A piece I am working on now (Tchaikovsky's German Song) has an interesting (for me at least) rhythm with a dotted eighth and then a sixteenth in several phrases.
There are many ways of counting this so I will suggest one and others will suggest other ways.
Bar 2 for example:
(G - Bb ) (G - dot - Bb ) (Bb - Bb )
(one - and) (twoooooooooooooand) (three - and)
This is the way that works better for me, I find all the others ways to count alphabet-notes distracting and confusing. It's easier with notes (Sol, Sib)
Your teacher method is a good one too, as long as you're consistent with the counting and applies the same method to all quarters not just the dotted ones:
(G - Bb ) (G - dot - Bb ) (Bb - Bb )
(one-two - three-four) (one-two - three - four) (one-two - three-four)
in this way of course you're counting sixteenth notes and you can be more accurate in determining when exactly you should count the 16th Bb after the dotted G
Fra