When educating... when to go beyond denotation of a word?

the denotation of a word is the actual meaning of it. As an example, take the word tree and define it:

"a tree is a perennial plant with an elongated stem,

 or trunk, supporting branches and leaves in most species."

Taken from: http://en.wikipedia.org/wiki/Tree

This does not end here. The word "tree" can be used in many ways. Just be aware of what we call a "family tree".  It is not a tree that belongs to a family, and I am not talking about a family whose last name is Tree; instead of this I am approaching to a "genealogical tree"; a chart showing the descent and relationship o all members of a family or genealogical group. 

In those two cases, the word "tree" changed. It was not a plant anymore. It was something different. 

Should english language learners be familiar with the variety of changes that a word may take?

The answer, walking around my mind, is: YES!

Of course everystudent should know all this kind of varieties of the words; if not, how could they tell the difference between have as a verb, and have as the auxiliary verb used for present perfect sentences? 

what to expect when they find that the verb "like", serving as a preposition? 

what is the mankind going to do when our students find out that the word "figure" can become a phrasal verb by adding "out"? Oh, the humanity...!

Nevermind, these are hipothetical cases. They won't get that far. 

I mean, what we do with our beginners is to teach them the denotations of a word. We are using lexical sets to teach them all the things they can find in a zoo. 

Oh! look, a monkey. Haven't you heard the expression "to monkey around", "monkey business", "make a monkey of someone" "monkeyshines"? 

No? 

OK... I won't have to explain anything. 

Maybe for beginners it won't matter; but, who knows, denotations won't help them for ever. Someday they will find some idiom, collocation, phrasal verb, suffix, prefix, synonim, antonym, verb pattern, etc..

Until that day, we are safe.