
Re: MathTeachers? >> sensibility of exponentials
Posted:
Mar 25, 2013 4:00 PM


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 knowledgepoints: 1) reasons for the graphic behavior of the 10logfunction [meaning logsub10 = logbase10] 2) all other poslog functions are posmultiples of the 10log function ... & conversely (graphically); ln(x) is roughly 3log(x) 3) The "a^x" formula is conceptually difficult to tie to the alog(x) formulas. As an intermediary, instructional alternative to "a^x", also use aexp(x) ["exponential, basea" or {expsuba}(x)] 4) all posbase exponentials are horizontal distortions of 10exp(x) 5) e^x is roughly 3exp(x) [i.e. expbase3 (x)] 6) transformation effects of the parametric families entailed in a[logsubb](xh) +k and in a[expsubb](xh) +k 7) why not negbase logs & exps? why not base1? why not base0?
  From: "Wayne Bishop" <wbishop@calstatela.edu> Sent: Monday, March 25, 2013 11:40 AM To: <mathteach@mathforum.org> Cc: <mathteach@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!

