https://www.coursera.org/course/maththink
Introduction to Mathematical Thinking
Dr. Keith Devlin
Stanford University

This course (and the textbook with the same name) looks interesting and does not overlap heavily with the usual algebra-through-calculus sequence. Course reviews (generally favorable) are at http://coursetalk.org/coursera/introduction-to-mathematical-thinking?sort=newest . The prerequisites are moderate:

"High school mathematics. Specific requirements are familiarity with elementary symbolic algebra, the concept of a number system (in particular, the characteristics of, and distinctions between, the natural numbers, the integers, the rational numbers, and the real numbers), and some elementary set theory (including inequalities and intervals of the real line)."

Devlin has written several books on math for popular audiences. I'll buy a few for my eldest son, such as "The Language of Mathematics: Making the Invisible Visible", and if he likes them, I will mention the course to him.