id: 06297578
dt: a
an: 2014c.00742
au: Ellis, Amy; Ozgur, Zekiye; Kulow, Torrey; Dogan, Muhammed F.; Williams,
Caroline; Amidon, Joel
ti: An exponential growth learning trajectory.
so: Lindmeier, Anke M. (ed.) et al., Proceedings of the 37th conference of the
International Group for the Psychology of Mathematics Education
“Mathematics learning across the life span", PME 37, Kiel, Germany,
July 28‒August 2, 2013. Vol. 2. Kiel: IPN‒Leibniz Institute for
Science and Mathematics Education at the University of Kiel (ISBN
978-3-89088-288-8). 273-280 (2013).
py: 2013
pu: Kiel: IPN‒Leibniz Institute for Science and Mathematics Education at the
University of Kiel
la: EN
cc: I20 C30 E50
ut: exponential functions; exponential growth; learning trajectory; reasoning;
instructional challenge
ci:
li:
ab: Summary: Exponential functions are an important topic in school algebra and
in higher mathematics, but research on students’ thinking suggests
that understanding exponential growth remains an instructional
challenge. This paper reports the results of a small-scale teaching
experiment with students who explored exponential functions in the
context of two continuously covarying quantities, height and time. We
present a learning trajectory identifying three major stages of
conceptions about exponential growth: pre-functional reasoning,
covariational reasoning, and correspondence reasoning. The learning
trajectory identifies relationships between these conceptions and the
nature of the tasks that supported their development.
rv: