A facility with signed numbers forms the basis for effective problem solving throughout developmental mathematics. Most developmental mathematics textbooks explain signed number operations using absolute value, a method that involves considering the problem in several cases (same sign, opposite sign), and in the case of subtraction, rewriting the problem as an addition problem. This method works, of course, but involves quite a bit of chalk to explain. It is neither a mathematically elegant way of understanding signed numbers, nor is it the method that experienced mathematics educators use themselves. "Crossroads in Mathematics: Standards for Introductory College Mathematics before Calculus" (American Mathematical Association of Two-Year Colleges, 1995) recommends developing student knowledge of mathematics by emphasizing intuitive justifications for mathematical principles and procedures. The topic of signed numbers provides an excellent context in which to develop fundamental mathematical conceptual understanding, explore properties of mathematics, and motivate students to understand higher-level structure of mathematics. This can be achieved using ring theory, which imparts a more organic understanding of numbers and illustrates why number systems are forced to operate the way they do.