Problem solving forms part of thinking. Considered the most complex of all intellectual functions, problem solving has been defined as higher-order cognitive process that requires the modulation and control of more routine or fundamental skills (Goldstein & Levin, 1987). It occurs if an organism or an artificial intelligence system does not know how to proceed from a given state to a desired goal state. It is part of the larger problem process that includes problem finding and problem shaping.
Solving problems is the only way to learn population genetics... Remember
that you cannot expect to know the answer to a problem instantly, or
merely by looking up the relevant page in the text; it may take time and
effort.
However, in most research into introductory-level science education, it has been realized that for students to gain conceptual understanding, the instructor must teach conceptual understanding. Hence, the focus of much recent physics education research has concentrated on what concepts students have of the world around them, and on finding ways to bring these concepts in line with those held by physicists.
However, it is important that problem-solving skills not be neglected in the search for improved physics education.
Perhaps the most compelling reason is given by the results of an American Institute of Physics survey from 1994. Members in all fields and with varying levels of degree completion were asked to rank how useful they found various skills in their lines of work. Along with interpersonal skills, computer skills, management skills and others, the importance of problem solving skills and knowledge of physics were ranked on a five point scale from "almost always used" to "almost never used."
The results were somewhat surprising. While almost all AIP members involved in teaching physics ranked knowledge of physics concepts very high on their list, those in non-teaching fields such as industry or basic research ranked such knowledge much less important. Less than half of industry professionals of all levels of degree completion found knowledge of physics concepts to be a frequently used skill. On the other hand, all groups across the board had nearly 100% of respondants ranking problem-solving skills as being frequently used. These results strongly suggest that it would be a good idea to expand research into problem-solving skills. Anything so broadly useful should be given some consideration. Secondarily, problem-solving skills are often a limiting factor on students. They may understand the concept...or think they understand it...but are blocked by inability to do the problem itself. Researchers in various fields of science education have pointed out how students often seem to have great difficulty with problems that are simply concatenations of several exercises the students can already work By improving the problem-solving skills of the student population, it may become easier to spot conceptual difficulties the students have. As cognitive science researcher J.G. Greeno said, "The processes used to generate concepts and procedures in novel situations probably correspond to general problem-solving skills..." In other words, as Stewart so ably paraphrased it, "...all problem solving is based on two types of knowledge: knowledge of problem-solving strategies and conceptual knowledge." If we can be confident the students possess the former, it's easier to see where they need help in the latter. Thus, even if the main interest of one's research is to draw out conceptual difficulties, improvements in problem-solving education will make this easier.
Some problem-solving techniques;
1-Hill-climbing strategy, (or - rephrased - gradient descent/ascent, difference reduction) - attempting at every step to move closer to the goal situation. The problem with this approach is that many challenges require that you seem to move away from the goal state in order to clearly see the solution.
2-Means-end analysis, more effective than hill-climbing, requires the setting of subgoals based on the process of getting from the initial state to the goal state when solving a problem.
3-Working backwards
4-Trial-and-error
5-Brainstorming
6-Morphological box
7-Method of focal objects
8-Lateral thinking
9-George Pólya's techniques in How to Solve It
10-Research: study what others have written about the problem (and related problems). Maybe there's already a solution?
11-Assumption reversal (write down your assumptions about the problem, and then reverse them all)
12-Analogy: has a similar problem (possibly in a different field) been solved before?
13-Hypothesis testing: assuming a possible explanation to the problem and trying to prove the assumption.
14-Constraint examination: are you assuming a constraint which doesn't really exist?
15-Take more time: time pressure can cause one to think in circles (the brain, unhelpfully, tends to be "pulled" towards a particular solution, or aspect of the problem)
16-Incubation: input the details of a problem into your mind, then stop focusing on it. The subconscious mind will continue to work on the problem, and the solution might just "pop up" while you are doing something else
17-Build (or write) one or more abstract models of the problem
18-Try to prove that the problem cannot be solved. Where the proof breaks down can be your starting point for resolving it
19-Get help from friends or online problem solving community
20-Root Cause Analysis
21-Wind Tunnel: based on Socratic Method whereby you outrun your logical constraints to reach for new insights to a problem. Developed by Win Wenger.
22-Rory O'Connor's Inner Vision Deck that combines Socratic Method with methaphorical thinking and assumption breaking.
These are also known as creativity techniques.
Hope this helps.