Effects of strategy instructions and practice on nine-dot problem solving.

Abstract

College students attempted the nine-dot problem with standard or strategy instructions, with or without practice on other dot-connecting problems. Strategy instructions emphasized extending, intersecting, and starting lines beyond the dots. Six practice problems differed in number and arrangement of dots and solution-line pattern, but all required lines extended/intersected beyond the dots. Both instructions and practice facilitated nine-dot performance, supporting the proposal that the ninedot problem belongs to a class of problems with similar strategic requirements, and contradicting Weisberg and Alba's (1981) proposal that facilitation requires knowledge of specific solution lines. Further analyses indicated that both the square shape of the dot pattern and the presence of a center dot contribute to difficulty, that extending (even wrong) lines early and persistently is important for solving the problem, and that self-evaluation of solution attempts requires theoretical attention. 804This document is copyrighted by the American Psychological Association or one of its allied publishers.This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

The dynamics of search, impasse, and representational change provide a coherent explanation of difficulty in the nine-dot problem

“…In particular, we examined the effects of perceptual information both pre-impasse and post-impasse -first, the amount of (perceptual) solution path information that is needed to restrict the initial search space to facilitate the problem solver reaching impasse and to overcome the boundary constraint; and second, how much information is needed to constrain the subsequent post-insight problem space in order to solve the nine-dot problem. Hitherto perceptual hints have provided minimal benefit in increasing the solution rate of the nine-dot problem (Weisberg & Alba, 1981;Lung & Dominowski, 1985;Kershaw & Ohlsson, 2004).…”

“…Providing diagonal lines can facilitate the solution as Lung and Dominowski (1985) demonstrated. However, all experimental conditions provided the diagonal information, and the perceptual conditions showed only a marginal increase of the solution rate.…”

“…In particular, we examined the effects of perceptual information both pre-impasse and post-impasse -first, the amount of (perceptual) solution path information that is needed to restrict the initial search space to facilitate the problem solver reaching impasse and to overcome the boundary constraint; and second, how much information is needed to constrain the subsequent post-insight problem space in order to solve the nine-dot problem. Hitherto perceptual hints have provided minimal benefit in increasing the solution rate of the nine-dot problem (Weisberg & Alba, 1981;Lung & Dominowski, 1985;Kershaw & Ohlsson, 2004).For example, providing explicit hints to draw lines beyond the virtual nine-dot square (Burnham & Davis, 1969;Weisberg & Alba, 1981) and providing explicit perceptual hints that indicate that lines go beyond the virtual square ) had limited influence on solution rates. Even when two additional dots in different colours were provided at the non-dot locations, there was little effect (Ormerod et al,1997, see Figure 2c).…”

“…In the present study we applied the above model to the nine-dot problem (Maier, 1930) that has kept problem solving researchers busy over the last decades (Burnham & Davis, 1969;Kershaw & Ohlsson, 2004;Lung & Dominowski, 1985;MacGregor et al, 2001;Maier, 1930;Scheerer, 1963;Weisberg & Alba, Nine-dot problem 6 1981). There is clear evidence for multiple causes of problem difficulty in this problem (Kershaw & Ohlsson, 2004) and it thus provides an opportunity to better understand the interplay of search and representational change.…”

Reinforced Variability in Animals and People: Implications for Adaptive Action.

“…Reinforcement of variability may also be functional when attempting to train an animal or person to solve problems (e.g., Lung & Dominowski, 1985). Arnesen (2000) used a rat model to ask whether a history of explicit reinforcement of variations would facilitate later problem solving.…”