There is an interesting reference to methods of teaching harmony in the
Board of Education Memorandum on Music, issued in 1914.

The writer says:

'It cannot be emphasized too strongly that the current method of
teaching harmony, whereby pupils are taught to resolve chords on paper
by eye, quite regardless of the fact that 99 per cent. of them do not
realize the sound of the chords they are writing, is musically
valueless.

* * * * *

'In no other language than that of music would it be tolerated that the
theoretical rules of grammar and syntax should be so completely
separated from the actual literature from which they are derived, that
the pupil should never have perceived that there was any relation
whatever between them.

* * * * *

'Another very common result of the neglect of an aural basis for harmony
teaching is that students who can pass a difficult examination, and
write correctly by eye an advanced harmony exercise, are often quite
unable to recognize that exercise played over to them on the piano, or
even to write down the notes, apart from the time, of a hymn or a tune
that they have known all their lives.'

The whole chapter in this memorandum is well worth reading.