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Lecture

Ch. 12 - Problem Solving.pdf

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Department
Psychology
Course
PSYCH 2H03
Professor
Judith Shedden
Semester
Fall

Description
PNB  2XA3   Chapter  12:  Problem  Solving  &  Intelligence     Problem  solving  as  search   • Initial  State:  Knowledge  &  resources  you  already  have  (the  “givens”)   • Goal  State:  Where  do  you  want  to  end  up?   • Operators:  Actions  that  can  change  your  current  state   • Path  constraints:  Limitations  on  what  moves  you  can  make  (i.e.  limited  time,  money…)   • Problem  space:  The  set  of  all  states  that  can  be  reached  in  solving  a  problem.   o For  some  problems,  it’s  possible  to  lay  out  the  entire  problem  space.  However,  looking  through  every  option   takes  WAY  too  much  time.  Need  a  HEURISTIC  (i.e.  hill -­‐climbing,  means-­‐end  analysis,  working  backwards).     General  Solving  Problem   Heuristics   • Hill  climbing  heuristic   o At  each  point,  you  choose  the  option  that  moves  you  in  the  direction  of  your  goal.   o PROBLEM:  Sometimes  solving  problems  requires  you   to  take  steps  away  from  your  goal   o Hobbit-­‐Orc  Example   § Operators:  the  moves  you  can  make   § Path  constraints:  no  Hobbits  to  be  eaten  &  limited  boat  size   • Means-­‐end  analysis   o What’s  the  diff  b/w  my  current  state  &  my  goal?   § I’m  in  a  restaurant.  Emergency  phone  call.  I  need  to  get  to  Halifax  NOW.  What’s  the  diff  b/w  here  &   Halifax?  DISTANCE.  How  can  I  reduce  that  distance?  AIRPLANE .  What’s  the  diff  b/w  me  &  getting   a   plane?  GET  TO  AIRPORT.  How  can  I  reduce  diff  b/w  this  restau rant  &  airport?  TAXI.   o Helps  break  the  problem  into  more  easily  solvable  sub-­‐problems.   o Most  complex  problem  solving  requires  the  use  of  more  than  one  heuristic.   o Can  involved  both  forward  &  backward  search   • Working  backwards   o Start  at  goal,  work  backwards  from  there   o Generally  working  backwards  is  helpful  when  the  #  of  directions  backward  from  the  goal  state  is  small,  &  the   #  of  possible  distractions…   o “Water  lilies  grow  on  Blue  Lake.  They  grow  fast,  so  that  the  amount  of  water  covered  by  lilies  doubles  every   th 24hrs.  On  day  1,  there  was  1  lily.  On  day  90,  the  lake  was  entirely  covered.  When  the  lake  ½  covered?”  (89 )   o “Peter,  Paul  &  Mary  found  a  treasure  of  diamonds.  They  buried  ½  &  divided  the  rest  evenly.  Paul  got  2000   diamonds.  How  many  diamonds  did  they  find?”     Problem  solving  as  representation   • Mental  models,  mental  imagery   • Sometimes,  solving  a  problem  requires  finding  a  diff  REPRESENTATION  of  the  problem   • Swimming  under  a  bridge  came  2  ducks  in  front  of  2  ducks,  2  ducks  behind  2  ducks,  &  2  ducks  in  the  middle.  H ow   many  ducks  were  there  in  all?   • Solving  the  problem  requires:  problem  representation  &  problem  execution   o Diff  representations  will  include  diff  info  in  the  problem  space   o Some  representations  will  include  the  right  kind  of  info  to  solve  the  problem,  some  w on’t.   o Some  representations  will  affect  the  operators  by  making  it  difficult  to  apply  &  evaluate  possible  moves,  &   keeping  track  of  both  relevant  &  irrelevant  info.   o Much  easier  if  states  &  operators  are  represented  efficiently.     Problem  Solving  viast  Analogy   • Example  (1  we’ll  use  the  literal  description):  Collapsing  stars  spin  faster  &  faster  as  they  fold  in  on  themselves  &  their   size  ↓.  This  phenomenon  occurs  b/c  of  a  principle  called  “conservation  of  angular  momentum”.   What  would  happen  if   a  star  expanded  instead  of  collapsing?  a)  rate  of  rota b)  rate  of  rotation  would  ↓  c)  orbital  speed  would  ↑   d)  orbital  speed  would  ↓   • Same  example  (this  time  using  an  analogy ):  Collapsing  stars  spin  faster  as  their  size  decreases.  Stars  are  thus  like   skaters,  who  pirouette  faster  as  they  pull  in  their  arms.  Both  stars  &  skaters  operate  by  a  principle  called   “conservation  of  angular  momentum”.   ß  More  able  to  come  up  w/  the  answe r   • Analogies  are  excellent  teaching  tools,  but  the  problem  is  that  often  you  don’t  have  an  analogy  to  use.  You  need  to   find  one  yourself.  Spontaneous,  uninstructed  use  of  analogies  seems  to  be  quite  rare.  Ability  to  draw  analogies  is  a   central  intellectual  tool.  Challenging  to  do  though!   • Tumor  problem  vs.  Fortess  problem  (Gick  &  Holyoak,  1980)   o Few  students  could  solve  the  tumor  problem   o When  explicitly  told  to  use  info  from  the  Fortress  problem  to  help  them,   over  90%  solved  the  problem.  Less   are  able  to  solve  when  they  are  not  told  that  the  Fortress  problem  relates  to  the  Tumor  problem.   o People  will  start  w/  a  memory  search:  “what  do  I  know  about  tumors”  but  this  will  not  trigger  the  hint:  the   Fortress  problem.  It  is  the  FORM  that  matters  most.   o The  DEEP  STRUCTURE  of  the  problem/analogy  is  important,  rather  than  the  surface  elements  of  the  analogy.   o Understanding  is  better  than  just  memorization     Expertise   • Experts  tend  to  think  about  the  deep  structure  of  problems  (more  than  novices  do)   • Experts  are  better  at  knowing  what  info  is  irrelevant  –  not  following  so  many  blind  alleys   • Experts  are  good  at  CHUNKING  (i.e.  chess  experts  can  memorize  pieces  on  a  board  by  recalling  plays  that  make  sense)   • Experts  have:  MORE  info,  DIFF  info,  CROSS-­‐REFERENCE  info  (more  connections  l inking  info  in  memory),  &   AUTOMATIZED  procedures   • Memory  advantage  leads  to  problem  solving  advantage.     • Being  able  to  see  the  larger  structure  also  helps  problem  solving.   o Don’t  get  bogged  down  in  irrelevant  details   o Able  to  more  effectively  identify   SUBPROBLEMS,  &  so  can  create  SUBGOALS   • Limits  of  Expertise   o Experts  sometimes  don’t  remember  details  of  problems  very  well   § Understood  the  gist,  forgot  the  rest   § Also  likely  to  make  INTRUSION  errors  (assumptions  based  on  prior  knowledge)   o Experts  are  no  better  than  novices  outside  of  their  own  domain.   o When  
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