Methodology is the general term to describe, as a whole, a system of methods (within a disipline/practice).
Possible aternatives to your sentence
In my research, I have used a method of trial and error.
In my research, a method of trail and error has been used.
In my research, I have taken a trail and error approach.
In my research, a trail and error approach has been taken.
I am not a teacher.
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