2009©Montana Council of Teachers of Mathematics & Information Age Publishing From Trapezoids to the Fundamental Theorem of Calculus

Abstract: The philosophy of Mathematics Education undergoes changes from the school to college level and students generally have a tough time coping with the transition. It is our endeavor to impress the importance of introducing college level topics at an early stage, so that students are not lost in the transition. Keeping this in mind, we suggest an early exposure to an important topic from Calculus; approximating the area of a planar region. Traditionally this topic is introduced using Riemann Sums but in this paper we try to follow a student’s natural inclination in approximating areas and explain how this approach can be adopted at the middle school or high school level. It is our belief that using suitable technology like TI- 83/84 or Maple, this approach can be adapted to various other college level topics providing the student with a sound footing to cope with college level mathematics