Problem solving and the quality of invention: An empirical investigation.

Abstract

Despite the significance of the conception of a problem in bringing about solutions, and the relationship between the quality of the problem and the quality of the solutions found for it, very little is known about the process of problem formulation. The present study focused on the development of an empirical measure of subjects' ability to create new problems and the relationship between this ability and their skill in solving similar types of problems. These issues were examined using items from the Raven Progressive Matrices Test. Among the results it was found that a reliable and valid quality score could be assigned to newly created matrix-type problems and that only a very low correlation existed between the ability to solve existing problems and the ability to invent new ones. Problem creation was found to be a more difficult task than problem solving, thereby supporting the theoretical notions regarding its significance in characterizing human giftedness and creativity.Albert Einstein said, the formulation of a problem is often more essential than its solution, which may be merely a function of mathematical or experimental skill. To raise new questions, new possibilities, to regard old questions from a new angle, requires creative imagination and marks real advance in science. (Einstein & Infeld, 1938, p. 92) This notion has been generalized by Wertheimer (1945), who stated that the function of thinking is not just solving an actual problem but discovering, envisaging, going into deeper questions. Often in great discoveries the most important thing is that a certain question is found. Envisaging, putting the productive question is often a more important, often a greater achievement than the solution of a set question, (p. 123) 377

Creative reasoning across developmental levels: Convergence and divergence in problem creation

“…Whereas some authors failed to spot a link between intelligence and creativity (Eisenman, Platt, & Darbes, 1968;Kim, 2005;MacKinnon, 1962;Sen, 1993;Smilansky, 1984;Wallach & Kogan, 1965), others found a positive linear relationship (Barron & Harrington, 1981;Guilford, 1967;Preckel, Holling, & Wiese, 2006;Runco & Albert, 1986;Silvia, 2008a;Yamamoto, 1964). Still others found the relation to disappear above a certain threshold level of IQ (e.g.…”

“…To satisfy this requirement we will consider a problem finding task (Smilansky, 1984;Smilansky & Halberstadt, 1986). These authors asked individuals first to perform the last two sets, Sets D and E, of the Standard Progressive Matrices test, (SPM, Raven, 1938Raven, /1998, and afterwards to create an SPM test item, i.e.…”

The effects of mathematical modeling on creative production ability and self-directed learning attitude

“…Furthermore, the students themselves can participate in posing problems with their own models. The ability to pose problems is quite different from the ability to solve problem (Smilansky 1984). The students should be allowed to foster ideas for cases where the models can be applied and adapted and also should be able to use the models through challenging tasks.…”

Sketches from a Design Process: Creative Cognition Inferred From Intermediate Products

“…In sketching, we may therefore look at the production of new items or features as an index of divergent production. Getzels (1975), Getzels and Czikszentmihalyi (1976), Smilanski (1984), Smilanski and Halberstadt (1986), and Wertheimer (1945/1968 argued that a design problem could not be solved by divergent activity alone. Both convergent and divergent thinking processes have to be integrated to arrive at a quality formulation.…”