What is the two string problem and the tower of hanoi
Two string problem (Maier 1931) tie 2 strings to each other but it is impossible to reach one string when holding the others, poles, pliers and extension cords in the room
Tower of hanoi: rings must be moved from on side to the other but can only place rings on larger ones.
2 types of problems:
1) insight: where solutions require a one off insight like the 2 string
2) non-insight which require incremental and sequential problem solving like the tower on hanoi and algebra
Jung-Beeman et al 2004
Found the right anterior superior temporal gyrus to be activated only when the solution involved insight.
6 theories of problem solving `
1- representational change theory Ohlsson 1992
2- The mutilated chessboard problem Kaplan and Simon 1990
3- Knoblich Ohlsson and Raney 2001
Ormerod and Chronicle 2001
4-Newell and Simon 1972
Representational change theory, Ohlsson 1992
Insight problems permit several mental representations and current representation is used to search memory for relevant information. However a block occurs when the problem representation is inappropriate.
So we change the representation to pass the block using 3 ways:
- Elaboration: new information such as hint
- Constraint relaxation: extend ideas of what actions are possible
- Re-encoding, for example realising pliers can act as a weight
Insight often follows.
The mutilated chessboard problem, Kaplan and Simon 1990:
An intact board can be covered by 32 dominoes, can the remaining 62 be covered by 31 dominoes?
- Most participants thought aloud while solving
- Each domino covers one white and one black square- re-encoding
- The board has lost 2 white squares- re-encoding and elaboration
- So no 31 dominoes cannot cover
Participants thought aloud while solving
Knoblich, Ohlsson and Raney 2001:
Moving a matchstick to produce a true statement.
Participants spent more time fixating the values rather than operators suggesting representations of the problem specified that the values needed to change and there was less constraint relaxation. As the fixations on the operators increased, they approached a solution- eye tracking study.
Newell and Simon 1972:
Problem solving involves a range of different knowledge states between initial and goal state.
In complex problems, operators are chosen using heuristics, based on participants thinking aloud during problem solving
theories criticism
However, these theories often only apply to restricted types of problems. And to what extent can the explain real-like problem solving. Individual differences aren’t considered. There is also a tendency towards being descriptive rather than predictive.
The candle problem Duncker 1945:
Attach a candle to a wall without it dripping. Negative transfer was seen as functional fixedness where people assume the box is for holding tacks not candles. When the box was empty there was improved performance
Luchins 1942:
Well-practiced strategies are often used in inappropriate situations and so past experience/ habituation can be detrimental to performance.
- Positive transfer is also seen using analogy and reasoning
Gick and Holyoak 1980:
- Participants read one of 3 stories before attempting radiation problem
1- A general capture a fortress by attacking it with groups of soldiers simultaneously from a number of directions (convergence)
2- One road to the fort is not mined, allowing for a concentrated attack (open passage)
3- A tunnel is constructed to get inside the fort (surgery)
They were then told it was a hint for the radiation problem. It was found that there was a low use of prior analogy in the no-hint control group
Holyoak and Koh 1987:
There was an analogy group who discussed radiation problem in class and control did not.
Up to a week later in experimental settings both groups presented with target problem and only 10% of the control group found the correct solution compared to 81% of the analogy condition.
Meaning spontaneous transfer was so high because of greater surface similarity between two problems
They then did the experiment with 4 different source stories which differed in surface (the settings and characters) and structural (underlying principles and relationships) similarity to the target radiation problem.
Dunbar and Blanchette 2001:
when participants produce their own analogies, these tend to be similar in structure rather than surface properties
