I hope you all don't think I am being too picky. I think this concept of
"in context" is one of the more useful ideas in the current reform efforts;
at the same time, I have seen too many "in contexts" being expressed as
modelling the probability that the yellow side of a pill will be facing up
in the package. Sometimes we get "concrete" and "context" confused, where
there really is a huge difference; "concrete" refers to a particular
learning style while "context" refers to a whole theory of learning. If
our reforms are going to last longer than prior attempts, we need to keep
challenging ourselves about what we mean.
To me, "in context" means that a learning situation has been structured so
that the student can at least see the connected-ness of the learning
outcomes; if they appreciate this connection, so much the better. I must
add, however (even though some of you will not agree), that "in context"
can include how the new learning relates to pre-existing learning -- it
does not have to always be an "application". (Please keep in mind that I
say this even though I am close to fanatical about "applications" in our
curriculum.) From the reading I have done in learning theory (not enough
recently), this is close to what the theory based on research is trying to
communicate to us.
So ... I would state the "context" does not equal "application", nor the
reverse. We can achieve "context" in a variety of ways, including
applications. If our students are to be life-long learners, we can not
restrict their current learning to applications that may have no bearing on
their known future. Learning needs a broader "context".
(Unless we support the notion of a "throw-away employee", where a person
needs to be laid-off and then re-trained before moving on to a new job.
Personally, I want to minimize long term pain as well as educate for
employment now.)
Anyway, thanks for reading!
Jack Rotman
Lansing Community College
rlkimbal@WTCC-GW.WAKE.TEC.NC.US on 11/24/97 12:03:36
Please respond to rlkimbal@WTCC-GW.WAKE.TEC.NC.US
To: RWTNTS@RITVAX.ISC.RIT.EDU
cc: mathedcc@archives.math.utk.edu (bcc: Jack Rotman/Math-Science/Student
Academic Support/LCC)
Subject: Re: [MATHEDCC] RE: Developmental Math Labs
Here is a real story to go along with Taylor's "piano analogy" (see
below).
A friend of mine has a beautiful daughter who has entered several
"beauty contests" over the last few years. She always does very
well, except in talent. This year, she decided to learn to play
one piece on the piano (a classical work that was somewhat demanding).
She had never taken piano. Six months ago she began practicing
under the tutorlidge of a piano instructor. One week before the
contest (which was last week) she decided to change her talent to
a poetry reading. It seemed that even with all the practice, the
attempt to learn piano "out of context" was not possible.
PS: She didn't win this year either.
Rob Kimball
On Thu, 20 Nov 1997, RWW Taylor wrote:
> Perhaps I can contribute some historical perspective on the issue of
> learning math by independent study. During the 70's and 80's we
> ran a large "Math Learning Center" through which we delivered all of
> our mathematics instruction at NTID (NTID is roughly the equivalent
> of a small community college in many respects). At times we had
> enrollments of over 500 students in our learning center, all being
> taught out of a single large room with instruction being provided on
> a shared basis by a cadre of trained faculty, augmented by student
> assistants. The basic arrangement was for students to study provided
> materials on their own until they could pass a test, then move on.
>
> Ten years ago we dropped this idea entirely in favor of classroom
> instruction. In retrospect I would have to call our efforts during the
> learning-center years, however earnest and well-intentioned, essentially
> a disservice to the students that we worked with. Our whole faculty is
> much happier with the relationships that can be developed in the
small-class
> model we follow now. Whether we would be sufficiently happy with a
> large-class model I don't know.
>
> The basic point at stake is the view of what needs to be learned.
> If one views mathematics as just a collection of techniques to be
> mastered (as many of our colleagues in the technical departments
> our courses serve did) then there might be some argument for
> simply providing access to methods for learning to apply these
> techniques to standard problems, and call that mathematics
> education. If, on the other hand, one wants to view mathematics
> as a _process_, as a way of looking at and understanding the world,
> as a way of coping with the non-standard problems that really
> make up life, then mastering a collection of canned techniques
> is a sterile exercise and of little use to students in the long run
> (especially as it is clear that the standard techniques can better
> be applied by using technology).
>
> The actual thinking and recognition of pattern that make up what we call
> "mathematical modelling", as well as appreciation of the subtle points
> that lead one to deeper levels of understanding and provide the real
basis
> for further learning, cannot be addressed in a situation where the
> responsibility posed to the student is simply to learn how to solve a
given
> set of problems of a particular type. I would pose an analogy to piano
> playing here. You have to learn how to position your hands at
> the keyboard, and to build up strength and dexterity by pursuing
> finger exercises. But all of this will buy you nothing if you are
> not paying attention to the _music_.
>
> RWW Taylor
> National Technical Institute for the Deaf
> Rochester Institute of Technology
> Rochester NY 14623
>
> >>>> The plural of mongoose begins with p. <<<<
>
>
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