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Project INTERMATH: An Interdisciplinary Approach to Cultural Change In 1993 the National Science Foundation called for a program of interdisciplinary activities to effect cultural change in undergraduate mathematics-based disciplines across the nation. Project INTERMATH is one of five major initiatives funded by the NSF under this program. A purpose of this program is to inspire mathematics and the disciplines it supports to continue in the spirit of the Calculus Reform movement in effecting change. Project INTERMATH is a consortium of eight schools four additional associated schools led by the United States Military Academy at West Point. Interdisciplinary activities included in this initiative are centered around the process and use of Interdisciplinary Lively Applications Projects (ILAPs), small-group projects developed by faculty and experts from more than one discipline. Our plan is to promote reform through ILAP production, curriculum design, and conferences and workshops. We believe that the process of developing and the classroom use of these ILAPs generate the communication, involvement, and connections needed to effect educational change. This change can take many forms. Yet, we believe a common goal for cultural change is to change the way we teach. In this paper, I would like to investigate the core characteristics of the national mathematics reform movement, discuss what it means to change one's culture, and make a case for the use of small-group interdiscplinary projects (ILAPs) as the impetus for change. Reform. In response to a national call for reform in mathematics that began back in the late 1970s, the Committee on the Undergraduate Program in Mathematics (CUPM), a Mathematical Association of America (MAA) committee responsible since 1953 for establishing guidelines for undergraduate curricula, issued its Recommendations for a General Mathematical Sciences Program (Tucker, A., 1981). The writers of this document called for a move away from the traditional mathematics sequence of courses to an integrated, more applied mathematical science curriculum (Tucker, A., 1981). Although educators appeared ready to solve many of the issues of the times, there was no consensus in the mathematics community about how to proceed, and the 1981 CUPM report generated little change. In subsequent reports (CBMS, 1984; NRC, 1984; National Science Board Commission on Precollege Education in Mathematics, Science and Technology, 1983; USDE, 1983), educators further documented deficiencies in the mathematics curriculum at all levels of schooling and called for similar changes to be made at the precollege level as well. Not until the publication of additional, more urgent cries of crisis (Douglas, 1986; McKnight et al., 1987; National Council of Teachers of Mathematics [NCTM], 1989; NRC, 1989; Steen, 1989) did many of the earlier recommendations get acted upon. These recommendations for change were published in summative form in 1989. At the precollege level, the NCTM published the Curriculum and Evaluation Standards for School Mathematics, and at the college level, the CUPM updated its 1981 report in the form of Reshaping College Mathematics (Steen, 1989). The curriculum goals addressed in both of these documents include content goals of integrating the topics of discrete mathematics and probability and statistics throughout the curriculum, and instructional goals of integrating the use of computer and calculator technologies as tools for instruction and learning. They also encourage the use of writing and mathematical modeling throughout the curriculum. In addition, college level mathematical sciences programs require a smoother transition from secondary to collegiate mathematics and a less special case- and topic-ridden (leaner) and more technology- and applications-oriented (livelier) calculus. In short, a major component of the reform effort is on preparing students to apply mathematics to everyday problem-solving situations, on motivating them to seek further learning in mathematics, and on enabling students to handle the technical and more complex problems of the applied sciences, engineering, and social sciences. Over the past 12 years, the focus of reform at the undergraduate level has been on changing calculus. Due to a number of NSF and Department of Education initiatives, many reform calculus texts are now on the market and the use of graphing calculators and computer algebra systems are being integrated into many calculus classrooms. In general, the calculus reform and the national reform movement have shifted the emphasis in the classroom from what we teach to how we teach. This shift could be further characterized as a move from teacher-centered to student-centered classrooms, the focus being on student learning rather than complete content coverage. At different institutions, reform has taken diverse forms, and the impetuses for reform are different. For some, changing the sequence of courses is called reform. For others, changing to a newer text may be called reform. Further, technology has added lab components at many institutions. And others have integrated math modeling and applications throughout their curriculum. By the previous argument, the measures of success of these implementations would be how effective was the reform in changing the way we teach and improving student learning. Cultural Change. To talk about cultural change, I first need to define "culture". I believe that the focus of any educational change from a faculty member's perspective should be limited to his or her institution. The culture may be further refined within the department or a discipline within the department. Once change has been successful within these limits it can be disseminated to a larger audience, other departments or other institutions. Therefore, the initial purpose of the change process is to reform the institution from within and as comprehensively as possible. As stated above, if we are to respond to the call for change from the national mathematics reform movement, we need to change the way we teach. Furthermore, to accomplish cultural change, the goals are best developed at the institution and for the institution. These goals should be focused on better student learning and be generated by the faculty who will teach these students. This comment is based on my experience as an evaluator of the curriculum change that has been going on at West Point since 1988. In 1990, West Point implemented a bold new curriculum of a four-course core mathematics for all of its students. The new curriculum builds on an initial course of discrete dynamical systems that includes matrix algebra and the analysis of systems of equations, followed by a two-course sequence of lively calculus that includes differential equations, vector calculus and multivariable calculus, and concludes with a course in probability and statistics. At the time of implementation, the Department of Mathematical Sciences, with help from others, outlined its expectations or goals for student growth after this two-year program -- a true seven-into-four curriculum. After a year of this new program, we saw a need to create formative objectives within the courses which lead to these summative goals. The conceptual framework for articulating these objectives took the form of five educational threads which weave themselves through the content of the four courses and beyond. These threads are mathematical reasoning, history of mathematics, scientific computing, mathematical modeling, and communications in mathematics. After five years of use of these threads and six years of the new curriculum, we are convinced of the worthiness of both endeavors. Data and interviews were collected for both the reform cohort and a comparison cohort that covered a more traditional core mathematics curriculum. Both of these cohorts had about 1000 students. The results indicate that the reform cohort either performed as well as or better than the comparison cohort in mathematics tests, mathematics courses, or common mathematics-based courses such as physics and engineering science. Also, the reform cohort's attitude toward mathematics appears to have increased positively over the first three courses and remained stable through the fourth course. Data continue to be collected for six more cohort classes of approximately 1000 students as they pass through the Academy. Finally, instruments are being fine tuned from term to term and analysis and database management are being set up to do real time evaluation which could facilitate between-course and midcourse curriculum adjustments. The change process continues -- even today. Significant changes previous to this current consortium project of expanding outside the institution were the implementation of small-group interdisciplinary projects (ILAPs) in 1992 and in 1995, the development of nine content threads to better connect the four-course core curriculum. In short, the change process has been successful. The process of change is still ongoing because of the involvement and ownership of the faculty, the consensus building across the institution, and the constant communication across disciplines. Faculty members have the sense that the change occurred because it was needed and the reform helps the students learn better. Further, student and faculty benefit in the enhancement of the relevance of mathematics, in a better connected and coordinated curriculum, in opportunities for extensions beyond the current content, and for a comprehensive educational experience. ILAPs. Interdisciplinary Lively Applications Projects are small group projects developed with partner disciplines that use mathematics. Students benefit from small-group projects, because they cooperate rather than compete. Students work together to formulate and solve problems rather than being compared individually against a standard. Communication is obviously enhanced through group work. Students feel more open to trying ideas out. Mathematical modeling and scientific problem solving are two of the hardest tasks for students to learn, and the group gives a good forum for evaluating and improving on informed conjectures. Further, ILAPs encourage the use of computer or calculator technology in the modeling, solution, and presentation processes. Finally and most important, these projects are opportunities for students to construct their own mathematics through discovery learning. The development of ILAPs is an enabling process for the faculty involved in the design and implementation of these projects. They communicate with members of other disciplines in the design process. They generate pedagogical ideas together in the implementation planning process. They feed on the excitement of learning as they are causing learning. This enthusiasm for the projects through application and ownership is carried into the classroom where students can benefit. It is our experience that once a faculty member has participated in the process of developing an ILAP and used it in the classroom, they are more willing to use their classrooms projects produced by others. Further, once teachers see the benefits to student learning of these interdisciplinary projects they want to use more and there is a shift of emphasis in the classroom from content coverage to student-centered learning. In short, faculty members change the way they teach. The resultant open communication across disciplines, the desire to connect mathematics to other disciplines, and the changes in the way we teach accomplish over time our desired cultural change. Project INTERMATH. At West Point, we see these ILAPs bringing about cultural change and accomplishing our goals. In each of the interdisciplinary projects used in our curriculum, we see each of our five educational threads coming together. Communication is needed both orally and in writing. Reasoning and modeling are needed in the formulation and analysis of the solution process. The use of technology is empowering by enabling the tackling of difficult problems. Students learn to value mathematics as a human endeavor used for solving real world problems. Further, through the projects we can connect to mathematics learned in the past, extend to mathematics understood more completely in the future, and connect to other disciplines. A next step is to effect change in the curriculum. At West Point this appears to have happened at the same time, except that we too will undergo another major change of the next two years by adopting new texts and a new computer algebra system to better weave our four core courses into an integrated program. Frank Giordano's article will address the aspects of curriculum change later. The cultural change at West Point has evolved to where we are now ready to continue our process of change and disseminate to others. We envision cultural change taking place at all of our 12 consortium schools. Our actions will be to enable the ILAP development process through workshops and conferences. This aspect of the project is covered in Don Small's article later. We want to further the dissemination process through publication and World Wide Web access. This aspect of the project will be covered in Chris Arney's article later. Finally, we would like to effect institution-wide cultural change by reforming curricula as envisioned in Giordano's article. In conclusion, we believe cultural change can accomplished through the development of interdisciplinary small-group projects (ILAPs) that change the way we teach and eventually change what we teach in the process. BIBLIOGRAPHY Conference Board of the Mathematical Sciences (CBMS). (1984). New goals for mathematical sciences education. Washington, DC: Author. Douglas, R. (Ed.). (1986). Toward a lean and lively calculus. MAA Notes Number 6: Mathematical Association of America (MAA). McKnight, C., Crosswhite, F., Dossey, J., Kifer, E., Swafford, J., Travers, K., & Cooney, T. (1987). The underachieving curriculum: Assessing U.S. school mathematics from an international perspective. Champaign, IL: Stipes Publishing. National Council of Teachers of Mathematics (NCTM). (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author. National Research Council (NRC). (1984). Renewing U.S. mathematics: Critical resource for the future. Washington, DC: National Academy Press. National Research Council (NRC). (1989). Everybody counts: A report to the nation on the future of mathematics education. Washington, DC: National Academy Press. National Science Board Commission on Precollege Education in Mathematics, Science and Technology. (1983). Educating Americans for the 21st Century. Washington, DC: National Science Foundation. Steen, L. A. (Ed.). (1989). Reshaping college mathematics. MAA Notes Number 13: Mathematical Association of America (MAA). Tucker, A. (Ed.). (1981). Recommendations for a general mathematical sciences program: A report of the Committee on the Undergraduate Program in Mathematics. Washington, DC: Mathematical Association of America (MAA).
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