Insight as discovery

ABSTRACT

Performance on the triangle of coins problem was observed when participants could physically change the configuration of the problem as they explored potential solutions. Participants were filmed as they worked on the problem. One group of participants could touch and move the “coins” on the screen, thereby enacting changes to the physical configuration of the problem (high interactivity) while a second group could not (low interactivity). In Experiment 1, participants could record as many possible solutions as they wished (with feedback), whereas in Experiment 2, they were limited to only one announcement; if the proposed answer was incorrect, the session was terminated. In both experiments, solution rates were generally better in the high than in the low interactivity environment, although participants were slower and made more moves before announcing their solution in the high interactivity condition of Experiment 2. Detailed analysis of the video data for the participants in the high interactivity task environment revealed a gradual appreciation of the solution, punctuated by many discontinuities in move latencies.

KEYWORDS:

• Problem solving
• insight
• interactivity
• distributed cognition
• creativity

Acknowledgement

We thank Lewis Watson for programming the interactive triangle of coins problem interface, Maxwell Vincze and Andrea Marin Alvarez for help with the coding of the high interactivity videos, Michael Morrison and Shabana Shafiq for their contribution to the recruitment and running of the participants in Experiment 1, Paul March, Amory Danek and two anonymous reviewers for their constructive comments on previous versions of this manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 Take the instructions to participants in Danek et al. (2014, p. 4): “As an example, imagine a light bulb that is switched on all at once in contrast to slowly dimming it up.”

2 This term is used here as a shorthand for the traditional problems employed in insight problem-solving research; this does not mean that the solution of these problems involves a classic insight sequence with a concomitant “aha” subjective experience.

3 Note: the post-task comprehension was accidentally not recorded for one unsuccessful participant in the low interactivity condition (P56).

4 Over 60% of the cells have expected count lower than 5 in this analysis. To correct for this, choice preferences were grouped in terms of correct and incorrect ones (viz. A+B+D vs C). The percentage of cells with expected count lower than 5 was reduced to an acceptable 25%: χ² (1, N = 28) = 1.67, p = .196. Eliminating the participants who could not solve the problem because they could not recognize the correct answers once presented to them from the overall sample, yields an even number of 25 participants in both conditions. The solution rates at the 5-min mark (Low = 40%, High = 68%, χ² [1, N = 50] = 3.95, p = .047) and 10-min mark (Low = 64%, High = 92%, χ² [1, N = 50] = 5.71, p = .017) were significantly greater in the high interactivity condition.

5 The task instructions might have encouraged participants to move coins up since the triangle is introduced as an arrow - that is, it is converted from a geometric shape into an iconic sign. The goal is to make the arrow point up. Thus, the signification of the arrow must change: the point must go from below to above. There is a semiotic logic in moving coins in the same direction as the new direction of the arrow: The coins migrate north because the arrow must point north. Different task instructions might reduce the likelihood of these initial moves. We thank Paul March for this point.

6 A more systemic explanation could also be offered: if the application was programmed to respect the rules imposed by the problem and would not allow participants to continue moving the coins after they moved three, such deep incomprehension would likely not manifest.

7 With an interesting exception: participant 39 in Experiment 2 simulated moving the corner coins Q and W down to project a new base simultaneously with two hands, then submitted the answer without actually physically constructing the solution on the interface.