Developmental progression of performance on the Tower of Hanoi problem

Byrnes, Maryann M.; Spitz, Herman H.

doi:10.3758/bf03329485

“…Most research on planning in well-defined problems (i.e., those that involve completely specified initial states, end states, and operators; Newell & Simon, 1972) has used the Tower of Hanoi and its variants (e.g., Bidell & Fischer, 1994;Byrnes & Spitz, 1977;Klahr & Robinson, 1981;Piaget, 1976). In the original Hanoi Tower task (Piaget, 1976), participants were presented with three pegs on which were placed a certain number of disks of variable size.…”

Section: Search In a Well-defined Problem Spacementioning

confidence: 99%

Early Development of Executive Function: A Problem-Solving Framework

Zelazo¹,

Carter

²

,

Reznick

³

et al. 1997

Review of General Psychology

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Executive function (EF) accounts have now been offered for several disorders with childhood onset (e.g., attention-deficit/hyperactivity disorder, autism, early-treated phenylketonuria), and EF has been linked to the development of numerous abilities (e.g., attention, rule use, theory of mind). However, efforts to explain behavior in terms of EF have been hampered by an inadequate characterization of EF itself. What is the function that is accomplished by EF? The present analysis attempts to ground the construct of EF in an account of problem solving and thereby to integrate temporally and functionally distinct aspects of EF within a coherent framework. According to this problem-solving framework, EF is a macroconstruct that spans 4 phases of problem solving (representation, planning, execution, and evaluation). When analyzed into subfunctions, macroconstructs such as EF permit the integration of findings from disparate content domains, which are often studied in isolation from the broader context of reasoning and action. A review of the literature on the early development of EF reveals converging evidence for domain-general changes in all aspects of EF.

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“…Nine-year-old children were chosen for this study because 9 is the age when children can, on their own, solve the Tower of Hanoi puzzle at least some of the time (Byrnes & Spitz, 1979). Although 4-and 5-year-old children are able to solve the problem, they do so only when exceptionally intelligent (Kanevsky, 1989), when given experimenter support (Kanevsky, 1989;Klahr & Robinson, 1981), or when given an abbreviated task (Borys, Spitz, & Dorans, 1982;Klahr & Robinson, 1981;Spitz, Webster, & Borys, 1982).…”

Section: Notesmentioning

confidence: 99%

“…The 4-disk version can be solved by adults but presents a challenge (Ewert & Lambert, 1932;Gagne & Smith, 1962), as does the 3-disk version for 9-year-old children (Byrnes & Spitz, 1979).…”

Section: Childrenmentioning

confidence: 99%

Gesture offers insight into problem‐solving in adults and children

Garber

¹

,

Goldin‐Meadow

²

2002

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When asked to explain their solutions to a problem, both adults and children gesture as they talk. These gestures at times convey information that is not conveyed in speech and thus reveal thoughts that are distinct from those revealed in speech. In this study, we use the classic Tower of Hanoi puzzle to validate the claim that gesture and speech taken together can reflect the activation of two cognitive strategies within a single response. The Tower of Hanoi is a well-studied puzzle, known to be most efficiently solved by activating subroutines at theoretically defined choice points. When asked to explain how they solved the Tower of Hanoi puzzle, both adults and children produced significantly more gesture-speech mismatches-explanations in which speech conveyed one path and gesture anotherat these theoretically defined choice points than they produced at non-choice points. Even when the participants did not solve the problem efficiently, gesture could be used to indicate where the participants were deciding between alternative paths. Gesture can, thus, serve as a useful adjunct to speech when attempting to discover cognitive processes in problem-solving.

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“…Many studies have demonstrated that successful problem-solvers do break the Tower of Hanoi puzzle into theoretically defined subroutines. Evidence for the existence of subroutines comes from a variety of sources: errors made by adults (Egan & Greeno, 1973) and children (Bidell & Fischer, 1995;Byrnes & Spitz, 1979); temporal patterning of moves in adults (Karat, 1982;Kotovsky, Hayes, & Simon, 1985) and children (Bidell & Fischer, 1995); verbal protocols provided by adults (Anzai & Simon, 1979;Hayes & Simon, 1977) and children (Klahr & Robinson, 1981); and computer simulations of human problem-solving (Ernst & Newell, 1969;Newell & Simon, 1972).…”

Section: Introductionmentioning

confidence: 99%

Gesture offers insight into problem-solving in adults and children

Garber

¹

,

Goldin‐Meadow

²

2002

View full text Add to dashboard Cite

When asked to explain their solutions to a problem, both adults and children gesture as they talk. These gestures at times convey information that is not conveyed in speech and thus reveal thoughts that are distinct from those revealed in speech. In this study, we use the classic Tower of Hanoi puzzle to validate the claim that gesture and speech taken together can reflect the activation of two cognitive strategies within a single response. The Tower of Hanoi is a well-studied puzzle, known to be most efficiently solved by activating subroutines at theoretically defined choice points. When asked to explain how they solved the Tower of Hanoi puzzle, both adults and children produced significantly more gesture-speech mismatches-explanations in which speech conveyed one path and gesture anotherat these theoretically defined choice points than they produced at non-choice points. Even when the participants did not solve the problem efficiently, gesture could be used to indicate where the participants were deciding between alternative paths. Gesture can, thus, serve as a useful adjunct to speech when attempting to discover cognitive processes in problem-solving.

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Developmental progression of performance on the Tower of Hanoi problem

Cited by 14 publications

References 4 publications

Early Development of Executive Function: A Problem-Solving Framework

Early Development of Executive Function: A Problem-Solving Framework

Gesture offers insight into problem‐solving in adults and children

Gesture offers insight into problem-solving in adults and children

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