How are the scales marked in the exam? Is it essential to have the "correct" fingering?
Another thought, - how about teaching her some of the 'black note' scales - this may help her to get used to using differnent fingers simultaneously
Get her to think about patterns of fingering related to the black notes - 234 for groups of 3, 23 for groups of 2.
E F GRH: 3 1 2LH: 3 2 1
This student MUST use the traditional fingering as it is a basis for fingering of many scales.
There is no rule of fingering that is violated by playing C major 1234123. It is absolutely just as good.
If she is going wrong only in the second octave, get her to play up the scale and land on the second F and stop there, concentrating on landing on the right fingering on that note.
I always show the clusters (as mentioned earlier) in this AND arpeggios; if you show how the hand should look based on where the thumb is, you should have two 123 clusters, and two 1234 clusters. -----Also, make sure that the student isn't just saying "ya ok, that makes sense" then goes home for a week practicing with the wrong fingering, forgetting everything you said during the lesson/wrote in the notebook. I've had a girl do that so many weeks in a row, that I actually wrote in her notebook "check off here if you read the note book this week", and sure enough no check mark. She's the kind of student who will totally forget any method you bring to the lesson, stumble through scales/pieces/whatever ONCE a day and consider that ample practicing.
using 1234123 makes the end of scales played with the 4th which seems strange. Also never using the 5th can't be good.
But no. You do 12312341, or 12341231, it makes no difference.
If you are determined to teach the standard fingering, and also determined to teach HT scales, here is an approach that will work.The more I think about this one the more I think the difficulty is in hand coordination, not fingering order. I like HS scales, I think there are more things to be learned that way by far than HT. But, try this. Do this scale HT in two note fragments, all the way up, many many repetitions. E.g., CDCDCDCDCD etc. with both hands together. Then DEDEDEDEDE etc. You can do them very very fast and crank out a hundred in a few seconds. All the way up. Then start over in three note fragments. CDECDECDECDECDE. DEFDEF etc. When they come easily quit early, the hard ones need a little extra work. Four note fragments. Five. etc. This will take a long time the first day. Probably a whole lesson period, if you decided to spend the lesson time. But once would be enough to thoroughly learn this scale. And because the hands have been forced into coordination, the right hand will never again diverge on the second octave.