Dont mix up two things here !
one: training your children to appreciate people they love, adn to say thank you for wowrk done well, and to grow a friendship with someone who has helped them- even, and including, their teacher!
two: the gift does NOT have to be expensive can be a home made card can be a cheap bottle of wine or an "accessory"- eg a cheap bracelet- a silly coffee mug--the idea of the child CHOOSING the gift.
I have been a teacher who very seldom got a gift- they were banned in my (second-level) school. But there is a feeling that you are taken completely for granted by parents, I must say,- especially as not a school in the country could be run well without the VOLUNTARY extras that teachers do. In my time I have gone to all sorts of meetings at night for all sorts of classses and events, Masses, shows. I have gone away on trips and weekends and brought them to outings, theatres etc etc etc-- and a thank you IS very acceptable, and always given by the kids.
My daughter is a primary teacher who gets lots of little gifts from the kids in her class at Christmas- never anything expensive, and she gets a real kick out of the home made ones, however amateurish--and of course - the wine...!!!!