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PSYC 221 Ch12 Problem Solving.pdf

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Queen's University
PSYC 221
Kevin G Munhall

PSYC  221  –  Problem  Solving   Chapter  12   Problem  Solving     Problem:  occurs  when  there  is  an  obstacle  between  the  present  state  and  a  goal  and  it  is  not   immediately  obvious  how  to  get  around  the  obstacle.       There  are  two  types  of  problems:  well-­‐defined  and  ill-­‐defined.     Well-­‐defined  problems:  when  a  procedure  is  applied  correctly  there  will  be  a  single,  correct   answer.  For  example,  math  problems.     Ill-­‐defined  problems:  do  not  necessarily  have  a  single  answer  or  a  “correct”  answer,  and  the  path   to  solving  them  can  be  unclear.  For  example,  relationship  problems.     Recall,  Gestalt  psychology  is  interested  in  the  laws  of  perceptual  organization  (perception),   learning,  problem  solving,  attitudes,  and  beliefs.  When  it  comes  to  problem  solving,  Gestalt   psychologists  take  the  perceptual  approach.  Gestalt  psychology  states  that  problem  solving  is   about  the  following:   • How  individuals  represent  a  problem  in  their  mind   • How  problem  solving  involves  a  reorganization  or  restructuring  of  this  representation     How  individuals  represent  a  problem  in  their  mind   • This  is  essentially  methodology.  For  example,  when  attempting  a  crossword  some  people   will  do  all  the  horizontals  then  use  these  to  fill  in  the  verticals.  Some  people  will  do  all  the   clues  they  know  at  once  and  then  fill  in  the  blanks.  Some  will  focus  on  a  corner  and  work   until  it  is  solved.  Everyone  represents  the  problem  differently.     • Gestalt  psychologists  believe  that  this  is  the  key  to  successful  problem  solving     Steps  to  problem  solving,  therefore,  are:   1. Perceiving  the  problem   2. Representing  the  problem  in  a  different  way  (restructuring)     Restructuring:  the  process  of  changing  a  problem’s  representation.       Insight:  sudden  realization  of  a  problem’s  solution.  This  usually  involves  discovering  a  crucial   element  that  leads  to  restructuring  and  subsequently  the  solution.  Think:  the  “Aha!”  moment.       Insight  problems  include  critical  thinking  problems  to  which  there  are  many  routes  but  essentially   one  solution,  such  as  the  link  problem  or  the  mounting  the  candle  problem.  See  any  of  the  figures   on  pages  328-­‐329  if  these  don’t  ring  a  bell.  Noninsight  problems  include  algebra,  in  which  you   have  to  be  methodical  in  reaching  the  answer.       To  test  whether  or  not  insight  is  a  real  occurrence  during  problem  solving,  researchers  gave   participants  either  insight  problems  or  noninsight  probles.  They  believed  that  participants  who   were  working  on  noninsight  problems  would  be  aware  of  how  close  to  the  answer  they  were,  and   1   PSYC  221  –  Problem  Solving   that  participants  who  were  working  on  insight  problems  would  be  less  aware  of  this.  They  had   participants  rate  on  a  scale  how  “hot”  or  “cold”  they  were  to  finding  the  solution.     • For  insight  problems,  median  warmth  rating  was  consistent  and  fairly  cold  until  just  before   the  participant  solved  the  problem.   • For  noninsight  problems  (algebra)  warmth  rating  systematically  increased  as  time  elapsed,   and  there  was  less  drastic  of  a  jump  in  warmth  rating  as  the  participant  came  to  the   solution.     Fixation:  tendency  to  focus  on  a  specific  characteristic  of  a  problem.  Gestalt  psychologists  believe   that  this  is  a  major  obstacle  to  finding  the  solution.  Think  about  it,  this   makes  sense  because  it  prevents  the  person  from  restructuring  the   problem.       Functional  fixedness:  restructuring  the  use  of  an  object  to  its  familiar   functions.  For  example:  you  are  given  a  box  of  matches,  thumbtacks,  and  a   candle.  You  have  to  mount  the  candle  to  the  corkboard  on  the  wall.  How  do   you  do  it?   • The  solution  is  that  you  empty  the  box  of  matches,  mount  the  empty   box  to  the  wall,  and  then  attach  the  candle  to  the  box.  The  thing   keeping  you  from  seeing  the  solution  is  functional  fixedness  –   thinking  that  the  box  of  matches  can  only  be  used  to  light  the  candle.     • Note  that  in  the  photo  I  found  online  it  is  a  book  of  matches  and  a   box  of  thumbtacks,  but  it  works  the  same  way.     Note  that  in  the  text  the  candle  problem  is  boldfaced  as  a  key  term.  It   would  be  advisable  to  remember  this  problem  and  the  implications  of  it.  It  was  developed  and   tested  by  Karl  Duncker.     In  a  spin-­‐off  experiment,  Duncker  either  presented  participants  with  the  materials  for  the  problem   inside  a  box,  or  the  materials  outside  of  a  box.  Participants  who  had  received  the  materials  inside   the  box  were  fixated  on  the  box  being  a  container  (functional  fixedness)  and  had  a  much  more   difficult  time  solving  the  problem  than  did  those  in  the  group  with  the  materials  outside  of  the   box.       Two-­‐string  problem:  the  participant’s  job  is  to  tie  together  two  separated   strings  that  are  hanging  from  the  ceiling.  In  the  room  is  a  chair  and  a  pair   of  pliers.     • The  solution  is  to  tie  the  pliers  one  piece  of  string  to  use  as  a   weight.  Then  the  idea  is  to  swing  the  string  like  a  pendulum.  This  way,  the   participant  can  stand  at  one  piece  and  have  the  other  piece  swing  over  to   them.  Most  participants  have  a  hard  time  with  this  problem  because  of   functional  fixedness  –  they  cannot  look  past  the  normal  use  of  the  pliers  to  see  them  as  a   weight.     2   PSYC  221  –  Problem  Solving   • When  Maier  “accidentally”  brushed  against  a  piece  of  string  and  set  it  in  motion,  most   participants  who  hadn’t  solved  the  problem  in  ten  minutes  were  then  able  to  solve  the   problem  in  sixty  seconds.     Mental  set:  preconceived  notion  about  how  to  approach  a  problem.  This  is  based  on  previous   experience  and/or  what  has  worked  in  the  past.     • Think  about  this  in  terms  of  functional  fixedness.  In  the  past  you  have  used  pliers  to  cut   wire.  When  you  go  into  the  room  to  complete  the  two-­‐string  task  the  idea  of  using  the   pliers  as  a  weight  is  not  in  your  mental  set.       Water-­‐jug  problem:  participants  are  given  three  jugs  of  different  capacities  and  are  required  to   use  these  jugs  to  measure  out  a  specific  quantity  of  water.  See  how  this  experiment  was  used  to   demonstrate  mental  sets:   • Luchins  had  8  water-­‐jug  problems.  Problems  1-­‐6  all  had  the  same  solution:  B  –  A  –  2C  =   desired  quantity  (with  the  capacities  of  the  three  jugs  changing  with  each  problem).   Problems  7-­‐8  required  only  two  of  the  jugs,  such  as  A  +  C  or  A  –  C.     • He  had  one  group,  the  mental  set  group,  complete  problems  1-­‐8.  He  had  the  no  mental   set  group  complete  only  problems  7-­‐8.   • The  no  mental  set  group  completed  the  two  problems  quickly  and  with  the  fewest  steps   (they  were  quick  to  come  to  a  solution  of  A  –  C).     • The  mental  set  group,  as  predicted,  had  developed  a  mental  set  that  B  –  A  –  2C  has  worked   in  the  past  for  the  same  problem.  They  took  longer  to  complete  the  problem  and  tested   more  complicated  solutions  than  the  no  mental  set  group.     If  there  is  one  thing  this  section  has  ironed  down,  it  is  that  Gestalt  psychologists  were  the  pioneers   in  problem  solving  research  by  discovering  that  problem  solving  depends  on  how  the  problem   is  represented  in  the  mind.  Now  we  move  to  more  modern  research  in  problem  solving.     Newell  and  Simon     Newell  and  Simon  were  interested  in  the  actual  search  for  the  answer  to  a  problem.  They   described  problem  solving  as:  a  search  that  occurs  between  the  posing  of  a  problem  and  its   solution.       Initial  state:  conditions  at  the   beginning  of  a  problem.       Goal  state:  solution  to  the   problem.     Tower  of  Hanoi  problem:   three  discs  are  stacked  on  a   left  peg  and  the  goal  state  is  to   have  the  discs  stacked  the   same  way  on  the  right  peg.   There  are  some  rules  that   3   PSYC  221  –  Problem  Solving   make  this  a  problem  solving  challenge.  See  figure.     Intermediate  state:  after  each  step  the  conditions  of  the  problem  change  slightly  –  this  is  the   intermediate  state.       Operators:  actions  that  take  the  problem  from  one  state  to  another.       Problem  space:  composed  of  the  initial  state,  the  goal  state,   and  all  possible  intermediate  states.  The  figure  shows  the   problem  space.  In  this  figure,  the  most  direct  path  to  the   solution  appears  down  the  right  (8  consecutive  moves  with   no  errors).  Of  course  there  are  other  possible  paths  to  take   (many  intermediate  states)  and  these  are  represented  in   the  figure  as  well.       Subgoals:  small  goals  that  help  create  intermediate  states   that  are  closer  to  the  goal.  When  setting  subgoals  it  is   important  to  look  slightly  ahead,  because  completing  a  current  subgoal  in  a  particular  way  may   hinder  the  completion  of  the  next  subgoal.  The  author  of  the  text  provides  a  good  example:   • He  recently  had  to  go  to  Copenhagen.  He  lives  in  Pittsburgh,  where  they  offer  no  direct   flights  to  Copenhagen.  He  had  two  rules:  he  had  to  choose  flights  that  would  give  him   enough  time  to  get  from  the  first  flight  to  the  connecting  flight.  The  second  rule  was  that   the  flights  had  to  be  within  budget.     • He  wanted  to  fly  Pittsburgh  direct  to  Paris,  but  there  was  only  90  minutes  between  this   flight  and  the  flight  to  Copenhagen,  so  it  violated  the  first  rule.  If  he  waited  for  a  later  flight   to  Copenhagen  the  price  increased,  which  violated  the  second  rule.   • He  looked  for  a  city  that  has  direct  flights  to  Copenhagen.  He  found  that  he  could  fly  to   Atlanta  and  then  directly  to  Copenhagen  within  his  set  rules.   • The  moral  of  this  anecdote  is  that  sometimes  subgoals  appear  to  put  more  space  between   the  initial  and  the  end  state,  but  this  is  necessary  to  get  to  subsequent  states.     Means-­‐end  analysis:  way  of  solving  a  problem  in  which  the  goal  is  to  reduce  the  difference   between  the  initial  and  goal  states.       [...] We  continue  with  modern  approaches  to  problem  solving,  ending  the  focus  on  Newell  and  Simon.     How  a  problem  is  stated  can  affect  its  difficulty.       Consider  the  acrobat  problem  and  the  reverse  acrobat  problem.     Acrobat  problem:  the  acrobats  are  performing  an  act  in  which  they  jump  over  each  other.  They   are  in  an  initial  state  and  need  to  be  arranged  into  the  goal  state  (see  figure,  next  page).  There  are   four  rules:   • Only  one  can  jump  at  a  time   • Whenever  two  are  standing  on  the  same  pole,  one  must  be  on  the  shoulders  of  another   4   PSYC  221  –  Problem  Solving   • An  acrobat  cannot  jump  if  someone  is  on  his  shoulders   • A  bigger  acrobat  cannot  stand  on  the  shoulders  of  a  smaller  acrobat     This  problem  takes  5  moves  to  complete  and   is  solved  in  an  average  of  5.63  minutes.       Next  I  will  describe  the  reverse  acrobat   problem.  As  you  will  see,  making  one  small   change  to  the  problem  made  it  much  more   difficult  ...             Reverse  acrobat  problem:  th
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