> ----------
> From: Edward Laughbaum[SMTP:elaughba@MATH.OHIO-STATE.EDU]
> Reply To: Edward Laughbaum
> Sent: Saturday, November 20, 1999 5:15 PM
> To: mathedcc@archives.math.utk.edu
> Subject: [MATHEDCC] Teaching in Context
>
> Hello All,
>
> Recently there has been considerable activity on the issue of contextual
> problems and "teaching in context." I have one more thought I wanted to
> add
> before the discussion dies off completely (course, maybe it already has).
> My thoughts may be out in left field and on the lunatic fringe, but I will
> post them anyway.
>
> I don't know what the reason, perhaps TV, movies, parenting (or lack
> thereof), schooling, etc., but our students don't seem to have common
> sense
> about how things happening in the world. Nor are they aware of serious
> problems outside of their own world. What an opportunity this is for
> teaching in context or teaching applications! Let me give just one
> example.
>
> Suppose that your objective is to teach the concept of "increasing" to
> beginning algebra students. Or maybe your intent is to teach your
> intermediate algebra students about why we sometimes need to restrict the
> domain of a function as we apply it to a situation. Maybe your goal is to
> just have your beginning algebra students calculate (for practice) some
> rates of change, but you want them to understand that it is a more
> important process than "difference of the y's divided by the difference of
> the x's". That it has a meaning in the world outside the math classroom.
> Maybe your goal is to have your beginning/intermediate algebra students
> decide if a linear function might make a good model of some given data.
> And
> if so, what would the model be? Maybe you want them to answer a series of
> questions about the model and the data situation. We could go on with
> other
> objectives, but let's stop here. So, what do you do? You use the following
> data:
> Year (t) 1960 1970 1980 1988
> 1993
> Garbage (g) in pounds per person per day 2.7 3.2 3.6 4.0
> 4.1
>
> While we have a wide variety of teaching objectives that can all be used,
> the objective I want to address here is the communication of the
> significance of the information in the contextual data. Do your students
> know we (US citizens) have a real problem with garbage? Do they know we
> are
> of the mentality that all we need do is take the garbage to the street and
> the garbage problem magically disappears? Do they know dumps are rapidly
> filling and new space is limited? Do they know the Japanese create garbage
> at a rate of less than half of what we do? Are your students aware of
> leaching problems with garbage dumps (military, industrial, or otherwise)?
> Are poisons from old garbage dumps leaching into their water supply? Is
> military garbage from WW II buried beneath their home site and leaching
> radioactive elements into their homes? Is the fact that the rate is
> increasing pose a problem? How big is a pile of garbage created by the
> people in the US in a year? Will it fill the Super Dome? Would it fill
> Lake
> Erie? Is this a problem? Who is responsible for solutions to problems like
> this? Can they describe two ways that the total amount of garbage created
> per year in the US could be lowered?
>
> So while I have belabored the point, please keep in mind this teaching
> opportunity happens daily when you teach in the context of a problem,
> situation, or data. Seize the opportunity. Is the opportunity worth the
> effort?
>
> Ed
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