Hello to you in Ukraine! Thank you for your question. I'm not sure why your textbook would relate "the" to prepositions. "The" is a word that points out a noun, such as "the tree," "the reason," or "the house." It does not point out prepositions.
The phrases you mention are prepositional phrases. The words "on," "in," and "under" are common English prepositions that show the relationship between two objects. For instance, if you have a book and a box, the book could be on the box, in the box, or under the box.
Prepositional phrases are important because they add information to a sentence. They can describe nouns, such as in this sentence:
The house on the hill is yellow. The prepositional phrase "on the hill" tells us which house is yellow.
Prepositional phrases can also modify verbs, such as in this sentence:
The children ran over the hill. The prepositional phrase "over the hill" tells us where the children ran.
This is a really simple explanation of prepositional phrases, but it shows how useful they are in English. They should be a part of studying the English language. If you would like to have an online discussion about English grammar, go to this eNotes link:
Good luck to you and your students!
First of all for teaching children you don't have to explicitly teach the definite article "the". For teaching the preposition you can use two methods. first using task based approuch; you draw a box on the board and show a ball in, on and under the box, then you can ask them to draw funny things in these placas. You can also use TPR method and order children to Physically answer to your orders e.g. you can say "put your bags on the table" " put put your pen in the bag" ,etc.