For a general musical education I always recommend a good music school or conservatory. For the study of the piano I think it best to take private lessons from an artist who is experienced both as an executant and as a teacher. Some music schools have such men on their staff, if not, indeed, at their head.
Where Outside Criticism Is Desirable
Having had twenty months' lessons and having now mastered Etudes by Berens, opus 61, by Heller, opus 47, and Smith's Octave Studies, do you think I am justified in continuing my lessons?
Assuming that you have really "mastered" the works you mention I can only encourage you to continue your lessons; I would, however, advise you to obtain an experienced pianist's criticism in order to assure yourself that your idea of "mastering" is right.
The Sex of the Piano Teacher
Is there any preference as to sex in the question of choosing a piano teacher; in other words, is a woman teacher preferable for any reason for a girl and a man teacher for a man?
Your question does not admit of generalization from a purely musical point of view. It must be—on this premise—decided by the quality, not by the sex, of the teacher. A good feminine teacher is better than a bad masculine one, and vice versa. The question of sex does not enter into the matter. Of course, the greater number of eminent teachers are found on the masculine side.
Too Much "Method"
My recently engaged teacher says that the word "method" jars on her nerves. Kindly advise me whether a method is not the best thing for a novice, and, if so, which one?
Your teacher, while possibly a little over-sensitive, is not wrong. America is the most method-ridden country in the world. Most of the methods in vogue contain some good points—about a grain of truth to a ton of mere ballast. Your teacher's utterance makes me think that you were lucky in finding her, and that you have excellent reason to trust in her guidance.