A play on the phrase sign on the dotted line, an instruction to place a signature in a specific spot on a document, which a person would do on an employement contract, in this case a teacher. Sine is a function in mathematics, that a math teacher would instruct in. A sine, which is a curve might also be represented on a graph that uses dotted lines for the x and y axes.
The first order of priority in hiring math majors is get them to sine on the dotted line