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Topic: integration
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Marty Gartzman

Posts: 6
Registered: 12/6/04
Posted: May 23, 1996 6:19 PM
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>I wonder if some of the problems associated with this idea (math being
>short-changed, for example) is partially due to the way we conceptualize
>"integration of subject matters."
>So, I would like to hear from the people who tried or heard about an
>"integrated" approach a little more details of how a lesson/unit was
>organized and what made it an "integrated" lesson/unit.
>Tad Watanabe

The various posts on integration of mathematics with other subject areas
have a familiar ring. I thought I would share the perspective of a group
that has been working on this issue for some time. While our perspective
about subject matter integration probably differs from the ideas of many
others, there might be some benefit derived from our experience.

Here might be a summary of our experience: Integration of math with other
subject areas creates contexts that bring life to the mathematics and adds
meaning to the other subjects as well. But if the integrated activities
are going to supplant other math instruction (rather than supplement it),
the program has to be developed carefully - with mathematics at the core
of the program structure instead of just an incidental part. Our view has
evolved over time, in particular through our experience during the past
six years in developing a math curriculum with strong connections to
science and language arts.

Howard Goldberg, Phil Wagreich, and others at the TIMS (Teaching Integrated
Mathematics and Science) Project at the University of Illinois at Chicago
have been working for many years on the development of integrated
math/science activities. Until 1990, our work focused on the development
of a series of hands-on laboratory experiments that emphasize several
fundamental math/science ideas:
-science as a process;
-focus on simple variables - length, area, volume, mass, time, density,
velocity, acceleration, force;
-data collection, organization, analysis.
The general process of the TIMS Laboratory Experiments is quite simple:
students use a version of the scientific method to collect data related to
one of the variables listed above, organize it in a data table, graph the
data, and analyze it. We have used this basic process with considerable
success in lots of different kinds of classrooms from kindergarten through
high school.

There is no big mystery to the math/science integration here. It is
sometimes characterized as "quantitative science." For the purposes of
this discussion, I won't go into more details about how the experiments are
put together. (Those that want more information can contact me directly.)
What is signficant is that a.) our view of science is one that emphasizes
the process of science and b.) we concentrate on a limited amount of
content that is fundamental to both math and science. We never attempted
to address all of the topics that most schools expect in their math or
science curricula. However, the topics we cover permeate all of science,
and imbedded in the scientific process are a wide variety of math topics,
such as probability, statistics, proportional reasoning, measurement,
computation, estimation, etc. - all of which derive meaning from an
experimental situation. By narrowing our focus, we were able to develop a
series of math/science activies that work with teachers and kids, resonate
with scientists and mathematicians, and grow in logical ways across the

As you might expect, there is a catch: the TIMS Laboratory Experiments
discussed above are designed as "supplemental" materials, i.e., they are
not intended to be a full curriculum. We confronted this issue in a
serious way when the TIMS Project was funded by the NSF in 1990 to develop
a comprehensive mathematics curriculum that integrates mathematics and
science. After six years of development and testing, Grades 1-3 of the
TIMS curriculum are now available (published by Kendall/Hunt Publishing as
"Math Trailblazers: A Mathematical Journey Using Science and Language
Arts."; Grades K,4 and 5 will be available next spring). The TIMS
curriculum is one of the three NSF comprehensive curriculum projects for
the elementary grades.

The process of trying to develop an integrated math/science curriculum has
been an odyssey that has taken many turns along the way. Our original
conception of the curriculum was to organize it around length, area,
volume, mass, et. al. and to build the mathematics around these science
concepts. We, in fact, pilot tested a version of part of the curriculum
built this way. We confronted major problems in doing this. The math did
not always fit in as nicely as needed - which was not a big issue when we
were developing supplemental activities but was very significant as we
planned a full curriculum that was supposed to build upon itself.
Furthermore, there were some holes in the mathematics. To make a long
story short, we were forced to rethink our organization for the curriculum.
In the end, we looked first at the program's mathematical requirements and
then (mostly) built the science (and language arts) ideas around the
mathematics. What we have now is a comprehensive mathematics curriculum
that has extensive, strong connections with science (and other areas) - but
is not a full science curriculum. We still don't cover dinasaurs,
penguins, parts of the body, and other topics that are typically part of
most schools' science curriculum and are often the focus of "integrated"
units. Yet the integration of the mathematics with science is quite
apparent and gives the curriculum an exciting dimension that adds
tremendous meaning to the mathematics.

If you extrapolate from our experience - which included six years of
development and testing, $5 million of NSF funding, and about 20 previous
years of messing around with these ideas - you can see how those who
attempt to develop "integrated" programs without carefully thinking about
the mathematics will almost always short change the mathematics. And thus
the concerns expressed by several folks on this listserv and many others...
Developing a solid and substantive integrated program requires a lot more
thought than meets the eye.

Marty Gartzman

Marty Gartzman
Institute for Mathematics and Science Education
University of Illinois at Chicago

phone: (312) 413-2971
fax: (312)413-7411

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