Should I say "I make a living by teaching" or "I make a living teaching"? Which one is correct? Is the preposition 'by' necessary?

I am confused about the correct usage of the phrasal verb, 'make a living'. I don't know whether I should add the preposition 'by' at the end of it.
I looked up several dictionaries, most of which suggest to add a preposition to the phrase. But an English teacher told me that I should not add a 'by', because the meaning will change.

Both are correct, there is not a need to insert a prepositional specifically because the word that the preposition would be associated with is a verb, if it were a noun or an adjective then it there be more president for a prepositional phrase.

To clarify, a Preposition does just what it sounds like, it pre-positions; quit especially in adjectives - in adjectives it is giving more of a spatial orientation, helping bring out the dimension in the adjective; simply put it makes it more 3D than 2D, so-to-speak.

Using a preposition in front of a noun, or pronoun is generally meant to specify or modify that noun.

You can see this in Shrunk & Whites book, you can also learn a great deal about it by looking at the etymology.

Personally, I find prepositional phrases useful in conversation - just as I would start a sentence with the word "And" if I were speaking but not if I were writing. Similarly, in writing I find they are often overused as are adverbs. When you get right down to it I believe it to be a matter of style, whichever you prefer is optimal. Hope that helps