In this study, the author discusses the concept of function from a historical and pedagogical perspective. The historical roots, ranging from ancient civilizations all the way to the twentieth century, are summarized. The author then details several different function representations that have emerged over the course of the concept's history. Special attention is paid to the idea of abstraction and how students understand functions at different levels of abstraction. Several middle school, high school, and college textbooks are then analyzed and evaluated based on their portrayal of the function concept. The author describes several common misconceptions that students have about functions and finally proposes a short educational module designed to help older high school students grow to a deeper level of understanding of this complex and often misunderstood concept.

Author Bio

Melanie Jones is currently enrolled in Trinity University㤼㸲s Masters of Arts in Teaching program. She graduated with a B.A. in mathematics in May 2006 and wrote this paper as senior research project under the supervision of Dr. Allen Holder. She hopes to teach mathematics to high school students in the future and enjoyed having the opportunity to research a topic with such a rich historical and pedagogical basis.