As a former librarian fairly well versed in copyright issues, I advise you to be careful. The fair use doctrine is not entirely a black or white legal protection, even for educational purposes. And if you do use cartoons while claiming fair use, be sure to credit the cartoonist and show any copyright notice that accompanies the cartoon you use. In fact, give credit and show any copyright claims on any piece you copy for the classroom.
Fair use applies to an insubstantial portion of the work being copied and used. For example, you could copy an article from a book, periodical or compilation under fair use, but you could not copy the entire book or publication to give to your students to use. The education school I recently graduated from (career change) made copies of articles for students, but required the articles to be returned to the teacher after use. According to that school's lawyer, such action would help substantiate fair use because there was no free distribution of an author's work that would diminish the author's market to sell the piece. Of course, you'll get as many opinions as lawyers if you ask for an interpretation of fair use.
There are a couple of opinions on cartoon copying. One view holds that the cartoon is an entire, individual work in and of itself and can't be copied without permission, even under fair use, because the whole cartoon is copyrighted as the work. This is usually the case of cartoons published in papers and magazines. The other view holds that a single cartoon is an insubstantial part of a cartoonist's body of work, and could be used under fair use. Which one is correct? It's ultimately an issue to be decided in court, and likely to be subject to a number of circumstances. An individual cartoon copied from a magazine or newspaper might be harder to defend under fair use because the individual cartoon is copyrighted as a complete work on the spot. A compilation of cartoons published as an entire book or collection, and copyrighted as such, might be considered a completed different circumstance. A single cartoon from the compilation might be argued successfully as a small portion of a larger work and used legally under fair use.
So the real question is whether or not you wish to risk being a test case in a potential copyright violation lawsuit if you don't have the cartoonist's permission. For me, I feel safer using cartoons from a variety of sources and cartoonists rather than focus on one author's work. I would avoid using Herman, Shoe, Doonesbury or Dilbert exclusively or consistently, as tempting as it is at times.