id: 06191328
dt: j
an: 2013d.00597
au: Lo, Jane-Jane; Kratky, James L.
ti: Looking for connections between linear and exponential functions.
so: Math. Teach. (Reston) 106, No. 4, 295-301 (2012).
py: 2012
pu: National Council of Teachers of Mathematics (NCTM), Reston, VA
la: EN
cc: I20 D70 C30
ut: misconceptions; mathematical concepts; mathematical models; mathematical
applications; problem solving; mathematics activities; mathematics
skills; algebra; graphs; structural equation models; linear functions;
exponential functions; connections; graphical representations;
algebraic representations; rate of change
ci:
li: doi:10.5951/mathteacher.106.4.0295
http://www.nctm.org/publications/article.aspx?id=34687
ab: From the text: Students frequently have difficulty determining whether a
given real-life situation is best modeled as a linear relationship or
as an exponential relationship. One root of such difficulty is the lack
of deep understanding of the very concept of â€śrate of change". The
authors will provide a lesson that allows students to reveal their
misconceptions and improve their understanding of this significant
concept as they explore the structural connections between these two
mathematical relationships. Students will develop flexible thinking by
comparing the structure of linear and exponential relationships and
translating fluently between and within representations. The lesson
focuses on tabular, graphical, and algebraic representations in a way
that allows time for rich discussions and debate. The lesson is best
used after students have some experience working with linear and
exponential relationships separately, typically toward the end of a
first-year algebra class or an integrated mathematics class.
rv: