Educa&onal  Neuroscience:                  

Educa&onal  Neuroscience:          

Using  Cogni&ve  and  Brain  Science  to  Enhance  our  Understanding  of  Math  

Learning    Susan C. Levine

University of Chicago Spatial Intelligence and Learning Center

Research  Ques&ons  •  Is there a “preparation gap” in math

knowledge related to parent math input in the early home environment?

•  Are variations in young children’s math achievement related to affective inputs – to teacher math anxiety in early elementary school?

•  Why does math anxiety not always disrupt math performance? •  Insights from a brain imaging study

Numerical  and  Spa&al  Skills:  Key  Elements  of  Early  Mathema&cs  

•  Numerical  and  spa&al  skills  are  vital  for  success  in  the  STEM  disciplines  (Science,  Technology,  Engineering  &  Math)  

•  These  skills  begin  to  develop  at  an  early  age  

(e.g.,  Delgado & Prieto, 2004;  Levine, Huttenlocher, Taylor & Langrock, 1999)  

Early  Individual  Differences  in  Children’s  Math  Knowledge:    Do  they  maOer?  

•  Children  show  wide  dispari&es  in  their  mathema&cal  knowledge  by  preschool.  

•  These  early  varia&ons  predict  children’s  later  math  achievement.  

•  Importantly,  early  varia&ons  in  math  knowledge  are  related  to  differences  in  the  cogni&ve  and  affec&ve  inputs  young  children  receive.  

Study  1:  Children’s  first  classroom  is  the  home  

•  Diverse  sample  of  parent-­‐child  dyads  followed  longitudinally.  

•  Coded  math  talk  –  talk  about  number  and  spa&al  rela&ons    -­‐-­‐  today  will  focus  on  number  talk.  

Large  Varia&on  in  Parent  Number  Talk  

•  Across  our  sessions  range  was  4  to  257  number  words  

•  Extrapola&ng,  translates  to  enormous  differences  in  children’s  opportunity  to  learn    28  to  1799  in  a  week    1456  to  93,548  in  a  year  

Children’s  Cardinal  Number  Knowledge  

•  Assessed  at  46  months      

•  Point-­‐to-­‐X  task  

Experimenter: “Point to three.”

Rela&on  between  parent  cumula&ve  number  word  tokens  (log)  and  child  cardinal  number    knowledge  

at  46  months  

Quality  of  number  talk  also  maOered  

•  Talk  about  number  with  present  objects  predicts  children’s  understanding  of  the  number  words  

•  Talk  about  number  of  objects  in  larger  sets  (4  to  10),  in  addi&on  to  1,  2,  and  3  also  predicts  children’s  understanding  of  number  words  

Why  is  talk  about  sets  >3  par&cularly  helpful?  

•  Unlike  smaller  sets,  sets  larger  than  3  cannot  be  enumerated  exactly  without  coun&ng.  

•  Hypothesis:  The  necessity  of  coun&ng  these  sets  to  determine  their  exact  numerosity  helps  children  link  coun&ng  to  the  cardinal  number  of  objects  in  a  set  –  to  understand  the  purpose  of  coun&ng.  

Gunderson & Levine (in press) Developmental Science

Future  studies  are  informed  by  classroom    prac&ce  and  by  cogni&ve  science  

•  Partnering  with  teachers  to  implement  lessons  that  strengthen  children’s  understanding  of  early  math  –  using  their  feedback  to  design  beOer  instruc&on  in  an  itera&ve  manner    – Cri&cal  classroom-­‐lab  interac&ons  

•  Examining  how  a  learning  principle  that  emerges  from  cogni&ve  science  –  spaced  learning  works  beOer  than  massed  learning  -­‐  applies  to  early  math  learning  

Spaced  vs.  Massed  Learning  

•  How  does  it  apply  to  math  learning    -­‐-­‐  what  is  the  op&mal  spacing?  – At  different  developmental  &me  points    – At  different  points  in  the  learning  trajectory  –  In  “real-­‐world”  learning  environments  – For  different  learning  goals:    facts,  procedures,  and  concepts  

– To  promote  long-­‐term  reten&on  and  generaliza&on  

Study  2:    Affec&ve  Input:      Teachers’  math  anxiety  predicts  students’  math  achievement  

•  We  also  inves&gated  the  role  of  teachers’  math  anxiety  on  children’s  math  achievement  because…  – Elementary  educa&on  majors  in  the  U.S.  have    high  levels  of  math  anxiety  (Hembree,  1990)  

– 91%  of  early  elementary  school  teachers  are  female  (Na&onal  Educa&on  Associa&on,  2003)  

 

Hypotheses    •  Teachers’  math  anxiety  may  impact  girls  by  confirming  a  self-­‐relevant  gender  stereotype  (e.g.,  Cvencek,  Meltzoff  &  Greenwald,  2009)  

•  Girls  who  confirm  tradi&onal  gender  stereotypes  (“boys  are  beOer  at  math,  girls  are  beOer  at  reading”)  will  learn  less  than  other  children  

Sample  and  Study  Design  

•  Students’  math  achievement  and  gender  stereotypes  were  assessed  at  the  beginning  and  end  of  the  school  year  

•  Teacher  math  knowledge  and  anxiety  assessed  at  end  of  school  year  

 Assessing  children’s  gender  stereotypes  

about  math:      Gender  ability  beliefs  task  

 One  story  about  math,  one  about  reading  

(adapted from Steele, 2003)

“This is a story about a student who is really good at math. This student is always the first to finish every math problem, no matter how hard. And this student also really likes doing math. If there is a math problem to be done, this student is the one to do it. This student is a really great mathematician.” “Can you draw a picture of this student?” “Is it a boy or a girl?”

Example  drawings  Reading = Girl Math = Boy

Children who confirm stereotype draw girl for reading and boy for math

Teacher  assessments  

•  Math  anxiety  (sMARS;  Alexander  &  Martray,  1989)  •  “Reading  a  cash  register  receipt  aoer  you  buy  something”  •  “Studying  for  a  math  test”  

•  Math  knowledge  for  teaching  (CKTM;  Hill,  Schilling  &  Ball,  2004)  

•  Teachers  varied  widely  on  both  

Media&on  Analysis  •  Teacher  math  anxiety  predicted  girls’  end  of  year  math  achievement  

(Beilock,  Gunderson,  Ramirez  &  Levine,  PNAS,  2010)  

Teacher  Math  Anxiety  

Girls’  Math  Achievement  

Teacher  Math  Anxiety  

Girls’  Math  Achievement  

Gender  Stereotypes   β = -0.23*

β = -0.21*

β = 0.31*

β = -0.16, n.s.

*p<.05

•  Mediated by girls’ gender ability beliefs

End-­‐of-­‐Year  Math  Achievement  by  Gender  Ability  Beliefs  

(Beilock,  Gunderson,  Ramirez  &  Levine,  PNAS,  2010)  

Implica&ons  

•  Teacher  math  anxiety  may  help  to  explain  the  forma&on  of  gender  stereotypes  and  the  divergence  between  boys’  and  girls’  artudes  toward  math  

•  To  reduce  these  effects,  it  is  important  to  directly  address  teachers’  math  anxiety,  as  well  as  their  math  knowledge,    as  a  component  of  teacher  training  

Study  3:  How  brain  imaging  can  help  inform  efforts  to  reduce  math  anxiety  

•  Anxiety  about  math  common  and  deleterious  to  learning,  but  not  all  math-­‐anxious  individuals  perform  poorly  in  math.  

•  Why  is  this  the  case?  

                                                 Lyons  and  Beilock  (2011)  

Math Trial Word Trial

tneimrepxe tneimrepxe

Lyons & Beilock (2011). Cerebral Cortex

Math anxiety deficit

Lyons & Beilock (2011). Cerebral Cortex

Lyons & Beilock (2011). Cerebral Cortex

Inferior frontal junction (IFJ) Inferior parietal lobe (IPL)

Lyons & Beilock (2011). Cerebral Cortex

Lyons & Beilock (2011). Cerebral Cortex

Study  3  Summary  •  High math anxiety individuals who recruit

additional working memory resources or exercise greater regulation of their anxiety response (or both) reduced math performance deficits that are typically associated with math anxiety.

•  These responses begin when individuals

anticipate doing math, before they even see the problem.

•  Its not that these individuals don’t feel anxious – they do, but are able to manage their anxiety successfully.

Overall  Summary  •  Both  cogni&ve  and  affec&ve  inputs  are  related  to  math  learning  from  an  early  age  

•  We  can  increase  our  understanding  of  how  these  factors  interact  –  •  By  carrying  out  studies  in  the  lab  and  in  real-­‐world  learning  environments  

•  By  collabora&ng  with  teachers  as  research  partners  •  By  examining  the  impact  of  math  learning,  math  anxiety,  and  stereotypes  at  the  behavioral  and  neural  levels  

•  Overarching  goal:    To  increase  math  achievement  in  all  children  

 

Acknowledgements…    

OECD    

Study  parCcipants    

Collaborators    

Funding  agencies:    

NSF,  SpaCal  Intelligence  and  Learning  Center  (SILC)  Grant  #SBE-­‐0541957  

 NIH-­‐NICHD  Grant  #P01HD040605