Examining the conceptual organization of students in an integrated algebra and physical science class

School Science and Mathematics, Feb 1998 by Westbrook, Susan L

The cross-disciplinary context of density and slope was used to compare the conceptual organization of students in an integrated algebra and physical science class (SAM9) with that of students in a disciplinespecific physical science class (PSO). Analyses of students' concept maps indicated that the SAM9 students used a greater number of procedural linkages to connect mathematics and science concepts on the SAM9 students' maps than did the PSO students. The maps produced by SAM9 students also tended to show a more compartmentalized approach to thinking about the content of the two disciplines, a finding contrary to the researcher's original assertion. Traditional teaching territories and conceptual complexity were examined as possible explanations for the discrepancy between the predicted and actual outcomes.

Attitudes and beliefs about teaching and learning in science and mathematics classrooms are rapidly being transformed through the work and publications of national and professional organizations. Rather than emphasizing computation and "drill and practice," the goals of the National Council of Teachers' Mathematics' Curriculum and Evaluation Standards (1989) include valuing mathematics, communicating mathematically, and reasoning mathematically. Moving beyond the traditional notion of science as information, the National Science Education Standards (National Research Council, 1996) identify science as an "active process" (p. 20) and inquiry as "the central strategy for teaching science" (p. 31). Making classroom mathematics a valuable enterprise, however, may be difficult to accomplish when students do not grasp the underlying disciplinary contexts within which problems are framed. Science teachers may also find inquiry-based science instruction hindered by the students' lack of understanding of necessary mathematics concepts and representations. Integrated-or crossdisciplinary-mathematics and science curricula could provide a means through which science and mathematics teachers engage students in meaningful inquiries with valuable outcomes.

Although calls to study the potential effects of integrated mathematics and science curricula have come from several sectors of the mathematics and science education communities (Berlin, 1989; Good, 1991; Rutherford & Ahlgren, 1990), little research data are available to provide theoretical support for pedagogical models or the development of suitable integrated learning environments. In A Bibliography of Integrated Science and Mathematics Teaching and Learning Literature, Berlin (1991) reported that only 7% of 555 articles, books, and manuscripts written about the integration of mathematics and science content represented research on the subject. Further examination of that "research" literature, however, revealed that the studies listed rarely applied directly to classroom environments where mathematics and science were conceptually integrated. Since Berlin's 1991 bibliography, editorials (e.g., Underhill,1995), "howto's" (Lonning & DeFranco, 1994; McBride & Silverman, 1991), models (Berlin & White, 1994; Davison, Miller, & Metheny, 1995), curricular evaluations (Deal, 1994), university programs (Lonning & DeFranco, 1994; Stuessy, 1993), and numerous examples of activities proposed to integrate mathematics and science content have been published. There is no deficiency in the dialogue about approaches to take to integrate mathematics and science curricula. There does appear, however, to be a lack of systematic, prolonged inquiry into the processes and products of integrating mathematics and science in actual classroom settings.

In an attempt to promote more investigation of learning in integrated mathematics and science contexts, Williamson, Westbrook, Wright, and Fischer (1997) suggested that research be conducted on two levels: (a) pragmatic inquiries into the effect that curricular programs have on student understanding, attitudes, and process skills and (b) theoretical studies to examine the nature of the learner and the learning process within the integrated context. In order to explore the pragmatic and theoretical aspects of learning in an integrated mathematics and science classroom, the perceived outcomes of that integration must first be determined. What benefits do students and teachers gain from the integration of mathematics and science content? The assets of curricular integration can be perceived in three areas: context, authenticity, and conceptual complexity.

According to Science for All Americans (Rutherford & Ahlgren, 1990), "Science provides mathematics with interesting problems to investigate, and mathematics provides science with powerful tools to use in analyzing data (p. 16)." An integrated curriculum has the potential to foster an environment in which a variety of contexts can be used-logically and meaningfully. Content integration helps the mathematics teacher develop what Ball (1993) calls representational contexts: dynamic, rich models and problems that provide opportunities for students to think about and do mathematics. The content of science can be used to facilitate students' understanding of mathematics as a conceptual tool available for daily application in real-world problem solving.