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Leveraging Knowledge

An interview with David Ferguson, SUNY at Stony Brook

One of NSF's current goals (and a goal that is probably shared by Stony Brook's program in Technology and Society) is to integrate the learning of science and mathematics with technical education through joint efforts by science, mathematics and technical faculty. What do you see as the main challenges in implementing interdisciplinary projects of this type? What would be the benefits?

The primary benefits of interdisciplinary projects are threefold:

I do not mean to imply that there cannot be rich exploratory environments for learning mathematics and science that do not take an interdisciplinary approach. However, it would appear to me that the interdisciplinary perspective should eventually come at some point, whether it be in the next course or the next year.

The primary challenge to implementing interdisciplinary projects is to get our educational institutions at every level--pre-college to graduate school--to look over the high walls of individual disciplinary boundaries to see common intellectual strands and goals. Perhaps an equally difficult challenge is to make the institutional changes (rethinking of departments, reward systems, etc.) that will foster such work. Currently, one gets the sense that interdisciplinary projects work, when they do, more in spite of the educational system than because of it.

Finally, another challenge is to develop assessment approaches that capture the relevant aspects of learning while remaining practical to implement.

What other strategies besides interdisciplinary courses might offer students the opportunity to learn to use mathematics in a variety of real-world contexts?

Quantitative reasoning and problem solving should have a natural role in many courses in such areas as the biological and social sciences. There are many ways of knowing. Quantitative methods, art, music, poetry, and other human endeavors have different purposes; each represents a different way of knowing the world. Each way of knowing has its own assumptions, models, and limitations. Students need to see the natural interplay of these ways of knowing. This means that even discipline-specific courses should reflect some of the spirit and methods of the web of knowledge.

Many mathematicians and mathematics educators worry that in most interdisciplinary programs mathematics exists to serve science and that the mathematics itself gets lost. How important is it that students see mathematics as a separate subject rather than just as a powerful tool in the service of other subjects?

My own feeling is that we should offer multiple opportunities for students to learn mathematics. Inquiry approaches that lean largely toward pure mathematics can be valid and appropriate for many students throughout much of their education. Similarly, interdisciplinary approaches can be valid and appropriate for most students. Different curricula may reflect different mixes of pure, applied and interdisciplinary perspectives. We should be discussing issues of "emphasis" and timing, rather than giving "either/or" arguments.

Let me add here that in an interdisciplinary program that spans several years of a student's education, it is critical that key mathematics ideas get expanded and developed. I would bet that if an interdisciplinary program meets that need, some students will develop an interest in the power of pure mathematical ideas. Indeed, more students may develop an interest in pure mathematics via an interdisciplinary program than through a diet of "pure mathematics" projects!

Many mathematics faculty also worry that the context-rich environment of an interdisciplinary course will impede rather than enhance learning, since it will be harder for students to sort out the mathematics principles from the surrounding context. And they worry that students will not have the opportunity to take the mathematics they are learning to "the next level." What has been your experience in this regard?

My response benefited from discussions with Michael Hacker, Executive Director of the NSF-supported Mathematics, Science, and Technology (MST) project (based at Stony Brook) for fostering elementary school teachers' abilities to integrate mathematics, science, and technology. (Michael was formerly with the New York State Education Department.)

An interdisciplinary (e.g., MST) approach need not dilute mathematics, science, and technology content. In each of the subjects it is important to identify key ideas or strands and to monitor the progression of these strands as students move from kindergarten through 12th grade (or into undergraduate education). That is, we must consider what it means for students to mature intellectually in these areas. Part of that maturity should reflect a greater ability to scaffold knowledge and engage in exploration that will lead to "the next level" of understanding of concepts, methods, and tools.

The challenge of Interdisciplinary education is to build a progression of contextual activities that would enable children to construct personally meaningful knowledge, while at the same time extending their knowledge of key ideas and concepts.

An interdisciplinary and process-oriented approach to the learning and teaching of mathematics, science, and technology need not compromise content or cohesiveness of central ideas in any of these subject areas. By emphasizing process and applications, students gain additional tools that enable them to leverage their knowledge and thereby learn more, not less content. Also, when knowledge is personally meaningful, it offers opportunities for the learner to dig deeper into concepts. We should not be misled into thinking that the barrage of techniques that exemplify much of mathematics education and the horde of "recipes" so common in science "labs" means "more content."

Let's give students the opportunity to dig more deeply and the tools to explore new domains. That should be the real meaning of "more content."

David Ferguson is an applied mathematician and mathematics educator at the State University of New York at Stony Brook where he directs the Educational Computing Program in the Program in Technology and Society. He can be reached via email at dferguson@dts.tns.sunysb.edu.

To add your voice to this discussion, e-mail comments, letters, and op-ed articles to: extend@stolaf.edu or click here

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Last Update: June 19, 1997