What are some Problem solving techniques that can be used in testing. For example I need to think of all the test ideas to test a module ..administrator module for instance.
How can I improve test coverage with using creative methods.
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Think up who will use the offered functionality.
What are the tasks of such a person? What are the main priorities that have to be safeguarded?
Crawl into the role. BE the role. Think up hideous happenings that make life hard for your chosen part. Newspaper headings and expert blogs can inspire you there. Risk management input should help as well.
Throw in a bit of Murphy effect and you are coming along quite nicely.
Edit : Murphy's law: "Anything that can go wrong, will go wrong."
Testing in general falls under the Hypothesis Testing facet of problem solving (I think this bit of software should do A given B (and C and D ad nauseam)).
I think you are more asking, "What problem solving techniques map to software testing."
Divide and conquer - Break each step in the workflow into pieces and validate each piece of action. (To get from A to D, make sure that A to B, B to C, and C to D each work)
Means-ends Analysis - How does each step offer a different way to get to the same solution (or to a dead end). (A to B to C to D works fine, but A to B to G doesn't let me map back to D in any way)
Research - Are there similar things that already exist in your software or similar software.
Trial and Error - Good old exploratory testing.
Personally I've always leaned towards identifying variables, grouping them into like things to limit scope, and using that to define my overall set of conditions and then growing test cases to fit. (matrix style testing)