Method - methodology
These two words should be more carefully distinguished than they often are by students. (And by some of their teachers; although good students will, like any good writers, consider the prejudices of their likely readers.)
- Method simply means the way one does something. In the Physical Sciences, it is used to describe the actions or procedures performed in the course of an experiment. 'This is how I tried to find out the truth.' 'This is what was done.' In cookery, it is used to label the part of a recipe that tells the cook how to make the dish - after the list of ingredients. 'Ingredients: boiling water, teabag. Method: place teabag in a mug or cup. Add boiling water' In Social Sciences, it should be used to describe how the data were collected or assembled.
- Methodology should mean 'the study of method'. It should not mean 'method'. However, it seems to be used in this sense in many academic subjects - among them, Philosophy, Education and some of the Social Sciences. If this usage is current in your own subject, it is sensible to use it.
The confusion may be because there is no good adjective to mean 'with method', 'to do with method'. The English adjective methodical means 'in a very well-managed way', 'done with control'. 'She worked methodically through her reading list, from the first title to the last.' It is usually applied to the behaviour of an individual. However, we have no word to mean 'to do with academic method' - unless we use methodological. Hence, by a process of back-formation, the word methodology has come to be the standard noun.