What does “in an effort” to mean?
I personally consider in an effort to a stock phrase1.
The meaning of the phrase should be clear even when we read it word by word:
In an effort to = "In an attempt to"
Traditionally, the phrase In an effort to create a culture within my classroom is an adverbial phrase. Here are some examples of adverbial phrases (from the Wikipedia page): in a short time, near the wall, in a civilized way, in an hour, when I've finished my book.
Seeing that you want to use it in your writing, I'd like to quote a couple of texts in The Redbook: A Manual on Legal Style by Bryan A. Garner (2nd ed.):
Language lovers often go through predictable phases of growth: first learning exotic new words and later avoiding them in favor of plain and clear terms. Using simple words and phrases instead of stuffy ones results in a more natural style. (p.183)2
In one section, the manual reads:
(c) Paring down phrases. By trimming your sentences you will make your prose tighter, more forceful, and more persuasive (see 13.3(e)). Wordy phrases are the biggest source of surplusage and can make your prose less clear, even confusing. For those reasons, these phrases are the first things to look for when you trim your drafts. Below are some common phrases used in legal writing and their simpler substitutions. (p.187)
And on page 188,
Instead of this: in an effort to
Try this: to
For example, you can replace in an effort to in your text with to without loss in meaning.
In an effortTo create a culture within my classroom where students feel safe sharing the intimacies of their own silences, I have four core principles ...
This is not to say that you cannot or should not use the phrase in your writing, but if your main goal is to write clearly, you may want to avoid using it, or use it only sparingly.