Negative Transfer in Matchstick Arithmetic Insight Problems

Negative Transfer in Matchstick Arithmetic Insight Problems Trina C. Kershaw (tkershaw@umassd.edu) Department of Psychology, University of Massachusetts Dartmouth 285 Old Westport Road, North Dartmouth, MA 02747 USA Jason L. G. Braasch (jason.braasch@univ-poitiers.fr) Centre de Recherches sur la Cognition et l’Apprentissage, Universite de Poitiers 5, rue Theodore Lefebvre, 86000 Poitiers, France Christopher K. Flynn (christopherkflynn@gmail.com) Department of Psychology, University of Massachusetts Dartmouth 285 Old Westport Road, North Dartmouth, MA 02747 USA Abstract The current experiment examined whether successful solution on one type of problem, indicating the relaxation of a constraint, had a negative impact on subsequent problems that did not involve the same constraints. One hundred and forty- five participants solved a series of matchstick arithmetic problems. In one group, participants were given three relatively simple “chunk decomposition” problems (CD). A second group solved one “operator decomposition” (OD) problem, involving more constraints, between the baseline CD problem and two later problems. The third group solved three OD problems, similarly placed. Results indicated that successful solution of an OD problem produced negative transfer to subsequent CD problems in the form of longer solution times. Participants who did not successfully solve OD problems did not slow down on subsequent problems; they displayed evidence of positive transfer. The findings were interpreted with reference to theories of constraint relaxation and its relationship to problem solving performance. Keywords: mental set; insight problem solving; negative transfer Procedures in Problem Solving Whenever new problems are encountered in everyday life, our general approach is to apply procedures or solutions that produced successful outcomes in the past. For example, in the event that you are moving a couch to a new apartment, it is possible that the couch will not fit through a particular doorway or up a particular flight of stairs. Solutions that worked in the past were to unscrew the feet on the couch, or to try the other stairway/doorway into the apartment. If we try one of these solutions and it works again, we will likely bring them to bear when similar situations arise in the future. Similarly, procedures or solutions that have worked in one context are often evoked and applied to another context. In the first author’s most recent move, her bookcase was too large to fit up the front staircase, but could be brought up the back staircase with little trouble. Because the try-the-other- staircase procedure worked in a different situation, it may be that the procedure becomes generalized, thus making it more likely to be employed in a variety of situations. However, known procedures do not always apply to new situations, and, in fact, may lead to situations of impasse. To use one final example, again from the first author’s most recent move, her box spring would not fit up the front staircase. The back staircase was next attempted with no success. She and her movers tried rotating the box spring in multiple orientations on each staircase to no avail. Over an hour was spent attempting to apply a known procedure that was not leading to any progress. Eventually, a neighbor suggested using a chainsaw to split the box spring and fold it in half. The chainsaw procedure was used and the box spring entered the apartment. Thus, a successful procedure was applied, but only after lengthy misapplications of known, and previously useful, procedures. The preceding everyday example of misapplying previously successful procedures to the moving of furniture is analogous to the sequence that occurs when solving insight problems. An individual’s initial representation of an insight problem is often faulty because unhelpful prior knowledge and experiences are activated by the problem (Kershaw & Ohlsson, 2004; Knoblich, Ohlsson, Haider, & Rhenius, 1999; Ohlsson, 1992). The individual’s initial problem-solving attempts are guided by this unsuitable knowledge. These initial attempts are usually unsuccessful and the individual then enters a period of impasse, in which no overt problem-solving behavior occurs. In order to exit the impasse, the individual must relax constraints (Knoblich et al., 1999; Ohlsson, 1992) or overcome mental sets caused by incorrect application of procedures (Luchins, 1942). The likelihood of relaxing constraints or breaking mental set depends on the number and strength of the constraints or procedures. Constraint Relaxation and Breaking Mental Set The difficulty of a particular insight problem is dependent upon several factors. For many insight problems, including famous examples such as the nine-dot problem, the necklace