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I seem to remember that there is a word or phrase to describe this following behavior, but I can't recall what it is.

The word describes a phenomenon where someone tries one approach to a problem, but then switches to another (possibly due to deficiencies in the original approach or just personal preference); this then repeats where the person abandons the second approach to pursue yet a third.

The word or phrase can be negative in connotation, but no not necessarily so.

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    Changing your mind? Trial and error? Being wishy-washy, indecisive, or picky? Simply trying on many hats? What's the reason for switching? Jun 8 '20 at 23:41
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Not sure if this helps in your search for an elusive word that seems to have been very specific, but this might help narrow the search:

fickle is one word that describes an unsteady state or attitude (such as in fickle heart). I imagine it could also be used in fickle attempts at solving a problem which would then clearly connotate indecisiveness and possible lack of consistency in the approach. (If that is what you want to say, such as seeming not very methodical or anyway not clearly sticking to it)

Someone constantly "trying alternate approaches" or "alternately trying a number of approaches" (or two approaches, for that matter) might be described as just that. Evaluating this negatively might lie in the eye of the beholder/observer, the degree of negativity depending on context, e.g. discpline of science (though I'm not sure in what science one would alternatingly try two approaches unless declaring this as methodical for a well-explained good reason).

Trying to find and verify a solution by trial-and-error would be called heuristics/heuristical. Not sure if that's the word you're after though.

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The phrase you may be looking for is “change tack”.

Refer: Collins Dictionary If you change tack or try a different tack, you try a different method for dealing with a situation.

In academia: “Iterative refinement”

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How about change gears. From Lexico:

change gears: Adopt a different approach to a situation or task.

Example:

Jane tried Approach #1. She then changed gears to Approach #2. After that, she changed gears again to Approach #3.

Whether changing gears is positive or negative in connotation depends on the context. In my example, changing gears is a neutral statement of fact.

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