Critical Thinking Vs. Systematic Thinking
The first and fundamental step in the creative process is to have a clear notion of what the problem is and to be able to state it clearly. The effective thinker begins by first focusing on the structure of the problem, rather than its technical detail. Also brought into working memory from creative operations are the potential solutions. These come from each person's permanent memory store, his or her lifetime database of knowledge and experience. Other potential alternatives are brought in from such external sources of input as reading, ideas from colleagues, data-bases, and other sources. The articles, "The Nature of Scientific Reasoning" written by William R.Hanna and "The Eureka Phenomenon" written by Isaac Asimov brilliantly compare different ways of scientific course of thought and approaches to problem solving.
Isaac Asimov's approach to problem solving is a unique one. He says that in any given situation let your mind relax after heading a road block while doing any sort of critical thinking. He goes onto mention how a bright man, Archimedes, solved a relatively hard problem for king Heiron II by having a flash of deep insight during a moment of relaxation. However, Hanna talks about thought in a more critical manner. His point of view concerning that of scientific thinking is a more disciplined one. He likes more systematic ways of thinking, while Asimov is a more down-to-earth and open minded type of thinker.
Both classes of thinking are valid and special in their own ways. But it's up to the individual to find out what best suits them when it comes to solving not only scientific problems but any problems that arise during the course of their life. As for me, I like Isaac Asimov's way better because I am a more relaxed person with a more open minded personality.