Vocabulary is the number of words you know. Learners have an Active Vocabulary which are the words they use when they speak or write; they also have a Passive Vocabulary which are the words they may well understand but do not actively use.
For more, see Vocabulary and TEFL.
Verbs tell us about an action; they are sometimes called doing words or action words. Verbs describe what is happening:
run, walk, read, talk
For more, see Verbs in English Grammar,
An Idiom is a phrase which has a figurative meaning which is very different from the literal meaning. For example, in The Godfather famously Luca Brassi sleeps with the fishes which does not literally mean that he sleeps with undersea creatures but that he is dead.
For more, see Teaching Idioms in TEFL.
Rote Learning is an old-fashioned method of learning by continuous repetition. It is derived from the idea that if a student says something enough times they will learn it and be able to produce it when the time comes.
In English it is also called learning by heart however there are more derogatory terms for it such as learning “parrot fashion” (in English and Greek) and “stuffing the duck” (in Chinese). Many of these imply force feeding of information.
A typical rote learning scenario might occur in learning the conjugation of irregular verbs.
The class might sit and chant the conjugation a dozen times. Likewise with vocabulary, a teacher may give the class a list of 20 or so words to learn by the next lesson and the students go home and learn them by repetition.
Whilst rote learning does have a place in learning (for example, it can be useful to learn the lines of a script or a times-table in maths) the main problem is that it lacks any kind of contextual learning and it can, in a worst case scenario, provide learning without understanding. A student may well be able to learn a list of 30 English idioms and be able to repeat them flawlessly without having any idea of their meaning or when they can be used.
Whilst rote learning can offer quick results (a student might be able to learn vocabulary very quickly) it lacks depth and understanding that only learning in context can offer.
Many school systems around the world use rote learning as a matter of course and your students may well expect to learn English in a similar way. In China, for example, students will expect tables and lists as part of their classes. In countries like