There are two kinds of logical reasoning: "inductive" and "deductive". Inductive reasoning proceeds from effect back to cause, from special case to general principle. Detectives use it, examining the clues and conjecturing the actions that caused them. On the other hand, deductive reasoning proceeds from cause to effect, from principle to instance. Pondering his own math education, the author recalls many uses of deductive reasoning. It is the cornerstone of school mathematics. This time the author makes a concerted effort to include inductive reasoning in the school mathematics curriculum. The activities he developed for gifted students provide them the opportunity to discover mathematical principles. The inductive method is to examine many special cases, formulate a conjecture about a general mathematical principle, and then test the principle to ensure its accuracy. These activities have been successfully used with gifted students, grades 1-10.