Procedure

The procedure section includes how participants were recruited for the experiment, a description of the location and layout of the laboratory in which the experiment took place, and the procedure and data collection.

Recruitment

Throughout the campus flyers were posted (Appendix 14-1) inviting students to participate in an experimental study on problem solving. To prevent potential signees from preparing for the study, the details of the types of problems or tests involved in this experiment were not communicated prior to the study. They were told only that the study would last around ~25 minutes and that participants would be compensated for their time and participation with £7.

Experimental Setting

The experiment took place in a laboratory which was about 3 X 3 meters in size. Two tables, a desktop computer table for the participant and a coffee table for the researcher were positioned face-to-face so that the researcher could observe each participant during the experiment (see Figure 5.14).

On the participant’s table were the eight coins positioned in the initial configuration (Figure 5.13) and above this workspace was attached an image of the initial configuration as a reminder to reposition the coins after each unsuccessful attempt of two moves (Figure 5.15).

The researcher sat across from the participant’s table. He started the experiment by activating the online stopwatch on the laptop. During the experiment, he asked the participant to rate his/her feelings after each attempt of two moves.

Also, the investigator provided the participant with the hints at the designated time, made notes, monitored if the instructions were properly followed, recorded the results and stopped the experiment after a total of six minutes.

Figure 5.14 Layout of the room for experimental study

Experimental Procedure

Before the test, each participant was handed two sheets of paper with a brief amount of information about the study (Appendix 14-3 and Appendix 14-4). Each participant left to read both pages and asked to sign the consent form if they agreed to participate in the study. Participants were randomly assigned to one of the six experimental conditions (Table 3) or the control group, and each was tested individually.

Participants were given a sheet of paper with printed text (for subjects in conditional groups see Appendix 14-6 and those in the control group see Appendix 14-5). They were instructed to rearrange the eight coins by moving two coins only (defined as a solution attempt) so that the correct solution would result in each coin touching exactly three others.

All participants were given a total of six minutes to work on the problem and were allowed to make as many solution attempts as they wished with the condition that for each new attempt they must start with the original coin arrangement (Figure 5.13). After each attempt of two moves to solve the problem, participants were also asked to rate their feelings in terms of how close they were to the solution, i.e. feelings of warmth (Metcalfe, 1986). Based on a scale of 0 to 10 (i.e. “0” being completely stuck and “10” extremely close) their responses were filled in on the template (Appendix 14-7) by the researcher along with the number of attempts made at the time at which each attempt was completed.

Participants in the six experimental conditions were provided with two visual hints (“grouping” and “stacking + grouping”), one every two minutes after the initial no hint period of two minutes. For example, participants in the conditional group Abstract

2D / No process (gr. 1), after two minutes of unsuccessful attempts to solve the problem

in the no hint period, received image A (see Table 3), printed on a 10 X 8 inch sheet of paper as a visual hint to the problem, and they were then allowed to work for two more minutes with the hint in front of them. If they had still failed to find the solution in this period, they were provided with image B in the same format and left to work on the problem for two additional minutes.

Participants in the control group were left to work on the problem for a total of six minutes without any hints.

The time intervals from the beginning of the experiment to the end were guided by a set of sounds from an online stopwatch (http://www.online-stopwatch.com/full-screen- interval-timer/?c=r48wfggiyj) customised for this experiment. After each period of two minutes, the stopwatch played an alarm sound reminding the researcher to provide the participant with the designed visual hint and after a total of six minutes working on the problem, there was a clapping sound to end the experiment.

Participants who solved the problem during the experiment were scored as successful and the time at which they found the solution to the problem was recorded, and those who did not solve it in the period of six minutes were stopped and scored as unsuccessful.

Participants who solved the problem in the first two minutes without receiving the hints were scored as successful and were excluded from analyses along with the ones who did not correctly follow the study instructions or who were previously aware of the 8- coin problem (Appendix 14-9).

Of the total of sixty-six participants, two of them solved the problem in the first two minutes, and they were excluded from further analyses. This left sixteen participants for the control group and eight participants for each of the six between conditions.

5.3

Results

The main results are illustrated in Table 5, which shows the percentage of participants who produced correct solutions for the control group and each of the six conditions. The numbers of times that each participant produced a correct solution was processed with an analysis of variance, with surface hints and structural process hints as between factors, and structural insight hints as the within factor.

Although the use of ANOVA for binary data has been previously criticised (Gabrielsson & Seeger, 1971), ANOVA analysis used by Ormerod et al. (2002) has led to almost identical patterns of results to the ones employing the recommended factorial design for binary data (Cox & Snell, 1989).

Our findings suggest two significant main effects and an interaction effect. There appears to be a main effect of structural insight hints with grouping plus stacking hints

leading to significantly more correct solutions (M = .19) than grouping only hints (M = .04), (F (1, 42) = 6.72, MSE = .51, p < .05).

The other main effect regards the surface cues (F (1, 42) = 4,26, MSE = .32, p < .05) and the post-hoc Tukey's HSD tests showed that abstract 3D hints lead to significantly more correct solutions (M = .19) than abstract 2D hints (M = .00) at .05 level of significance. Without being significant, post-hoc Tukey's HSD tests suggest that the representational 3D hints also lead to more correct solutions (M = .16) than abstract 2D hints (M = .07). The other comparison was not significant.

Table 5 Number of problem solvers in each condition after the visual hints

There also appears to be an interaction effect between all three factors: surface cue and both structural cues (F (2, 42) = 8.65, MSE = .66, p < .05). Thus the most successful hints, both with a success rate of 50%, are stacking hints without process information and in abstract 3D representational format, together with stacking hints with process information and in representational 3D format. Furthermore, representational 3D hints only work, and work well, together with stacking insight hints rather than grouping ones. On the other hand, abstract 3D hints work with grouping hints with process information.

Visual Analogy

Conditions

Ctrl. Group = 16 Cond. Group(s) = 8 in each

Structural aspect:

Process Insight Total:

Grouping Stacking + Grouping

Control Group N/A N/A N/A 0

Surf ace aspect: Depth Abstract 2D hint No process 0 0 0 Process 0 0 0 Abstract 3D hint No process 0 4 (50) 4 (50) Process 2 (25) 0 2 (25) Representational 3D hint No process 0 1 (12.5) 1 (12.5) Process 0 4 (50) 4 (50) Total: 2 (4.16) 9 (18.75) 11