I hated math in high school. I stopped taking it after the tenth grade, and continued to avoid it during my undergraduate years. In retrospect, I can see that I never actually knew what mathematics is. Had I known, I'm sure I would not have been so alienated from the subject. I worry that many of our students feel the same way that I did in high school. To them, math seems tedious and pointless. There has to be a better way. I created the Quantitative Reasoning course so that I could give my students the math course that I wish I had had in high school. Briefly stated, this is the mission of QR:
The name "Quantitative Reasoning" is purposely vague. Basically, it means I get to teach whatever I want to! The goal of the course is to offer students a chance to be mathematicians, and that can be achieved within any content area. The course begins with a unit on number theory, including unique sums, modular arithmetic, rational numbers, number bases, and infinite series. This subject works especially well, because there are no prerequisite skills beyond elementary arithmetic. This allows me to accomodate a diverse group of students. Some of them have just finished Algebra II, either at the Honors level or at the standard level. Some of them have completed Pre-Calculus, and a few already know Calculus. That's fine. Any of those students is equally prepared to discuss why the long division algorithm works or why certain fractions have repeating decimals while others terminate.
Most of the content in QR comes from recent developments in mathematics. ("Recent" means from the 19th and 20th centuries. Typical high school math comes from the 17th century and earlier.) The field of dynamical systems,our second major unit, has emerged only recently with the invention of high speed computers. As with number theory, the arithmetic involved is very simple, but one must execute tedious computations repeatedly in order to be able to draw conclusions. Study of dynamical systems enables students to understand chaos theory and fractals.It's very exciting for students to be involved in an area of mathematics that is still in its infancy; discoveries are occurring in their lifetime.
While much of the content we study in QR is "delightfully useless," our third major unit on chance includes material that is more relevant to everyday life than anything else taught in high school. Teaching concepts of probability and statistics creates intelligent consumers of information. Are you going to need the quadratic formula in your future? Probably not. Will you watch TV news, use birth control, buy car insurance, serve on a jury, or make major health care decisions at some point? Virtually certain. The element of chance confronts you constantly in your everyday life, whether you're aware of it or not.
The final stretch of the course examines the mystifying field of cardinality. The students have been thinking about infinity all year long; at last they get their official definition. We then go on to figure out how some infinities can be greater than others. In the throes of such an abstraction, students find themselves both bewildered and amazed. It's marvelous to watch and that's why I love to teach it.