id: 05711016
dt: j
an: 2010c.00322
au: Gratzer, William; Krishnan, Srilal
ti: From trapezoids to the fundamental theorem of calculus.
so: Mont. Math. Enthus. 6, No. 3, 459-476 (2009).
py: 2009
pu: Information Age Publishing (IAP), Charlotte, NC; Department of Mathematical
Sciences, The University of Montana, Missoula, MT
la: EN
cc: G34 R24 I54 I55
ut: calculus; collegiate mathematics; fundamental theorem of calculus; Riemann
sums; trapezoids; teaching with technology; area approximation
ci:
li:
ab: Summary: 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 studentâ€™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.
rv: