Key message: A problem is solved by a method.
(The text is still in progress.)
I have a problem when I am dissatisfied with an initial situation (the current situation), but at the moment I am not able to achieve a desired target situation (the goal). It may be that I do not know what the goal looks like or the means to achieve the goal are unknown or an obstacle must be overcome on the way to the goal (e.g. the required means may be known but not available). So a problem has three main elements: the initial situation, the obstacle and the goal (the target situation).
"If there is a problem there is a discrepancy between an actual and a desired state, there is a barrier between the two states
[that needs to be overcome] ... A task is a mental requirement, but the methods of coping with it are known. ...
The difference between problem and task depends on prior knowledge, ... i.e. the same situation can be a task for one person and a problem for another ... " (www.psychologie.uni-heidelberg.de/ae/allg/mitarb/ms/PH_Einfuehrung.pdf, S. 11, 02.04.14, pages 1 - 13 are of interest, my translation)
In order to solve a problem, three main steps must always be carried out:
(Lindemann, U.(2009). Methodische Entwicklung technischer Produkte. Heidelberg: Springer, S. 46, my translation)
I would need a method to solve the problem and reach the goal.
method is a way to a specific goal. In order to find a
suitable method, I have to analyze the unsatisfactory situation, the obstacle and the goal.
Because I want to solve the problem optimally, I am not satisfied with the first idea for a method,
but look for other alternative methods. From these I select the method that promises the greatest success and test it. This allows me to
optimize the chosen method.
For further explanations see "How to develop and apply methods?".