The textbook’s section on ‘future forms’ introduced [be] Ving, [be] going to V, will V and shall I/we V? Shall used to be used in statements, the traditional explanation being that I/we shall and you/she/he/it/they will showed a simple intention for the future, while the reverse – I/we will and you/she/it/they shall showed a strong intention. This distinction was probably not ever strictly observed, but throughout the 20th century the use of shall in statements declined. The last remaining holdout is the use of shall in questions of offer or suggestion. Even then, there are many contexts in which I would never use it. One example was (something like) ‘A: Let’s go to the cinema tonight. B: Sure. What shall we see?’. I said to the students that I would never say that, and I can’t imagine that anyone I know would. I would probably say ‘What do you want to see?’, even though that’s much longer and goes against my general principle of ‘keep it short and simple’.
I searched my diary for the two and half years of my first stay in Korea. I used shall twice, both in formulaic expressions. The first was about a night out with colleagues. I left early-ish because I had an early class the next morning, but ‘Most of my colleagues stayed and two (who shall remain nameless) and got falling-down drunk (literally).’ (Google Ngrams shows that shall remain nameless has always been more common than will remain nameless, and grew rapidly in the second half of the 20th century, against the general decline in shall.) The second was ‘One of the level 4 students said that his dream vacation would be to Andromeda […] He said that a fortune teller had told him that he had previously lived there. i asked how he got to earth, and he said that he had “borrowed” a human body. All .. right … err, let’s stick to the planet earth, shall we?’. He then nominated Peru, which kind of makes sense; maybe the Nazca Lines were made by Andromedans.