A mnemonic like CRAAP is not protected by copyright. The Copyright office says "Copyright does not protect names, titles, slogans, or short phrases", so you do not run afoul of copyright law using that or any other abbreviation. There is a registry of copyright-registered works, maintained by the copyright office, where authors may register their works, but legal protection exists regardless of registering.
Some abbreviations are protected under trademark law, which you can search here. There are 50 registrations that include "AAA" and three that are just "AAA", also you'll find WTF and LOL. Trademark protection doesn't forbid all uses of an registered abbreviation. It turns out that "CRAAP" is not a registered trademark, but it could be the registered trademark of a manufacturer of crab traps, so you would not likewise call your crab trap company CRAAP, but it would be okay for plumbing supplies (trademark is relative to business uses, which are described in the registration).
The only other imaginable scenario that would impede your plan is a non-disclosure agreement. For that to be relevant, there would have to be a valid contract between you and the teacher which specifically prohibits disclosure of the acronyms. The chances that there is a contract between you and the teacher is so low that it is hardly worth considering, but let's explore that for a moment. A contract is an agreement between parties where each party promises to do something that they are not already obligated to do, in exchange for getting something that they do not already have a right to. You had a contract with the college, not with the teacher. The college clearly would not prohibit "using any information gained in the course of study here", and the courts would not enforce any such "don't use" wording in a contract as unconscionable (why else do you go to college?). Your contract with the college allows you to take classes and use the knowledge that you gain. The teacher's contract with the college requires her to teach some content, and probably allows her to set certain rules of class conduct. She might have been able to toss you out of class for disseminating her methods, but at this point she has no legal recourse. NDA enforcement is generally limited to protecting "trade secrets", which are defined in terms of information with independent economic value deriving from the fact that the information is non-obvious". Also, an NDA will have a time limit associated with it except in the case of highly-sensitive personal information (social security numbers), so the courts will not enforce language saying "you can never make use of this information, or these names".