Burns, Bruce D.

Vollmeyer, Regina

English

eScholarship - University of California

UC MercedProceedings of the Annual Meeting of the Cognitive Science SocietyTitleGoals and problem solving: Learning as search of three spacesPermalinkhttps://escholarship.org/uc/item/3093v34kJournalProceedings of the Annual Meeting of the Cognitive Science Society, 18(0)AuthorsBurns, Bruce D.Vollmeyer, ReginaPublication Date1996 Peer reviewedeScholarship.org Powered by the California Digital LibraryUniversity of CaliforniaG o a l s a n d p r o b l e m solving :  L e a r n i n g a s searc h o f  thre e space s Bruc e D .  Burn s un d Regin a Vollmeye r Institu t  fi r  Psychologi c Universita t  Potsda m 1441 5 Postda m Germany { b u r n s , v o l l m e y e } @ r z . u n i - p o t s d a m . d e A recen t  tren d i n computer-base d learnin g ha s bee n t o se t  u p system s tha t  th e learne r  explores ,  rathe r  tha n settin g ver y specifi c  goal s t o reach .  Ou r  previou s researc h o n comple x proble m solvin g ha s supporte d thi s approac h (Vollmeyer , B u m s,  &  Holyoak ,  1996) .  W h e n learnin g h o w t o contro l  a syste m wit h a  se t  o f  input s linke d t o a  se t  o f  outputs , participant s learne d mor e abou t  th e syste m whe n the y wer e give n a  nonspecifi c  goa l  rathe r  tha n a  specifi c  goal .  Thes e result s coul d b e explaine d usin g Simo n an d Lea' s (1974 ) dual-spac e framewor k (o r  tha t  o f  Klah r  &  Dunbar ,  1988 , who exten d thi s framewor k t o scientifi c  discovery )  i n whic h inductio n i s  see n a s a  searc h o f  instanc e spac e (i.e. , examinin g state s o f  th e system) ,  integrate d wit h searc h o f rul e spac e (i.e. ,  formulatin g an d testin g rule s tha t  migh t gover n th e system' s behavior) . Protoco l  analysi s b y Vollmeye r  an d Burn s (1995b ) provide d evidenc e tha t  a  specifi c  goa l  increase s searc h o f instanc e space ,  whil e a  nonspecifi c  goa l  increase s searc h o f rul e spac e i n tha t  i t  increase s th e amoun t  tha t  proble m solver s tes t  an d modif y hypotheses .  Th e protoco l  studie s als o sugges t  w h y som e proble m solver s d o ver y poorly : the y tes t  rule s tha t  ar e impossible .  Thu s a  thir d typ e o f searc h ca n b e proposed ,  searc h o f  mode l  space .  Th e proble m solver' s mode l  define s th e rul e spac e s o i f  a  learne r  ha s th e wron g model ,  searc h o f  rul e spac e wil l  b e ineffectua l  an d the y ma y lear n mor e fro m searc h o f  instanc e space . A test of a multispace model To tes t  i f  mode l  spac e i s  separat e fro m rul e space ,  w e manipulate d th e mode l  participant s ha d a s wel l  a s thei r goals .  Participant s wer e give n a n input/outpu t  syste m simila r  to ,  thoug h simple r  than ,  tha t  use d b y Vollmeye r  e t al .  (1996) .  Thi s tas k require d proble m solver s t o contro l  a syste m tha t  consiste d o f  a  se t  o f  output s (wate r  qualit y measure s i n a  tank )  tha t  coul d b e manipulate d b y a  se t  o f input s (catalysts) .  Th e input s ha d weighte d link s t o th e outputs .  Presente d i n Figur e 1  ar e th e links ,  whic h wer e no t show n t o th e participants .  Simila r  t o Vollmeye r  e t  al. , participant s wer e give n a  specifi c  goa l  (the y wer e tol d a t  th e beginnin g th e exac t  goa l  value s the y woul d late r  tr y t o reach )  o r  a  nonspecifi c  goa l  (the y wer e no t  tol d th e goa l unti l  the y ha d t o reac h it) .  I n addition ,  w e manipulate d th e model  tha t  participant s ha d o f  th e tas k b y givin g the m a goo d o r  poo r  mode l  o f  th e task .  Protoco l  analysi s b y Vollmeye r  an d Burn s (1995b )  foun d tha t  on e typ e o f incorrec t  hypothesi s teste d wa s tha t  input s interacted , althoug h non e did .  Accordingly ,  i n thi s experimen t participant s give n a  poo r  mode l  o f  th e tas k wer e tol d tha t input s ma y interact .  Participant s give n a  goo d mode l  o f  th e tas k wer e tol d tha t  ther e wa s n o possibilit y  o f  interaction s betwee n input s becaus e tw o catalyst s wer e neve r  pu t  int o th e tan k a t  th e sam e time .  W e predicte d a n interactio n betwee n goal  specificit y an d mode l  type . sal t carbo n lim e carbo n CI  concentrat . temperatur e Figur e 1 :  Syste m use d i n th e experiment . Method Participants. One hundred and eighty-six students at the Universit y o f  California ,  Lo s Angele s participate d i n th e experimen t  fo r  cours e credit . Procedure. A 2x2 design was used with the factors goal specificit y (specifi c  vs .  nonspecific )  an d mode l  (goo d vs . poor) .  Participant s wer e give n instruction s appropriat e t o thei r  condition ;  the n the y ha d tw o round s o f  si x trial s each . On eac h tria l  participant s coul d manipulat e th e input s an d observ e th e resultin g outputs .  A t  th e en d o f  eac h roun d participant s complete d a  diagra m o n whic h the y indicate d what  the y kne w abou t  th e structur e o f  th e system .  Fro m thes e diagram s a  structur e scor e wa s derive d i n th e sam e wa y as describe d b y Vollmeye r  e t  al .  (1996) . I n th e thir d round ,  participant s trie d t o reac h a  goal ,  on e whic h specific-goa l  participant s ha d k n o w n sinc e th e beginning .  The n al l  participant s wer e give n a  ne w goa l  t o reac h i n a  fourt h round .  Thi s goa l  teste d h o w wel l participant s coul d transfe r  wha t  the y kne w t o a  ne w goal . Transfe r  erro r  wa s a  measur e o f  h o w clos e participant s go t  t o thi s goa l  (se e Vollmeye r  e t  al. ,  1996) . 23 Result s a n d Discussio n As Vollmeye r  e t  al .  (1996 )  found ,  nonspecific-goa l participant s \ m =  2.36 )  learne d mor e abou t  ho w th e syste m worke d tha n di d specifi c  goa l  participant s ( M =  1.93) ,  a s measure d b y structur e scores ,  F(l,182 )  =  8.83 ,  p  <  .005 . However ,  ther e wa s n o effec t  o f  mode l  typ e o n structur e scores .  Thes e finding  replicate s th e result s o f  Vollmeye r  e t al .  an d suggest s tha t  nonspecific-goa l  participant s searche d rul e spac e more ,  regardles s o f  mode l  type . Ther e wer e n o significan t  effect s o f  goa l  o r  mode l  o n transfe r  error ,  no r  wa s ther e a n interactio n betwee n thes e tw o factor s (thoug h th e patter n wa s a s predicted) .  However ,  ther e was a  significan t  interactio n betwee n mode l  type ,  goa l specificit y an d outpu t  type .  Becaus e th e Chlorin e Concentratio n outpu t  i s affecte d b y tw o inputs ,  i t  i s  harde r t o control .  Vollmeye r  an d Burn s (1995a )  foun d evidenc e tha t  i n a  syste m lik e th e on e use d i n thi s experiment . Chlorin e concentratio n ma y sho w th e stronges t  effect s o f manipulations .  Thu s w e examine d th e transfe r  erro r  fo r Chlorin e concentratio n (se e Figur e 2 ,  not e tha t  lo w score s indicat e greate r  accuracy) .  W e foun d a  significan t  interactio n betwee n goal-specificit y an d mode l  type ,  F(l,182 )  =  4.09 ,  p < .05 .  I f  participant s wer e give n a  goo d model ,  the y performe d bette r  i f  give n a  nonspecific-goal ,  jus t  a s i n Vollmeye r  e t  al .  (1996) .  However ,  i f  give n a  poo r  model , participant s performe d bette r  whe n give n a  specifi c  goal . 10 TO 0. 5 4 -•  NS G 0SG Good Poo r Model Manipulation Figure 2: Transfer error for Chlorine concentration. This experiment supports the theory proposed earlier, that i n orde r  t o explai n problem-solvin g behavio r  i t  i s  necessar y t o propos e a  three-spac e search .  I n thi s mode l  searc h o f model  spac e define s hypothesi s space ,  searc h o f  hypothesi s spac e guide s searc h o f  experimen t  space ,  an d provide s evidenc e fo r  searc h o f  mode l  space .  Searc h o f  experimen t spac e allow s testin g o f  hypotheses ,  an d lead s t o th e goal . Implications Whil e w e hav e propose d a  three-spac e searc h theory ,  w e ar e no t  committe d t o proposin g onl y thre e spaces .  Ther e m ay b e mor e tha n thre e conceptuall y differen t  spaces , especiall y fo r  othe r  tasks .  Wha t  criteri a shoul d b e use d when proposin g separat e searc h spaces ? Conceptually ,  ne w space s nee d t o mak e sense ,  bu t  ultimatel y empirica l  suppor t fo r  th e existenc e o f  multipl e searc h space s mus t  b e found .  I f conceptuall y differen t  type s o f  searc h space s exis t  the n experimenta l  manipulatio n a t  th e leve l  o f  differen t  space s shoul d lea d t o differen t  results .  Th e experimen t  presente d her e i s a n exampl e o f  ho w empirica l  evidenc e ca n b e use d t o suppor t  th e ide a o f  separat e searc h spaces ,  especiall y whe n i t i s  possibl e t o predic t  interaction s betwee n factors . One weaknes s o f  th e abov e result s i s tha t  thi s experimen t coul d no t  b e use d t o establishe d tha t  movemen t  i s occurrin g betwee n differen t  models .  Thu s w e di d no t  demonstrat e tha t actua l  searc h wa s occurrin g a t  th e leve l  o f  models .  Furthe r evidenc e i s  required ,  suc h a s protoco l  analysi s a s i n Vollmeye r  an d Burn s (1995b) ,  whic h showe d tha t  proble m solver s searche d differen t  rules ,  an d differen t  instances . Thes e results ,  an d multispac e model s i n genera l  hav e implication s beyon d proble m solvin g an d scientifi c discovery .  Mos t  obviously ,  i f  the y ca n b e generalize d the y hav e stron g implication s fo r  learning .  Th e result s sugges t tha t  whethe r  a  specifi c  o r  nonspecifi c  goa l  i s  beneficia l  fo r learnin g wil l  depen d o n ho w goo d i s th e learner' s mode l  o f th e task .  Furthermore ,  thes e type s o f  model s sugges t  way s t o understan d result s i n othe r  area s o f  cognition .  Fo r example ,  implici t  learnin g o f  artificia l  gramma r  ma y b e wors e fo r  someon e lookin g fo r  underlyin g rules ,  tha n fo r someone w h o doe s no t  loo k fo r  rule s (Reber ,  1976) . However ,  th e resul t  doe s no t  hol d i f  th e gramma r  i s simpl e enough .  I n term s o f  ou r  three-spac e model ,  participant s i n experiment s wit h difficul t  grammar s hav e a  poo r  mode l  o f th e situation .  Searc h o f  rul e spac e wil l  therefor e b e ineffectual ,  s o tha t  a  specifi c  goa l  (i.e. ,  focu s o n instance s o f letter-strings )  lead s t o bette r  learning . One challeng e fo r  thi s researc h i s t o establis h wha t  make s model  "poor" .  Th e ke y facto r  coul d b e th e relationshi p betwee n th e tru e hypothesi s spac e an d proble m solvers ' hypothesi s space ,  bu t  thi s proposa l  require s mor e research . References Klahr ,  D .  &  Dunbar ,  K .  (1988) .  Dua l  spac e searc h durin g scientifi c  reasoning .  Cognitiv e Science ,  12 ,  1-55 . Reber ,  A. S (1976) .  Implici t  learnin g o f  syntheti c languages : th e rol e o f  instructiona l  set .  Journa l  o f  Experimenta l Psychology :  H u m a n learnin g an d Memory ,  2 .  88-94 . Simon ,  H.A .  &  Lea ,  G .  (1974) .  Proble m solvin g an d rul e induction :  A  unifie d view .  I n L .  W .  Greg g (Ed.) , Knowledg e an d cognition .  Hillsdale ,  NJ :  Erlbaum . Vollmeyer ,  R .  &  Burns ,  B .  D .  (1995a )  Doe s hypothesis -instructio n improv e learning ? I n Proceeding s o f  th e Seventeent h Annua l  Conferenc e o f  th e Cognitiv e Scienc e Societ y (pp .  711-776) .  Hillsdale ,  NJ :  Lawrenc e Erlbau m Associates . Vollmeyer ,  R .  &  Burns ,  B .  D .  (1995b) .  Goa l  specificit y an d hypothesi s testin g i n learnin g a  comple x system . Poste r  presente d a t  th e Thirty-sixt h Annua l  Meetin g o f  th e Psychonomi c Society ,  Lo s Angeles ,  California . Vollmeyer ,  R. ,  Burns ,  B.D. ,  &  Holyoak ,  K.J .  (1996) .  Th e impac t  o f  goa l  specificit y o n strateg y us e an d th e acquisitio n o f  proble m structure .  Cognitiv e Science .  20 , 75-100 . 24 

Goals and problem solving: Learning as search of three spaces

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Goals and problem solving: Learning as search of three spaces

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