Which is better, calling the tutor or texting during the holiday?

Call, of course. This shows your respect for him.

The first thing you should say is to introduce yourself. You may not know who you are when you call, and then you can say hello, such as how are you? You can ask a tutor about the textbook. Although it's not very important, at least lengthen your chat time, and then slowly move on to other household things ... remember to come out for dinner and tea when you have time. It's easy for me to say, but it depends on you. After all, he is a respected mentor, and he should be very happy that you have this heart. I hope I can help you.