"Of" and "For" Before "-ing"

What are the rules for choosing whether to use "of" or "for" before a word ending in "-ing?"

Example:

We propose a method of simplifying algebraic expressions.
We propose a method for simplifying algebraic expressions.

I have seen it written both ways, and would like to know which way is proper. Or is this a case where "it depends?"

Solution 1:

The choice of preposition has less to do with the following gerund (-ing word; in your example, the word simplifying) than with the word method. It appears from the following NGram (corpus English, 1800 to 2008) that "method of" is much more commonly used than "method for." I think both are understandable, however, and both are used.

Solution 2:

It's not a simple matter of "always use 'of' before a word ending in -ing" or "always use 'for' ...". It depends on the context of the whole sentence. It would depend more on the word that precedes the "of" or "for" than on the word that follows. Like you would write, "What is your reason FOR doing that?" but "What is the result OF doing that?"

"Of" and "for" have fairly similar meanings. I'm trying to think of a general rule about when you use either. "Of" generally means "belonging to" while "for" means "related to the purpose of". For example, "book of mine" means the book I own. "Book for math class" means a book intended to be used in math class. But there are so many shades and ranges of meaning that this is really inadequate. I fear you have to take them case by case.

Solution 3:

Both of these statements are grammatical.

"For" would be more common. I think that "method of" is idiomatic, and in general wouldn't be correct. An example of the more general case where this won't work is "I'm collecting pictures for testing colour recognition by children" and "I'm collecting pictures of testing colour recognition by children", which have contradictory meanings. (The first means pictures to be used in the tests as opposed to pictures of the test taking place.)