When it comes to writing, the most advanced secondary textbooks for English and most state rubrics for judging writing do not deal with what is involved in critical thinking in writing. Rather, they opt for vague discussions of "persuasive writing." Those who know the needs of college writers and who are familiar with the new ACT and SAT writing samples know that persuasive writing will not suffice. For college and career one needs to know how to make an effective case, to make a good argument. This article presents a brief introduction to the teaching of argument using a system of logic that is widely accepted in colleges and universities. The author provides information and an example from a real classroom for teaching logical argument in a complex and effective manner. (Contains 1 figure.)