Bridging Part 1 and Part 2 Design Work)
  • 28. Implicit Influences•  Breaking Apart (Translating, Unpacking)StandardsTeachers will, as architects-designers, spend extensivetime studying the explicit and implicit intent of the codes,but need to first consider design influences.•  Math CCSS - 3 Key Shifts•  Depth of Knowledge (PARCC, SMARTER Balance)
  • 29. CCSS Mathematics – 3 Key Shifts (www.achievethecore.org)1.  FOCUS Focus Strongly Where the Standards Focus (narrow the scope of content to allow in-depth learning; no “but we have so much to cover”; need “inch wide, mile deep” mindset to ensure time necessary for students to explore, test, and reach personal conceptual understanding)2. COHERENCE Think across grade levels (systemic design) (each new standard is not a “new event” … each new standard is an extension of previous distinct or linked learning) Link learning among domains within one grade level (leverage) (conceptual relationships across and among standards to aid in conceptual understanding and reasoning)3. RIGOR Equitable, balanced curriculum (learning/teaching): –Conceptual Understanding –Procedural Skills and Fluencies –Application of Math Process using real-world/authentic problems/tasks (within/across disciplines)
  • 30. 1.  FOCUS   2.  COHERENCE  Presenta.on  Slide  from  CCSS  for  Mathema/cs:  Key  ShiYs  -­‐Sandra  Alber.,  Student  Achievement  Partners  
  • 31. 3.  RIGOR   Grade  7    (Content  lis/ng  in  an  Essen/al  Map  unit)     --Conceptual Understanding Algebraic  Representa.ons:                                         --Procedural Skills and Fluencies --Application of Math Process   Equa.on  Fluency  Involving  4  Opera.ons   Mul.-­‐Step  Word  Problems  (Posi.ve/Nega.ve   Ra.onal  Numbers,  Inequali.es,  Complex   www.achievethecore.org   Frac.ons)   CCSS  Fluency  ≠  Rote  Memoriza4on   CCSS  Fluency    =    Speed  and  Accuracy         using  self-­‐selected  strategies     High  School  Fluencies:  Algebra,  Func4ons,   Geometry,  Sta4s4cs  &  Probability,  and  Modeling  
  • 32. Implicit Influences•  Breaking Apart (Translating, Unpacking)StandardsTeachers will, as architects-designers, spend extensivetime studying the explicit and implicit intent of the codes,but need to first consider design influences.•  Math CCSS - 3 Key Shifts•  Depth of Knowledge (PARCC, SMARTER Balance)
  • 33. Cognitive Complexity New BLOOM’S DOK
  • 34. New Bloo m’sEvaluate Predict HypothesizeGenerate Speculate Forecast Output Creating/Imagine If/then Create E/C EvaluatingJudge Apply SpeculateCompare Distinguish AnalyzeContrast Explain Synthesize Process Analyzing/Classify Discriminate Reason A/A ApplyingInfer Sequence InterpretDuplicate Identify ParaphraseCount List Recite Input Understanding/Define Memorize Locate R/U RememberingDescribe Name Reproduce
  • 35. Cognitive Complexity New BLOOM’SR/U A/A E/CInput Process Output DOK
  • 36. Norman  Webb’s     Depths  of  Knowledge   DOK  Model  (1997)  created  to  analyze  the  cogni.ve  expecta.on  demanded  by  standards,  curricular  ac.vi.es,  and  assessment  tasks.     redesign.rcu.msstate.edu       Several  things  are  involved,   including  the  content,  the  ac4vity   and/or  thinking  processes,  and  the   complexity  of  both  the  content  and   ac4vity/thinking  processes.     -­‐-­‐Debbie  Baughman,     The  Standards  Company  
  • 37. DOK    Four  Levels  Level  1  Recall/Reproduc4on              Recall  facts,  informa.on,  procedures,                              basic  concept  founda.ons                                                                                            (minor  comprehension  involved  at  this  level,                                                                                                  no  depth,  no  complexity)  Level  2  Skill/Concept                                      Apply/process  facts,  informa.on,  procedures,  conceptual  understanding  involving  at  least  two  steps  that  require  reasoning                                                                                      (a  need  to  interpret  material  and  make  simple  decisions  about  how  to  approach  a  problem,  but  does  not  yet  have  a  deep  complexity)  
  • 38. DOK    Four  Levels  Level  3  Strategic  Thinking                    Requires  deeper  reasoning,  developing  a                                                        plan  or  sequence  of  steps  to  complete  a  task;                    more  than  one  possible  solu.on/answer                                                          (deal  with  abstrac/ons  and  open-­‐ended  conclusions  and  able  to      support  one’s  reasoning;  wrestle  with  complex  concepts,  tasks,  material)  Level  4  Extended  Thinking  Process  mul.ple  condi.ons  and  solu.ons  for  the  problem;  extend  thinking  by  comple.ng  much  deeper  and  complex  tasks                                                                                                          (according  to  Webb,  higher-­‐level  thinking  is  absolutely  central;  interac/on  with  concepts,  tasks,  material  is  in-­‐depth  and  purposeful)  
  • 39. CAUTION!  Bloom’s  Verbs  cannot  be  applied  with  the  same  mindset  for  what  students  must  cogni9vely  do  when  applying  Webb’s  Depth  Of  Knowledge  (DOK)  to  student  learning,  teaching,  and  assessment  items/tasks.  
  • 40. The  “cau4on”  influences  wri4ng  skills…     Measurable  Verb  +  Descriptor  DOK  1  –  Describe  shape-­‐pabern  term/number-­‐pabern  rule  using  real-­‐world  examples  (e.g.,  Pretend  you  are  walking  outside.  Draw  and  explain  a  natural  or  man-­‐made  pafern’s  term.)  DOK  2  –  Describe  number/shape  paberns  that  follow  determined  term/rule  and  jus.fy  reasoning  (e.g.,  Look  at  the  bowling  pins  pafern.  What  will  the  next  two  rows  look  like  in  this  pafern?  Explain  the  increase  using  textual,  visual,  and  number  representa/ons.  Without  drawing,  what  would  be  the  number  of  pins  in  the  15th  row?  Explain  your  reasoning.  )  
  • 41. Cognitive Complexity New BLOOM’S R/U A/A E/C Input Process Output 1 2 3 4 Recall/ Skill/ Strategic ExtendedReproduction Concept Thinking Thinking DOKPARCC Smarter Balanced www.smarterbalanced.org/wordpress/wp-content/uploads/2012/03/www.parcconline.org/parcc-content-frameworks DRAFTMathItemSpecsShowcase2.pdf
  • 42. www.illustrativemathematics.org
  • 43. Implicit Influences•  Breaking Apart (Translating, Unpacking)StandardsTeachers will, as architects-designers, spend extensivetime studying the explicit and implicit intent of the codes,but need to first consider design influences.•  Math CCSS - 3 Key Shifts•  Depth of Knowledge (PARCC, SMARTER Balance)
  • 44. Part 1 – Phase II•  Breaking Apart (Translating, Unpacking)Standards(Design Influences – Key Shifts, Depth of Knowledge)•  Systemic Content / Skills Development(Process: Format … Collaborative Agreement on Tight and Loose)•  PreK-12 Vertical Reviews(Internal Alignment – Content/Skills& External Alignment to CCSS)•  Horizontal Units of Study(Bridging Part 1 and Part 2 Design Work)
  • 45. Part  2  –  Phase  II  K-­‐8  Process  For    “Pla4ng”  Quartered  Learning  Expecta4ons   Step  1:  Code  hard-­‐copy  of  each  Part  1  “full-­‐year”  UNIT’s  Content/ Skill  statements  to  aligned  standards.   Step  2  (Quartered  Units):  Cut  out   Content/Skills  Sets  and  create   graphic  organizers  that  represent  full           year  of  “quartered”  UNIT  learning.  
  • 46. Part  2  –  Phase  II   K-­‐8  Process  For    “Pla4ng”  the  Learning  Expecta4ons  Step  3:  Create  quartered  UNITS  in  mapping  system  (ensure  newly  created  UNITS  include  aligned  standards  for  each  quarter’s  learning).  Step  4:  Ensure  abachments  are  included  properly  in  each  quartered  UNIT  (preferably  as  .pdf  files).    
  • 47. Part  2  –  Phase  II   Process  For    “Pla4ng”  Sequen4al  Learning  Expecta4ons  Step  1:  Code  hard-­‐copy  of  each  UNIT’s  Content/Skill  statements  to  aligned  standards.  Step  2  (Sequen.al  Units):  Cut  out  Content/Skills  Sets  and  create  graphic  organizers  that  represent  full  year  of  learning.  Step  3:  Create  sequen.al  UNITS  in  mapping  system  (ensure  newly  created  UNITS  include  aligned  standards  for  each  UNIT’s  learning).  Step  4:  Ensure  abachments  are  included  properly  in  each  UNIT  (preferably  as  .pdf  files).    
  • 48. Part 1 – Phase II•  Breaking Apart (Translating, Unpacking)Standards(Design Influences – Key Shifts, Depth of Knowledge)•  Systemic Content / Skills Development(Process: Format … Collaborative Agreement on Tight and Loose)•  PreK-12 Vertical Reviews(Internal Alignment – Content/Skills& External Alignment to CCSS)•  Horizontal Units of Study(Bridging Part 1 and Part 2 Design Work)
  • 49. Wearing  the  right  design  gear,  dive  on  in!            (Even  though  it  may  feel  a  liple  unnerving  at  first…)  
  • 50. Janet  Hale   www.CurriculumMapping101.com  teachtucson@aol.com      520-­‐241-­‐8797