Sometimes when I get new violin students I can't help wondering what previous teachers have been doing with them. I have a lovely new student with about seven years of experience playing the violin. Some of her music is heavily marked with "idiot marks," or pencil lines clearly marking where each beat falls within a measure. (Note: These marks are not really for idiots as the slang term implies; I use them rather frequently in orchestral settings.) They are, no doubt, a useful way to denote beats, particularly in measures with dotted rhythms or ties - rhythmic concepts that can be challenging for a student. However, when I asked this student if she understood the meaning of the marks, she replied, "I don't know, my old teacher used to sing the melody or something and make those marks everywhere; I never really knew what it was all about."
I hope I am able to equip all my students with solid understandings of rhythm, intonation, melody, harmony, tone, and violin technique so that their future teachers don't wonder, "What was that teacher thinking?!"