Interconnecting Science and Mathematics Concepts
Kalyani Raghavan, Mary L. Sartoris, Robert Glaser University of Pittsburgh
Historically, practically, and intellectually, mathematics has played an integral role in the investigation of nature. As a study of space and quantity, mathematics directly contributes to the understanding and mastery of the real world. Physical problems, when idealized and formulated in the language of numbers and geometry, become mathematical problems. Some of the world's greatest mathematicians, including Archimedes, Newton, and Riemann, were also great scientists. In addition to being conceptually interconnected, the two disciplines share common process skills ( Berlin & White, 1991; Gallagher, 1979; Kouba, 1989). It is therefore not surprising that recent educational reform movements advocate coordinating instruction to reinforce and exploit this interdisciplinary connection ( National Research Council, 1994; Project 2061, 1990). Unfortunately, however, the mutually supportive nature of mathematics and science is often underemphasized or even ignored in school curricula.
Area and volume, measures of basic properties of matter, are central concepts in science, yet they are commonly presented in fifth- and sixth- grade mathematics classes. Moreover, instruction is mostly quantitative in nature, emphasizing rote application of formulas to solve a limited set of problems rather than fostering qualitative understanding that supports meaningful application of concepts within a variety of contexts. Most science textbooks incorporate a brief review of definitions and formulas into a chapter on units and measurement, assuming that students have acquired the necessary background from the mathematics curriculum. No explicit link is made to science concepts for which area and volume are components, such as surface force and mass. As a result, students must generate their own connections and devise their own strategies for using rote knowledge in nonroutine situations.
An alternative approach would be to interconnect mathematics and science instruction so that the links between concepts are clearly depicted