Date: Mar 25, 2013 4:10 PM
Author: Dave L. Renfro
Subject: Re: MathTeachers?

Danielle T wrote:

> Hello....I am currently a pre service math teacher working on
> my masters...I'm working on some lesson plans about exponential
> growth... I was curious from your experience... What are some
> of the common misunderstandings and errors you find your students
> have with learning exponential growth?

Did you grade papers for the math department when you were an
undergraduate or tutor other students for extra money? If so,
think about the kinds of mistakes you saw most often and how
you might go about preventing them. What about the errors
you saw your classmates make when you took high school
algebra 2 and precalculus?

Off-hand, the most common conceptual errors I can think of
(algebraic procedural errors, of course, are obvious -- x^2
times x^3 is not x^6, etc.) is not fully realizing the rapidity
of growth of exponential functions and incorrectly interpolating
exponential behavior (e.g. the midpoint of 2^4 and 2^8
is not 2^6). For the rapidity of exponential growth, an
example I often used was that about 42 foldings of a sheet
of paper results in a (theoretical) folded thickness equal
to roughly the distance from the Earth to the Moon. [Every
10 foldings results in very nearly a 1000 factor increase,
due to the fact that 2^10 = 1024 is almost 1000. Hence,
40 foldings results in a 1000*1000*1000*1000 = 10^12 factor
increase, so 42 foldings results in a thickness of about
2*2*10^12 = 4 trillion times the thickness of a sheet of paper,
and it's not hard to show that this is roughly the Earth-Moon

See the attached .pdf file handout for more ideas.

Dave L. Renfro