Key message: A method is the way to a goal.
A method is a systematically planned way to a goal. Nobody wants to wait for coincidence to reach a goal. No one can reach a goal if he / she does not know what it looks like.
Systematically planned means the plan was devellopped "based on a system". A system is a set of elements that are interrelated.The behavior
of a system is the result of the interaction of all its elements, so a systematic method takes into account all the elements that affect the path to the goal (see
The way to the goal is fixed in a writen systematic instruction (method regulation).
"Methods are well-planned, well-founded procedures for achieving defined goals ... A method is a
systematic instruction for action (a procedure) to solve tasks of a certain class. It is based on one or more principles. The instruction describes how, starting from given
conditions, a goal can be achieved with a defined sequence of steps."
(http://www.informatikbegriffsnetz.de/arbeitskreise/vorgehensmodelle/themenbereiche/prinzipMethodeWerkzeug.html, 12.02.14, my translation)
A goal is achieved by applying a method step-by-step. A method starts from an initial situation. (A situation is a system at a certain point in time.)
Now there are two possibilities:
1. The execution of the method is a task
Often the goal and the way from the initial situation to the goal (the method) are known and it is possible to execute the method. If this is the case, the way to the goal is the execution of a task.
2. The execution of the method is a problem
If I am dissatisfied with an initial situation (the current situation), but at the moment I am not able to achieve a desired target situation, then I have a problem. In the case of a problem, there don't exist clear ideas about the desired goal 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 are not available). To solve a problem see "How to solve problems".
"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)
... to be continued