Solving and Creating Raven Progressive Matrices: Reasoning in Well- and Ill-Defined Problem Spaces

Abstract

We studied the development of creative cognition in children ranging from nursery school to Grade 6 (4–12 yr old, N = 511), performing a problem generation task. The task involved inventing a novel item for a classical problem solving task they had completed beforehand: the Raven Progressive Matrices (RPM). This task and the generating task both comprise matrixes of components, to which a set of transformational relations are applied; only in the first case these are inferred to solve a puzzle, but in the second they are invented to create one. We analyzed the matrixes invented in the generation task and compared them to those of the original solving task. We observed that (a) both in solving and generation, the ability to combine more than 1 relation increased with grade level, (b) within all 8 grades, except Grades 3 and 6, performance was uncorrelated between both tasks, (c) relations that were applied in the generation task often did feature in the solving task, and (d) relations occurring in both tasks were applied with different frequencies. Overall, we conclude that standard problem solving ability is not a precondition for creative reasoning and that the comprehension of relations between components featured in solving task differs from that applied in generation.

We thank Frits Peters who wrote the software to compute the frequency profiles for Rule, Components, and Specifications.

Notes

¹Because of this, ill-defined problems constitute a powerful mechanism for promoting understanding and conceptual advancement (Chi & VanLehn, 1991; Mestre, 2002; Siegler, 2005). They, therefore, are most suitable to assess a pupil's, student's, or job candidate's understanding, reasoning mechanisms, and presuppositions (Carey & Flower, 1989; Vosniadou, Ioannides, Dimitrakopoulou, & Papademetriou, 2001).

Note. A total of 511 Dutch children participated in the study (52% girls); 64 children from nursery schools and 447 children of elementary schools. Age limits within grades were not absolute, but the averaged age increased with 1 year.

Note. Values represent relative frequencies of rules featured and solved in one of the RPM tests, and applied in the CRT.

^a Rule 1 = Idiosyncratic and Semantic Coherence, Rule 2 = Four identical Components, Rule 3 = Continuous Pattern, Rule 4 = Symmetry, Rule 5 = Change, Rule 6 = Increase and Decrease, Rule 7 = Exchange and Combine, Rule 8 = Rotation and Succession, Rule 9 = Disappear and Remain, Rule 10 = Indication of Form, Texture, Amount or Orientation, Rule 11 = Indication of Arithmetic Operation, Rule 12 = Groups of Three Components.

Note. Scores of the solving (SPM) and generation task (CRT) increased with grade. However, within the eight groups no relation was found between the scores of both tasks, except for Grade 3 and Grade 6.

^a Scores include CPM scores converted to SPM standards. Scores are the number of items solved correctly. ^b CRT scores are additions of the mean frequencies of rules, components, and specifications. ^c/d SPM mean scores related to the graphical character of the components in the CRT. These scores only differed in Grade 6.

*p < .05.

Note. With increasing grade level items featured more rules (Number of rules = 1 to 4), and components and specifications (CS), indicating an increase in the complexity of the items created in the CRT.

^a Percentage of the number of rules applied within a created item. ^b Sum of the averaged frequencies of components and specifications. r _s **p < .01, *p < .05.

Note. Chi squares for rules solved and featured failed to show significance, except for nursery school children. The comparisons between the rules applied and featured and applied and solved all showed significance.

^a,b Featured is expected. ^c Solved is expected. ^d Comparisons with df = 6 are calculated over Rules 2 to 8. ^e Comparisons with df = 4 are calculated over the Rules 3 and 5 to 8.