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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