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Topic: MathTeachers?
Replies: 31   Last Post: Apr 15, 2013 1:17 AM

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Clyde Greeno @ MALEI

Posts: 220
Registered: 9/13/10
Re: MathTeachers? >> sensibility of exponentials
Posted: Mar 25, 2013 4:00 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

To elaborate on Bishop's summarizing comment, & on GSC's generalities, the
original question may be addressed through the (MKT) perspective of
Mathematical Knowledge for Teaching mathematics as common sense.

How can the teacher overcome textbooks' & students' myopic focus on
manipulations of formulas, resulting in inadequate study of the nature of
the functions described by those formulas? [These are clinical findings.
More details available by request.]

Commonly lacking knowledge-points:
1) reasons for the graphic behavior of the 10-log-function [meaning
log-sub-10 = log-base-10]
2) all other pos-log functions are pos-multiples of the 10-log function ...
& conversely (graphically);
ln(x) is roughly 3-log(x)
3) The "a^x" formula is conceptually difficult to tie to the a-log(x)
formulas. As an intermediary, instructional alternative to "a^x", also use
a-exp(x) ["exponential, base-a" or {exp-sub-a}(x)]
4) all pos-base exponentials are horizontal distortions of 10-exp(x)
5) e^x is roughly 3-exp(x) [i.e. exp-base-3 (x)]
6) transformation effects of the parametric families entailed in
a[log-sub-b](x-h) +k and in a[exp-sub-b](x-h) +k
7) why not neg-base logs & exps? why not base-1? why not base-0?

- --------------------------------------------------
From: "Wayne Bishop" <wbishop@calstatela.edu>
Sent: Monday, March 25, 2013 11:40 AM
To: <math-teach@mathforum.org>
Cc: <math-teach@mathforum.org>
Subject: Re: MathTeachers?

> Failure to understand the exponential function primarily due to poor
> preparation prior to that.
>
> W Bishop
>
> At 09:13 AM 3/24/2013, 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?
>>
>>Thank you in advance!




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