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Tools and methods developed during the era of quality and optimization have shown their limitations and become inappropriate in the context of the requirements of innovation. Nowadays the need to rebuild design practices in enterprises is strongly felt both in terms of human skills and methodological expertise. In part, a way to face the innovation era's difficulties has been provided through the theory of inventive problem solving. This theory represents a significant breakthrough in driving problem statement and solving in a direction that is expressed through the idea that technical systems are driven by objective laws. A second postulate concerns the notion of contradiction, but so far only few contributions have addressed the relations between laws and contradictions. This paper, through a qualitative approach, presents a solution to this limitation and proposes a possible use of laws within the choice of the appropriate conflicting pair, prior to the use of any TRIZ solving techniques. Tests to observe the impact of the proposed approach were conducted in a French engineering ‘grande école’ during three semesters with 180 engineers. The contribution of this paper is twofold. On the one hand, there is a theoretical contribution to the theory of inventive problem solving. In addition, the proposed method offers especially TRIZ practitioners new ways for problem understanding and problem formulation. [ABSTRACT FROM AUTHOR]

This study examined average-, high- and top-performing US fourth graders' rational number problem solving and their understanding of rational number representations. In phase one, all students completed a written test designed to tap their skills for multiplication, division and rational number word-problem solving. In phase two, a subset of students sorted cards that showed part-whole, ratio, quotient, measure, and operator perspectives of rational number representations. Each perspective was shown in numerical notational, word-problem, and visual formats. The results indicated that top-performing students scored significantly higher in problem solving and showed more effectively linked rational number representations than the other groups. The results imply that successful rational number problem solving is intertwined with representational knowledge for a wide range of rational numbers and that the bulk of US students do not possess effective skills for working with rational number representations. [ABSTRACT FROM AUTHOR]