Insight and the 9-dot problem |
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An Investigation of the Concept of ‘Insight’ and the Difficulties and Solutions Associated with Insight in Relation to the 9-Dot Problem. Aims and ObjectivesThis project will have the following aims and objectives:(1) To establish the theoretical and conceptual base for the idea of ‘insight’ in its relation to the 9-dot problem. To investigate the various academic theories about ‘insight’ and ‘difficulty’ in respect to the 9-dot problem, and to show the various attempts at solutions to the problem. (2) To design and conduct an empirical experiment to test the theories that manipulation of the experiment conditions and its instructional and presentational features will affect and alter the ‘difficulty’ of the problem and participants ‘insight’ into the 9-dot problem.
 Background and RationaleThe 9-dot problem is a classic example of an experiment used to measure problem-solving ability. Theorists generally agree that the solution to this problem requires ‘insight’: which is defined as ‘… the recognition or restructuring of a key feature of a problem that allows a solution to be found’. (MacGregor, 2001). That is, participants must determine the central difficulty of the problem and seek the solution by focusing upon this difficulty. Several theories have been put forward to determine the nature of this difficulty. The famous Gestalt theory is an example of a perceptual model: it states that participants usually concentrate upon the area defined by the dots and therefore do not contemplate a solution outside this area. Critics of the Gestalt theory -- see Burnham and Davis (1969) and Weisberg and Alba (1981) -- produced evidence to show that when the instructions for the test are manipulated so as to give the participant explicit instructions to seek a solution outside of the dotted area, that this failed to facilitate a high improvement in solution rates. From this, the above theorists inferred that the 9-dot problem is a cognitive problem more than a perceptual problem. Others though – see Lung and Dominowski (1985) -- have challenged these criticisms, and sought a perceptual and heuristic explanation of the difficulty. Theorists such as MacGregor have also stressed the importance of the influence of ‘information processing’, ‘impasse’ and ‘promising states’ upon insight. Several theorists also argue that the difficulty of 9-dot problem is increased by the difficulty of visualizing and conceptualizing the abstract goal of the problem.In the context of these discussions, ‘problem’ is defined as a problem of ‘insight’ – where the participant needs to identify the crux of the difficulty to solve the problem. Thus problem-solving in this context, means a heightening and concentration of insight on the part of the participant as a means to finding the solution. Accordingly, individual differences of insight levels affect the success a participant has solving the 9-dot problem – where, obviously, those with greatest insight are most successful. ‘Functional fixity’ refers to mental processes that a participant is used to making in normal thought and which he turns to as an aid when problem-solving; this project will examine how functional fixity has been argued to influence insight into the 9-dot problem. Research questions and hypothesesTraditionally, the difficulty of the 9-dot problem has been attributed by psychologists to a ‘failure of insight’ (MacGregor, 2001) on the part of the problem-solver. Gestaltists and Non-Gestaltists alike agree that this difficulty arises from an ‘inappropriate imposition of constraints’ (MacGregor) indicated by the phrasing of the question. Certain instructional manipulations such as explicitly advising the solver to look outside the dotted area for a solution failed to facilitate a correct answer, and so led many to discredit the Gestalt model. Several alternatives to the Gestalt model have been devised, emphasizing cognitive rather than perceptual factors.This project proposal considers a heuristic investigation of the problem, and sets up the following question and hypothesis. Question: To what extent does the difficulty of the 9-dot problem depend upon having to extend the lines beyond the dotted area and onto unseen and unmarked points? Hypothesis: Taking away the need to extend lines beyond the dotted area significantly reduces the difficulty of such problems. DESIGNThe two experimental conditions will be:(i) The standard 9-dot problem. (ii) The variant 11-dot problem of Burnham & Davis (1969). (The solution to this 11-dot problem does not require lines to extend out of the dotted area.) The instructional manipulation will be: (i) One group will be given one attempt only to solve the problem; a second group will be given two attempts. The presentational manipulation will be: (i) The time given for participants to solve the problem will be varied: one group being given two minutes and a second group five minutes. Note: the fact that this experiment will be conducted online immediately manipulates the traditional presentation of the problem which is usually on paper. The online presentation will change the visual and spatial presentation of the problem. ParticipantsParticipants for this experiment will be male or female, aged 18-65, with good-correct eyesight, and previously unaware of the 9-dot experiment. The participants will be split into groups of ten for the two conditions: the standard 9-dot problem and the 11-dot problem.Proposed materialsThe experiment will require the following equipment, apparatus and software:(a) Since the experiment is being conducted on line, all participants will need access to a computer that has email as well as Microsoft Word. (b) A standard 9-dot problem sheet and a sheet with the Burnham and Davis 11-dot problem will be prepared for computer use. The dots for both sheets will be 0.5cm in width and horizontally and vertically separated by 3cm of white space, and represented as black. Both the 9-dot and 11-dot will be centrally located on the page. (c) The participants’ time to solve the problems will be set and controlled by their computer: allowing them 2 minutes or 5 minutes depending upon the particular experiment. (d) Separate instruction-sheets will need to be supplied for each group and each experiment. (e) Each participant will need to complete an online consent form, and this will be returned by email. Experimental procedure-- Participants in the experiments will be asked to volunteer and to fill-in an online consent form for their participation, which outlines all ethical issues. -- Volunteers will be given an appointment time for their experiment and attend either in groups or individually. All the necessary instructions and details will be ready online, and easily accessible. -- Volunteers will be split into the following conditions: (1) 9-dot problem (2) 11-dot problem Separate instruction sheets will be provided online for each condition and each experiment. Condition 1: 9-Dot Problem:(1a) 9-dot, 2 minutes, 1 attempt.(1b) 9-dot, 2 minutes, 2 attempts. (1c) 9-dot, 5 minutes, 1 attempt. (1d) 9-dot, 5 minutes, 2 attempts. Condition 2: 11-Dot Problem (2a) 11-dot, 2 minutes, 1 attempt. -- Results will be recorded automatically by computer and sent back to the researcher for analysis. ANALYSIS OF RESULTSThe principal means of analyzing these results will be to compare the percentages of correct solutions of the standard 9-dot problem against its variant forms and against the 11-dot problem; results about insight and difficulty change will be inferred from these percentages.
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