
06191328
j
2013d.00597
Lo, JaneJane
Kratky, James L.
Looking for connections between linear and exponential functions.
Math. Teach. (Reston) 106, No. 4, 295301 (2012).
2012
National Council of Teachers of Mathematics (NCTM), Reston, VA
EN
I20
D70
C30
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
doi:10.5951/mathteacher.106.4.0295
http://www.nctm.org/publications/article.aspx?id=34687
From the text: Students frequently have difficulty determining whether a given reallife 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 ``rate 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 firstyear algebra class or an integrated mathematics class.