In the 'Same Note Game' you repeat a note relying only on your ear, that is, you cannot also see what note is played.
Trust your ear and go immediately to the note. Make it more difficult by specifying the string or the finger on which the note needs to be played. You can sing the note before playing.
It is interesting how often students with intonation issues can find the note accurately. We often assume that students with intonation problems have poor aural skills. (This of course may be true and if so is best addressed by aural training programs such as the Kodaly method.)
Commonly, however the problem is elsewhere caused by tightness in the hand or jerky and unreliable shifting. Another possibilty is that the student has a good ear, relatively fluid actions on the instrument, yet still plays out of tune. This can be caused by the student simply not using their inner hearing and not directing the finger strongly enough.
Intonation - Introduction
- for Practise the Violin, Mentally and Physically by Kievman