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Designing Common Core State Standards Systemic Mathematics Curriculum: Part 2

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This slideshare represents the visuals used in a Webinar I presented highlighting critical considerations for designing systemic curriculum based on the CCSS. To listen to the archived podcast, please visit my Web site: www.CurriculumMapping101.com.

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Designing Common Core State Standards Systemic Mathematics Curriculum: Part 2

1. 1. Designing  Common  Core  State  Standards   Systemic  Mathema4cs  Curriculum                   Part  2   Presented  By  Janet  Hale        www.CurriculumMapping101.com
2. 2. Architects Contractors design. build. LEARN TEACH
3. 3. Aspen Grove MentalitySystemic Design - Interdependent 1 Grove…1 Root System
4. 4. Phase 1 Design / Phase 2 Design Vertical Alignment Horizontal Alignment Design units that represent Design units of study that K-12 learning continuum integrate learning among(e.g., Geometry, Measurement/Data) strands in one grade level by domains (e.g., intradisciplinary, with cross-connections program-based, interdisciplinary)
5. 5. Designing Systemic K-12CCSS Math Collaborative Maps How long will it take for the K-12 Task Force to complete Phase 1?
6. 6. Part 1: Laying a Solid Foundation•  Unit Names•  Enduring Understandings/ Essential Questions•  Standards forMathematical Practice•  Vocabulary
7. 7. Part 2•  Breaking Apart (Unpacking)Standards(Explicit Process, Implicit Influences)•  Systemic Content / Skills Development(Process: Format … Collaborative Agreement on Tight and Loose)•  PreK-12 Vertical Reviews(Internal Alignment – Content/Skills &External Alignment to Standards; if using, EUs/EQs)
8. 8. Part 2•  Breaking Apart (Unpacking)Standards(Explicit Process, Implicit Influences)•  Systemic Content / Skills Development(Process: Format … Collaborative Agreement on Tight and Loose)•  PreK-12 Vertical Reviews(Internal Alignment – Content/Skills &External Alignment to Standards; if using, EUs/EQs)
9. 9. Implicit Influences•  Breaking Apart (Unpacking) StandardsTeachers as designers will spend time explicitly studyingthe codes, but need to first consider design influences.•  Math CCSS - The 3 Key Shifts•  Depth of Knowledge•  When to incorporate the use ofstate-provided Crosswalk andGap Analysis documents.
10. 10. CCSS Mathematics – 3 Key Shifts (www.achievethecore.org)1.  FOCUS Focus Strongly Where the Standards Focus (narrow scope of content to allow in-depth learning; no “but we have so much to cover”; “inch wide, mile deep” mindset to ensure time necessary for students to have time to explore, test, and reach 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)
11. 11. 1.  FOCUS   2.  COHERENCE  Presenta)on  Slide  from  CCSS  for  Mathema-cs:  Key  Shi4s  -­‐Sandra  Alber),  Student  Achievement  Partners
12. 12. 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
13. 13. 1.  Use  mul)media.   2.  Encourage   student   intui)on.   3.  Ask  the  shortest   ques)on  you   can.   4.  Let  students   build  the   problem.   5.  Be  less  helpful.  hMp://www.ted.com/talks/lang/en/dan_meyer_math_curriculum_makeover.html
14. 14. Implicit Influences•  Breaking Apart (Unpacking) StandardsTeachers as designers will spend time explicitly studyingthe codes, but need to first consider design influences.•  Math CCSS - The 3 Key Shifts•  Depth of Knowledge•  When to incorporate the use ofstate-provided Crosswalk andGap Analysis documents.
15. 15. Cognitive Complexity New BLOOM’S DOK
16. 16. The  Three-­‐Story  Intellect   NewBloom’s Duplicate Identify Paraphrase Count List Recite Input Understanding/Bena Kallick Define Memorize Locate R/U RememberingCCSSPresentation Describe Name Reproduce
17. 17. The  Three-­‐Story  Intellect   Compare Distinguish Analyze New Contrast Explain Synthesize ProcessBloom’s Classify Discriminate Reason A/A Analyzing/ Applying Infer Sequence Interpret Duplicate Identify Paraphrase Count List Recite Input Understanding/Bena Kallick Define Memorize Locate R/U RememberingCCSSPresentation Describe Name Reproduce
18. 18. The  Three-­‐Story  Intellect   Evaluate Predict Hypothesize Generate Speculate Forecast Output Creating/ Imagine If/then Create E/C Evaluating Judge Apply Speculate Compare Distinguish Analyze New Contrast Explain Synthesize Process Analyzing/Bloom’s Classify Discriminate Reason A/A Applying Infer Sequence Interpret Duplicate Identify Paraphrase Count List Recite Input Understanding/Bena Kallick Define Memorize Locate R/U RememberingCCSSPresentation Describe Name Reproduce
19. 19. Cognitive Complexity New BLOOM’SR/U A/A E/CInput Process Output DOK
20. 20. Norman  Webb’s     Depths  of  Knowledge   DOK  Model  (1997)  created  to  analyze  the  cogni)ve  expecta)on  demanded  by  standards,  curricular  ac4vi4es,  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
21. 21. 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)
22. 22. 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)
23. 23. CAUTION!  Bloom’s  Verbs  cannot  be  applied  with  the  same  mindset   for  what  students  must  cogni0vely  do  when                             applying  Webb’s  Depth  Of  Knowledge  (DOK)  to                  student  learning,  teaching,  and  assessment  items/tasks.
24. 24. This  cau4on  inﬂuences  wri4ng  skills…     Measurable  Verb  +  Descriptor  DOK  1  –  Describe  shape-­‐paMern  term/number-­‐paMern  rule  using  real-­‐world  examples  (e.g.,  Pretend  you  are  walking  outside.  Draw  and  explain  a  natural  or  man-­‐made  paJern’s  term.)  DOK  2  –  Describe  number/shape  paMerns  that  follow  determined  term/rule  and  jus)fy  reasoning  (e.g.,  Look  at  the  bowling  pins  paJern.  What  will  the  next  two  rows  look  like  in  this  paJern?  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.  )
25. 25. 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
26. 26. Implicit Influences•  Breaking Apart (Unpacking) StandardsTeachers as designers will spend time explicitly studyingthe codes, but need to first consider design influences.•  Math CCSS - The 3 Key Shifts•  Depth of Knowledge•  When to incorporate the use ofstate-provided Crosswalk andGap Analysis documents.
27. 27. walk  C ross Gap  A nalys is
28. 28. walk   Most  Beneﬁcial  Use  of      C ross Crosswalk  Documents                                   for  Curriculum  Design     Veriﬁes  what  task-­‐force  members     discover  acer  ﬁrst                                                           studying  and  analyzing                                         ver)cal/horizontal  Math  CCSS.
29. 29. nalysis  G ap  AMost  Beneﬁcial  Use  of  Gap  Analysis  Documents  for  Curriculum  Design     Indicates  to  task-­‐force  members  who  may  be  called  upon  to  be                                                                 resident  experts  for  fellow  task-­‐force  members  who                                                                                       may  need  some  or  a  lot  of  aid  in  designing  unfamiliar  learning  (content  –  skills).
30. 30. walk   ss Best  to  incorporate  use  of  C ro Crosswalk  and  Gap  Analysis   documents  AFTER  task-­‐force   teachers  have  systemically   studied  and  discussed                 the  Math  CCSS  Domain(s).   Gap  A nalys www.LiveBinders.com   Search  for:  Curriculum  21   is
31. 31. Part 2•  Breaking Apart (Unpacking)Standards(Explicit Process, Implicit Influences)•  Systemic Content / Skills Development(Process: Format … Collaborative Agreement on Tight and Loose)•  PreK-12 Vertical Reviews(Internal Alignment – Content/Skills &External Alignment to Standards; if using, EUs/EQs)
32. 32. Part 2•  Breaking Apart (Unpacking)Standards(Explicit Process, Implicit Influences)•  Systemic Content / Skills Development(Process: Format … Collaborative Agreement on Tight and Loose)•  PreK-12 Vertical Reviews(Internal Alignment – Content/Skills &External Alignment to Standards; if using, EUs/EQs)
33. 33. 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)
34. 34. Math CCSS Courses UNIT NAME SIGNIFIERS: ____________Math (K-8)GEOMETRY (K-8) = Suggested Starting Point K-8DATA: 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/EQUATIONSLINEAR FUNCTIONS Determine DesiredEXPOTENTIAL FUNCTIONS PathwayDATA ANALYSISCOORDINATE PLANE Math CCSSINEQUALITIES Appendix AAnalytic Geometry (10) Advanced Algebra (11)(Above examples based on work in Muscogee CSD, Columbus, GA)
35. 35. Math CCSS Courses Progression of Systemic UNIT NAMES once task-force teachers began studying the architectural codes (clusters/standards) while considering influences and beginning to determine potential content listings.GEOMETRY (Grades K-2)GEOMETRY/MEASUREMENT (Grades 3-5)GEOMETRY (Grade 6)Phase 2 … GEOMETRY: AREA AND VOLUMEGEOMETRY (Grade 7)Phase 2 … GEOMETRY: GEOMETRYGEOMETRY (Grade 8)Phase 2 … GEOMETRY: GEOMETRIC APPLICATIONSOF EXPONENTS(Above examples based on work in Muscogee CSD, Columbus, GA)
36. 36. Content = What Students Must KNOW Noun/Noun Phrase: Descriptor Think … Table of “Contents” 3-Dimensional Shapes : Needs A Descriptor 3-Dimensional Shapes: Sphere, Cone, Cylinder 3-Dimensional Shapes: Sphere  Time: Analog Face (Hour Hand, Minute Hand), Digital Face (Hour Digits,Colon, Minute Digits) / O-clock, ThirtyTime: Nearest Minute, ElapsedTime: Comparison (Second, Minute, Hour, Day, Week, Months, Year,Decade, Century, Millennium) / Conversion Of Units (Within SingleSystem)Distance/Weight/Mass/Capacity/Time/Money: Conversion Of Unlike Units- Same System (Smaller to Larger/Larger to Smaller) / 2-Step & Multi-Step Word Problems
37. 37. Noun/Noun Phrase: DescriptorLength/Height/Width: ½ Inch, Inch, Foot, Yard / Centimeter,MeterFractions/Equal Shares: 2 Shares, 3 Shares, 4 Shares(Circle, Rectangle)Quadratic Polynomials: Fundamental Theorem of AlgebraMeasures Of Central Tendency: Mean, Median, Mode,Range, Outlier Whenever possible (in any element field), use numeral instead of number word for 0-9. It is easier on the eye/mind to locate information quickly.
38. 38. Use of Intra-Alignment Coding for Internal Alignment The  legers’  job  is  to  align  Content  to  Skills
39. 39. Skills = What students must cognitively be able to DO in relationship to the intra-aligned KNOWingThere are technically three parts to a quality written skill statement:1.  Measurable Verb (can “see” the thinking)2.  Target (how learning is measured - assessments)3.  Descriptor (provides clarity/detail related to the intra- aligned Content)Do not begin skill statements with:The student will…A skill statement startswith a capital letter,but needs no periodat end of statement
40. 40. 1.  Measurable Verb Not Measurable Verbs = Demonstrate, Understand, Know, Show, Use Use appropriate tools to measure and record to nearest abbreviated unit (½ in., 1 in., 1 ft. / 1 cm, 1 m, 1 yd) ☺Measure manipulatively and record in writing to nearest unit nearest abbreviated unit (½ in., 1 in., 1 ft. / 1 cm, 1 m, 1 yd) using appropriate tools Use number line to order up to 5 rational numbers (based on place value of each number) ☺Order up to 5 rational numbers (based on place value of each number) using number lineIf using Apply… Apply to what? Apply in writing self-selected strategies to solve real-world 2-step word problems and justify reasoning
41. 41. 2.  Target          The  measurement  mode(s)  …  In  other  words,  “how”   learning  is  formally  assessed.        -­‐-­‐in  wri4ng,  orally      /  -­‐-­‐manipula4vely,  visually        Note:  in  wri4ng  =  not  orally    •  (Gr.  3)  Iden)fy  in  wri)ng  value  of  given  digit  based  on  base-­‐ten   placement  (e.g.,  3,491  …  What  does  the  digit  3  represent  in  3,491?  Student   writes:  The  digit  3  represents  3  thousands.)  •  (Gr.  K  –  Qtr  1.)  Correlate  manipula)vely,  visually,  and  orally   concept  of  “1  real/illustrated  object  in  pictograph  represents                         1  unit  in  bar  graph”  using  labeled  graph  paper/adult  support  •  (FUNCTIONS)  Iden)fy  in  wri)ng  center  and                                                                     radius  of  circle  by  comple)ng  the  square
42. 42. 2.  Target    Important  Note:  Some4mes  a  measureable  verb  does   not  need  a  target.    Obvious:  Recite…    Write…  Mathema4cs/Science:  Solve…  Find…  Calculate…   Construct…  and  other  math-­‐speciﬁc  cogni4ons         are  considered  to  be  in  wri4ng  unless  otherwise   noted.  Ba.  Solve  for  unknown  to  make  equa)on  true   (e.g.,  53  +  □  =  73  …  53  +  20  =  73)    Universal  Verbs:  Such  as  Iden4fy…  Compare  and   contrast…  do  need  a  target/targets
43. 43. Classify Differentiate JustifyCompare Discriminate OrganizeCommunicate Distinguish PredictContrast Estimate PrioritizeConvert Evaluate ProveCorrelate Explain RankCriticize Generalize RecognizeCritique Identify SequenceDefine Infer SummarizeDescribe Interpret TransferDetermine Invent*This is a sample list and therefore not comprehensive.
44. 44. 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.,  Ali  par--ons  a  circle  into  2  shares.  She  writes:  The  circle  has  2  equal   shares  or  2  halves.)  (e.g.,  _____________  )  =   for  example  (i.e.,  ______________)  =   that  is  (______________)    =   that  is
45. 45. 3.  Descriptors  add  clarity/details  to  the  aligned   content  lis4ng,  not  duplicate  it.  Not  Yet  Quality  Content    C.  Addi)on/Subtrac)on:  1-­‐Step/2-­‐Step  Word  Problems    Skills  C.  Solve  word  problems   If  you  were  the  Assessment  Fairy,   could  you  design  a  quality   assessment  to  measure  the   required  skill  learning?
46. 46. Math  CCSS  Glossary,  Page  88
47. 47. Quality  Content  C.  Addi)on/Subtrac)on:  1-­‐Step/2-­‐Step  Word  Problems    Skills  Ca.  Solve  5  types  (adding  to,  taking  from,  puing  together,  taking  apart,   comparing  (more  /  less))  of  1-­‐step  word  problems  (compose/ decompose/  regroup  with  minuend  up  to  100,  sum  up  to  100)  using   self-­‐selected  strategies  and  jus)fy  reasoning:  -­‐-­‐Adding  to  (Result  Unknown)  (e.g.,  Twenty  bunnies  sat  on  the  grass.  Thirty-­‐ three  more  bunnies  hopped  there.  How  many  bunnies  are  on  the  grass  now?)    -­‐-­‐Adding  to  (Change  Unknown)  (e.g.,  Twelve  bunnies  were  si]ng  on  the  grass.   Some  more  bunnies  hopped  there.  Then  there  were  thirty-­‐seven.  How  many   bunnies  hopped  over  to  the  twelve?)  -­‐-­‐Adding  to  (Start  Unknown)  (e.g.,  Some  bunnies  were  si]ng...)     Could  the  skill  statement                                                               s4ll  be  improved  design-­‐wise?
49. 49. ContentG.  Scale  Drawings:    Square,  Right  Triangle,  Rectangle  /  Unique  FiguresSkillsG.  Reduce  larger  image  using  graph  paper  to  reproduce  larger  image  as  a  similar  ﬁgure  (e.g.,  see  Edwins  Reduc-on  example)  G.  Enlarge  smaller  image  using  graph  paper  to  reproduce  smaller  image  as  a  similar  ﬁgure  G.  Iden)fy  in  wri)ng  scale  key  in  scale  drawings  (e.g.,  city  maps,  architect  blueprints,  landscape  plans,  engineering  blueprint  /  e.g.,  see  Scale  Keys  example)  G.  Correlate  in  wri)ng  scale  key  to  drawing  representa)on(s)  (e.g.,  Michael  is  looking  at  a  scale  drawing.  The  scale  key  reads:    1"  =  1  Foot      Michael  writes:  In  this  scale  drawing,  1  inch  represents  1  foot  of  the  actual  boat.)  G.  Reduce  larger  image  (2-­‐dimensional  quadrilaterals)  based  on  given  scale  using  graph  paper  (e.g.,  see  Campbelles  Parallelogram  example)  G.  Enlarge  smaller  image  (2-­‐dimensional  quadrilaterals)  based  on  given  scale  using  graph  paper  (e.g.,  see  Harpers  Rectangles  example)  Ga.  Determine  dimensions  of  ﬁgures  when  given  scale  and  iden)fy  impact  of  scale  on  actual  length  (1-­‐dimension),  area  (2-­‐dimension)  and  jus)fy  reasoning  (e.g.,  see  Coach  Cleggs  Problems  example)
50. 50. A bit of “fine tuning” is oftentimes needed when first writing skill statements.Sometimes difficult for task-forcemembers to differentiate betweena SKILL/STRATEGY or ACTIVITY. A skill is focused on what students must cognitively be able to do. An activity is focused on providing practice concerning a particular skill’s or skills’ development or reinforcement. No: Practice orally addition facts No: Review steps to solve … No: Walk around room to measure…
51. 51. Wearing  the  right  design  “gear”  …  Dive  on  in!                   (Even  though  it  may  feel  a  ligle  unnerving  at  ﬁrst…)
52. 52. While  breaking  apart  standards  and   determining  content,  and  especially  skills,   task-­‐force  members  are  always  ques4oning   and  inquiring  using  on-­‐line  resources  as   well  as  each  another’s  exper4se.    Researchers
53. 53. www.LiveBinders.comSearch for: Janet Hale > Select Author > Click Search
54. 54. www.azed.gov/standards-practices/mathematics-standards/
55. 55. http://www.azed.gov/standards-practices/mathematics-standards/
56. 56. www.illustrativemathematics.org
57. 57. Part 2•  Breaking Apart (Unpacking)Standards(Explicit Process, Implicit Influences)•  Systemic Content / Skills Development(Process: Format … Collaborative Agreement on Tight and Loose)•  PreK-12 Vertical Reviews(Internal Alignment – Content/Skills &External Alignment to Standards; if using, EUs/EQs)
58. 58. Part 2•  Breaking Apart (Unpacking)Standards(Explicit Process, Implicit Influences)•  Systemic Content / Skills Development(Process: Format … Collaborative Agreement on Tight and Loose)•  PreK-12 Vertical Reviews(Internal Alignment – Content/Skills &External Alignment to Standards; if using, EUs/EQs)
59. 59. Seven-Step Review Process 1. Collecting the Data 2. First Read-Through 3. Small Group Review 4. Large Group Comparisons 5. Determine Immediate Revision Points 6. Determine Points Requiring Research and Planning 7. Plan for Next ReviewHeidi  Hayes  Jacobs,  Mapping  The  Big  Picture  (1997)
60. 60. Seven-Step Review Process 1. Collecting the Data 2. First Read-Through 3. Small Group Review 4. Large Group Comparisons 5. Determine Immediate Revision Points 6. Determine Points Requiring Research and Planning 7. Plan for Next Review
61. 61.  1.  Collec4ng  the  Data