I have an adult student working on 2-oct arpeggios. When she began piano lessons 3.5 years ago she had a very stiff arm/wrist, although it's been loosening up in the last 2 years. She has a very stubby thumb and struggles to turn her wrist so that her thumb can reach under to play.
For example, she was working on the D Maj arpeggio using fingers 1-2-3-1(thumb under)-2-3-5. Because of the stiffness in her wrist, it seems nearly impossible for the thumb to reach the D unless she lets her elbow and upper arm jut out in an awkward way. I'm not sure what advice to give her, as my thumbs seem to be a good inch longer than hers. I wouldn't normally consider it a huge problem, but she's participating in the exams and will be graded in a couple months. I'd love to hear some ideas of ways to help her. Thanks!

When up to speed, the thumb will probably not go under the hand at all, only beside it. This leaves a gap in the sound, but at high speed you don't really hear the gap.

Smooth horizontal arm motion takes precedence in most cases I think.

+1

So have her practice moving her hand horizontally across the keyboard along with preparing the thumb to strike the first key of the next octave of the arpeggio (in your example the second D).

Thanks for the explanations. Do you mean that the wrist will not turn at all? We are not working at a high speed - in fact she will only be graded on playing it in quarter notes, as she's only level 4. I feel like the gap in sound would be rather awkward.

At high speed, the wrist does not turn at all. At lower speed, it has to, exactly because of that awkward gap in the sound.

I would recommend instructing the student to try not to push the elbow out to the right when going for the thumb cross over. Instead try to keep the arm perpendicular to the piano as much as possible and focus on moving smoothly with your whole arm from left to right. Once you get the arm movement timing down, your thumb is really hitting the 2nd D without much crossover or tension needed. This is because your arm is actually leading your thumb to the note rather than your thumb leading your arm.

Hope that makes sense:)

JPE

It makes perfect sense to me, but in very slow tempos it probably doesn't work.

I found that doing it at slow tempos is what helps you to get the hang of this technique. You just have to move your arm slower and more evenly in time towards the right as you go. Once you start to feel the timing of the rightward arm movement you then can speed it up and it will become more natural