>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 grades.
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 Institute for Mathematics and Science Education University of Illinois at Chicago