Theory Driven Hints in the Cheap Necklace Problem: A Preliminary Investigation

Abstract

In this paper we conducted three experiments using the cheap necklace problem, which is regarded as an insight problem. The effects of two hints derived from two contemporary theoretical accounts of insight-Criterion for Satisfactory Progress theory (CSP) and Representational Change Theory (RCT)-were investigated. In Experiment 1, 78 participants made a single attempt at the problem, and significantly fewer participants given the CSP hint used an incorrect (maximizing) first move than participants given the RCT hint or control participants given no hint, Fisher's exact test for 2x3 table, p = .029, with an approximation in χ² effect size, phi = .340. Experiment 2 explored the performance of 60 participants in the same hint conditions over ten problem-solving trials. The number of trials to solution was significantly fewer in the CSP hint condition than in the control condition, t(30) = 2.23, p = .033, η² = .14; this was not so for the RCT hint condition, t(30) = .44, p = .666, η² = .006. Furthermore, there were significantly fewer incorrect (maximizing) first moves in the CSP hint condition than in the other two conditions, F(2, 59) = 15.31, p < .001, η² = .35. The CSP hint here appears to promote the exploration of the problem space, such that the correct move may be found. The lack of effect of the RCT hint suggests in preliminary fashion that representational change may not be the primary cognitive process required to solve the cheap necklace problem. However, in Experiment 3 with 110 participants, the CSP and RCT hints were combined yielding a 75% solution rate over a 34.88% solution rate in the control condition, χ²(1) = 16.03, p < .001, phi = .402. This result indicates that perhaps aspects from both theories are employed during the problem solving process.

Insight Problem Solving: A Critical Examination of the Possibility of Formal Theory

“…Among the earlier ideas are Luchins' concept of einstellung (blind spot) and Duncker's functional fixedness, as in Maher (1992). More recently, there have been two developed theoretical ideas: (1) Criterion for Satisfactory Progress theory (Chu, Dewald, & Chronicle, 2007;MacGregor, Ormerod, & Chronicle, 2001), and (2) Representational Change Theory (Knoblich, Ohlsson, Haider, & Rhenius, 1999). We will discuss these theories in more detail in Section 4.…”

“…1 (Fall 2012) is given on how to represent the problem. This is the approach initiated originally by the Gestalt psychologists, as in Luchins (1942), Duncker (1945), Birch and Rabinowitz (1951), and it has continued to the present day as the common experimental paradigm for studying insight problem solving, as in MacGregor, Ormerod, and Chronicle (2001), Ormerod, MacGregor, and Chronicle (2002) and Chu, Dewald, and Chronicle (2007). Differences in the proportion of solvers may then be traced to the differences in the way that a problem is presented and therefore processed.…”

“…1 (Fall 2012) Satisfactory Progress (CSP) theory. Chu, Dewald, & Chronicle (2007) developed the CSP theory and applied it to understand solution behavior in the so-called cheap necklace problem. In this problem, subjects are presented with four, three link pieces of chain, and their task is to make a single necklace with twelve links.…”

Algorithmic Puzzles: History, Taxonomies, and Applications in Human Problem Solving

“…One can speculate that its smaller version, with just three 2-link chains and the total allowed cost of 10 cents, contains a good hint for solving the standard version: the very small number of reasonable alternatives in the former includes the right solution of breaking one of the given chains into individual links, which is harder to see for the larger version. In fact, it would be interesting to compare the usefulness of this hint with those used by Chu, Dewald, and Chronicle (2007) in their experiments with solving the Cheap Necklace problem by students.…”

Heuristics in Problem Solving: The Role of Direction in Controlling Search Space

“…The Criterion for Satisfactory Progress (CSP) theory (Chu, Dewald, & Chronicle, 2007), formerly known as the Progress Monitoring Theory (MacGregor, Ormerod, & Chronicle, 2001), suggests that the difficulty with insight problems is that, initially, general problem-solving (GPS) heuristics are employed. Individuals appear to have a set when faced with difficult problems, that is, they perform the same incorrect sequence of moves over and over again before changing their mental representation of the problem.…”