id: 06597599
dt: j
an: 2016d.00865
au: Murawska, Jaclyn M.; Nabb, Keith A.
ti: Corvettes, curve fitting, and calculus.
so: Math. Teach. (Reston) 109, No. 2, 128-135 (2015).
py: 2015
pu: National Council of Teachers of Mathematics (NCTM), Reston, VA
la: EN
cc: M50 I20 N50
ut: calculus; curve fitting; real-life problems; problem solving; modeling;
speed
ci:
li: http://www.nctm.org/Publications/Mathematics-Teacher/2015/Vol109/Issue2/Corvettes,-Curve-Fitting,-and-Calculus/
ab: Summary: Sometimes the best mathematics problems come from the most
unexpected situations. Last summer, a Corvette raced down a local
quarter-mile drag strip. The driver, a family member, provided the
spectators with time and distance-traveled data from his time slip and
asked “Can you calculate how many seconds it took me to go from 0 to
60 mph?” Although initially this question seemed like a
straightforward one, it was soon clear that depending on the solution
strategy and assumptions, different answers were possible. Thus began
the ongoing discussions with colleagues ‒ and with high school
mathematics teacher friends over pizza and with mechanical engineer
family members at holiday dinners ‒ to collectively decide on the
“best” method. The mathematical discussions that arose on how to
best solve the problem prompted two questions: (1) What makes this
problem so intriguing? and (2) What would students do? Any interesting
mathematical task will likely encourage teachers to wonder what aspects
of the task make it special. The authors of this article wanted to know
why this problem generated these mathematical conversations and how
they could incorporate it into a calculus class. Insights from
colleagues and students revealed several qualities of the problem that
they believe contribute to its intrigue and worth. What they found
illustrates what they consider to be three hallmarks of a good problem:
(1) The problem solver must decide what mathematics to introduce; (2)
The task users real-life data; and (3) The task requires mathematical
modeling. A nonroutine task with three hallmarks of a good problem
offers the flexibility to model real-life, messy data. (ERIC)
rv: