This question is stated not in the context of philosophy (of science) where methodology is the branch that analyzes the principles and procedures of inquiry in general or in a particular discipline. It is stated in the context of problem solving in a particular discipline (e.g. engineering design or design research or engineering education) where a methodology is a structured and systematic approach of achieving specific objectives efficiently. Are the features of a descriptive or a prescriptive methodology different?
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Interesting topic. Taking the work of Kuhn standing for philosophy of science in general, the writings of Dasgupta for computers science, Hubka and Eder for engineering design and design science and Polya for problem solving in mathematics I would say that all of these are intertwined sharing common features. Maybe the best example is Polya’s work which prescribes how to achieve results in mathematics. Math as a field for itself, abstract and logical, thus not technical or physical, according to Polya possess a prescriptive methodology. However the results of math pretty much tackle the salient features of our universe being descriptive in the essence.
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