id: 05760271
dt: j
an: 2010e.00563
au: Johnson, Heather L.
ti: Investigating the fundamental theorem of calculus.
so: Math. Teach. (Reston) 103, No. 6, 430-435 (2010).
py: 2010
pu: National Council of Teachers of Mathematics (NCTM), Reston, VA
la: EN
cc: I54 I55
ut: calculus; upper secondary; graphing calculators; integrals; integral
calculus; concept formation
ci:
li: http://www.nctm.org/eresources/article_summary.asp?URI=MT2010-02-430a&from=B
ab: Summary: The fundamental theorem of calculus, in its simplified complexity,
connects differential and integral calculus. The power of the theorem
comes not merely from recognizing it as a mathematical fact but from
using it as a systematic tool. As a high school calculus teacher, the
author developed and taught lessons on this fundamental theorem that
were reasonably successful with students. However, she was dissatisfied
with the level of her students’ understanding of the theorem and
reflected that they would need to understand that an integral with a
variable upper limit is a function. In this article, the author shares
how she was inspired to create a lesson on the fundamental theorem of
calculus that drew on students’ current understanding of definite
integrals and allowed them to develop the understanding that an
integral with a variable upper limit is a function. A student’s
response to the lesson on the fundamental theorem of calculus expands
the lesson to include representing accumulated area as a function.
(Contains 3 tables and 5 figures.) (ERIC)
rv: