DVD  2  –  Daniel  Ansari,  Cathy  Bruce,  Doug  Clements,  Dan  Meyer  

Daniel  Ansari    Daniel  Ansari  is  an  Associate  Professor  and  Canada  Research  Chair  (Tier   II)   in   Developmental   Cognitive   Neuroscience   in   the  

Department   of   Psychology   at   Western   University   in   London,  Ontario,   Canada.   Ansari   received   his   bachelor's   degree   in  Psychology   from   the   University   of   Sussex   at   Brighton,   an  MSc   in  

Neuroscience  from  the  University  of  Oxford  and  his  PhD  from  the  Institute  of  Child  Health,  University  College  London.  Before  moving  to   Western   University,   Ansari   was   an   Assistant   Professor   in   the  

Department   of   Education   at   Dartmouth   College,   USA   from   2003-­‐2006.  

Ansari’s  research  focuses  on  gaining  a  better  understanding  of  how  children   develop   numerical   and  mathematical   competencies,   why   some   children   fail   to   acquire   basic  

calculation   skills   (Developmental   Dyscalculia)   as   well   as   what   brain   circuits   are   associated   with   the  processing  of  number  and  our  ability  to  calculate.  One  of  the  central  aims  of  our  research   is   to  better  understand  how  basic   numerical   competencies,   those   that  humans   share  with  other   species,   become  

transformed   through   the   processes   of   development   and   enculturation.   Ansari   and   his   team  use   non-­‐invasive  neuroimaging  technologies  such  as  fMRI,  DTI  and  ERPs  as  well  as  traditional  behavioral  methods  to   explore   these   questions.   Ansari   is   interested   in   forging   greater   links   between   neuroscience   and  

education,   as  part  of   the  emerging   field  of   ‘Mind,  Brain  and  Education’  or   ‘Educational  Neuroscience’  and   therefore   in   using   insights   from   the   study   of   neurocognitive   mechanisms   to   inform   educational  practice  and  policy.  

In  2009  Ansari   received   the   ‘Early  Career  Contributions’  Award   from   the  Society   for  Research   in  Child  Development   and   in   2011   he   was   awarded   the   Boyd   McCandless   Early   Researcher   Award   from   the  Developmental  Psychology  Division  of  the  American  Psychological  Association  He  serves  as  an  associate  

editor  for  the  journals   ‘Developmental  Science’  and  ‘Mind  Brain  and  Education’  and  since  2011  he  is  a  member  of  the  Board  of  Directors  of  the  International  Mind,  Brain  and  Education  Society.  

 What  is  Developmental  Dyscalculia?          4:53    Dr.  Daniel  Ansari  defines  and  discusses  what  underlies  Developmental  Dyscalculia.  He  puts  forth  a  theory  that  it  involves  a  magnitude  processing  deficit.  Ansari  briefly  talks  about  the  relationship  with  

fact  retrieval,  phonological  awareness,  and  dyscalculia.  

Implications            6:41    Dr.  Daniel  Ansari  discusses  early  math  learning  and  number  talk  in  the  home  as  well  as  the  use  of  calculators.  He  speaks  about  dot  comparisons,  symbol  comparisons,  subitizing,  and  developmental  

dyscalculia.  

How  do  we  know?          3:48    It  is  important  to  focus  on  multiple  assessment  points  to  develop  a  clear  picture  of  the  student.  

Gender            3:19    Effect  sizes  for  gender  differences  are  small  but  cultural  and  gender  stereotypes  have  a  negative  impact  on  females.  Accurate  information  can  reverse  this  phenomenon.  

Anxiety,  Neuropsychology,  and  Mind  Sets          5:18    

Mathematics  anxiety  usually  found  in  children  with  dyscalculia  has  negative  cognitive  consequences.  Students  need  to  believe  their  math  abilities  can  be  changed  and  shaped.  Teachers  need  to  be  knowledgeable  in  the  area  of  neuroscience.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Cathy  Bruce    Catherine  D.  Bruce  is  an  Associate  Professor  at  Trent  University,  in  Peterborough,  Ontario,  Canada  where  she  teaches  mathematics  methods  courses  in  the  School  of  Education  and  

Professional  Learning.  Cathy  collaborates  with  teachers  and  researchers  to  engage  in,  and  assess,  professional  learning  models  for  mathematics  and  technology  use,  and  she  

researches  the  effects  of  these  activities  on  teachers  and  students.  Her  mathematics  interests  focus  on  in  algebra,  rational  numbers  and  spatial  reasoning.  Cathy’s  research  can  

be  accessed  at  www.tmerc.ca.  You  can  also  follow  her  on  Twitter:  @drcathybruce  

 Professional  Learning  

Key  Features          5:57    Based  on  her  research  and  the  research  of  others,  Dr.  Cathy  Bruce  identifies  five  important  professional  

learning  characteristics  that  link  with  student  efficacy,  teacher  efficacy,  and  student  achievement.  

Efficacy            2:54    Teacher  efficacy  is  a  better  predictor  of  student  achievement  than  socio  economic  status.  Dr.  Cathy  Bruce  describes  some  aspects  of  both  teacher  and  student  efficacy.  

Research  Supported          2:45    

Dr.  Cathy  Bruce  describes  how  collaborative  action  research,  educator  research,  gathering  evidence,  and  referring  to  research-­‐based  literature  are  all  ways  of  informing  professional  learning.  

The  Role  of  the  Principal            2:32    The  principal  supports  student  learning  through  structure,  a  sustained  focus  on  difficult  content,  and  

through  personal  participation  in  professional  learning  and  demonstrating  a  co-­‐learning  stance.  

Scaling  Up          4:58    Conditions  conducive  to  scaling  up  include  working  in  small  teams,  maintaining  a  content  focus,  providing  time,  and  building  trust.  Explicitly  developing  math  curriculum  and  leadership  capacity  for  

classrooms,  schools,  and  the  system  are  important  as  districts  move  forward.  

Learning  and  Technology  

Information  to  Experience,  Consumption  to  Production          3:52    Infusing  technology  supports  enhanced  learning  and  builds  community.  One  must  consider  the  “how”  rather  than  the  “wow”.  We  need  to  think  about  how  deeply  learning  is  enhanced  through  technology.  

 Benefits  and  Challenges          5:46    Technology  can  change  the  questions  we  ask  to  higher  order  thinking,  can  build  collaboration  and,  when  

used  thoughtfully,  can  support  students.  Providing  equitable  access  to  technology  has  the  potential  to  support  learning  for  all  students.  

Math  Talk  

Negotiating  Meaning  and  More            3:25    Math  talk  provides  a  way  of  negotiating  meaning.  It  increases  the  depth  of  understanding.  The  talk  needs  to  be  genuine  with  less  teacher  talk  and  more  student  to  student  talk.  

Math  Talk  Guidelines            2:19    

It  is  important  to  establish  norms  about  how  to  talk  to  each  other  about  mathematics.  The  first  layer  of  math  talk  is  to  explain  your  idea.  The  second  layer  is  to  agree  or  disagree  with  reason.  The  third  layer  is  to  go  beyond.  The  fourth  layer  is  to  want  to  build  on  the  ideas  of  others.      

Implications          4:00    

Math  problems  must  be  rich  enough  to  invite  discussion.  That  discussion  encourages  students  to  make  

multiple  connections.  There  will  be  interactions  among  representations.  Students  need  to  present  their  ideas  in  different  ways.  The  expectation  is  that  students  will  talk  about  why  “a”  is  the  best  answer  and  why  “b”  and  “c  “are  not  good  answers.  It  is  important  to  take  up  wrong  answers.  

Early  Years  

Challenges          2:34    

Challenges  in  the  early  years  include  focus,  background,  our  adult  tendency  to  underestimate  what  young  children  can  do,  and  leveraging  teachable  moments.  

Interventions          3:23    Early  intervention  can  close  gaps  and  provide  all  children  with  the  foundation  for  success  in  

mathematics.  What  might  this  look  like?  

Learning  Through  Task  Based  Interviews            2:13    Through  precise  focused  observation  and  task  creation,  we  can  uncover  students’  math  understandings,  relate  this  to  the  curriculum,  and  build  from  there.  

 

 

 

 

 

 

Doug  Clements    Dr.  Douglas  Clements,  Kennedy  Endowed  Chair  in  Early  Childhood  Learning  and  Professor  at  the  University  of  Denver,  is  widely  regarded  as  "the  major  scholar"  in  the  field  of  early  childhood  mathematics  education,  one  with  equal  relevance  to  the  academy,  to  the  classroom,  and  to  the  educational  policy  arena.    At  the  national,  level,  his  contributions  have  led  to  the  development  of  new  mathematics  curricula,  teaching  approaches,  teacher  training  initiatives,  and  models  of  “scaling  up”  interventions,  as  well  as  having  a  tremendous  impact  on  educational  planning  and  policy,  particularly  in  the  area  of  mathematical  literacy  and  access.        He  has  served  on  President's  National  Mathematics  Advisory  Panel,  the  Common  Core  State  Standards  committee  of  the  National  Governor’s  Association  and  the  Council  of  Chief  State  School  Officers,  the  

National  Research  Council’s  Committee  on  Early  Mathematics,  the  National  Council  of  Teachers  of  Mathematics  national  curriculum  and  Principles  and  Standards  committees,  and  is  and  co-­‐author  each  of  their  reports.  He  is  presently  serving  on  the  Common  Core  committee  of  the  National  Governor’s  Association  and  the  Council  of  Chief  State  School  Officers,  helping  to  write  national  academic  standards.  A  prolific  and  widely  cited  scholar,  he  has  earned  external  grant  support  totaling  nearly  $19  million,  including  major  grants  from  the  National  Science  Foundation,  the  National  Institutes  of  Health,  and  the  Institute  of  Education  Sciences  of  the  U.S.  Department  of  Education.  See  http://portfolio.du.edu/dclemen9.    

Learning  Trajectories          8:34    Understanding  learning  trajectories  assists  teachers  in  differentiating  instruction.  

Intentional  Play-­‐based  Learning          5:10    Good  mathematics  involves  all  approaches  in  teaching  and  learning.  

Intentional  Instruction          4:19    

Mathematics  is  developmental  and  follows  specific  learning  trajectories.  Students  need  to  learn  the  mathematical  language  to  identify  the  math  during  their  play.  They  need  to  connect  mathematical  ideas  to  each  other  and  be  able  to  talk  about  them.    

Integrated  Concrete  Concepts          8:40    

“Integrated  concrete  concepts”  refers  to  students’  abilities  to  manipulate  things  in  their  mind,  based  on  their  past  experience  with  concrete  objects.    

Early  Math  Learning          1:40    Early  math  learning  can  predict  student  success  in  reading,  math,  and  graduating.  Teachers’  skills  are  

enhanced  by  their  knowledge  of  learning  trajectories.  

Dan  Meyer  Dan  Meyer  taught  high  school  math  for  six  years  to  students  who  in  many  cases  did  not  like  high  school  math.  He's  currently  a  doctoral  candidate  at  Stanford  University  

in  the  field  of  math  education.  He  speaks  internationally  and  works  with  textbook  publishers,  helping  them  transition  from  print  to  digital  media.  He  was  named  one  

of  Tech  &  Learning's  30  Leaders  of  the  Future  and  an  Apple  Distinguished  Educator.  He  lives  in  Mountain  View,  CA.  

 

 

Experiencing  Applied  Mathematics          3:41    Dan  offers  some  thinking  around  the  contexts  in  which  we  position  mathematics  tasks  and  invites  us  to  

consider  different  perspectives.  

Activation  and  Accessibility          3:49    “Activation”  means  different  things  to  different  people.  Dan  asks  us  to  consider  what  is  important  in  activating  thinking  and  how  we  might  differentiate.  

Transforming  Classroom  Culture          5:04    

Shifting  to  a  classroom  that  incorporates  inquiry  as  a  way  of  being  is  a  journey.      

Thoughts  About  Inquiry          5:19    Planning  for  inquiry  is  intentional.