I have to wonder if you didn't miss my point. I may not have been clear.
You reference the modeling objectives only, but what I was doing was
listing some of the objectives I have used in the past for the data listed.
The point being that when you use contextual situations, problems, or data
there are many levels for the use of the same data. You will also note that
the audience was beginning and intermediate levels, so we need simplified
situations. Some of the questions asked of students were to make
conjectures. This is to say that we need to start letting students think of
all the complexities of the situation - even though they are not in a
position to mathematically handle the complexities. Save this for later
courses. You never know when you have a student who is curious enough to
follow through and actually take more mathematics so they can bring closure
on their conjectures of real-world situations we take to the classroom when
we teach in context. Even if you don't have any students like this, we have
provided worthwhile and useful information to the class that they are not
getting elsewhere.
The bigger picture of my posting had nothing to do with modeling, but with
teaching our students about the world they live in, how we view it, and how
mathematics can help them understand the world "real" people live in as
opposed to what is promoted/caused by MTV, E-TV, and lack of good adult
parenting.
I most certainly agree with your comments; it's just that they seemed
unrelated.
Ed
==============================================
At 08:30 AM 11/22/99 -0600, David Beach wrote:
>The problem that you can run into is one of interpretation of the model you
>are using. One problem with "contextual" and "relevant" problems is that
>with the math skills you are trying to teach, the models we can present in
>the classroom are almost hopelessly simplified ones in many cases. The
>study of models and their intepretation, use and modification should
>constitute its own course. Frankly, in some ways it might be closer to what
>we would truly desire a good, general ed, college level math course to be.
>
> > ----------
> > 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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