Appalachian Collaborative Center for Learning, Assessment and Instruction in Mathematics Mathematics Teaching and Learning in Rural Contexts: A Social Systems Perspective Working Paper No. 5 Michael L. Arnold Mid-continent Research for Education and Learning March 2003 ACCLAIM’s mission is the cultivation of indigenous leadership capacity for the improvement of school mathematics in rural places. The project aims to (1) understand the rural context as it pertains to learning and teaching mathematics, (2) articulate in scholarly works, including empirical research, the meaning and utility of that learning and teaching among, for, and by rural people, and (3) improve the professional development of mathematics teachers and leaders in and for rural communities. Copyright ? 2003 by the Appalachian Collaborative Center for Learning, Assessment, and Instruction in Mathematics (ACCLAIM). All rights reserved. The Working Paper Series is published at Ohio University, Athens, Ohio by the ACCLAIM Research Initiative. Funded by the National Science Foundation as a Center for Learning and Teaching, ACCLAIM is a partnership of the University of Tennessee (Knoxville), University of Kentucky (Lexington), Kentucky Science and Technology Corporation (Lexington). Marshall University (Huntington, WV), University of Louisville, and Ohio University (Athens, OH). ACCLAIM Research Initiative All rights reserved Address: 210A McCracken Hall Ohio University Athens, OH 45701-2979 Office: 740-593-9869 Fax: 740-593-0477 E-mail: [email protected]
Web: //acclaim.coe.ohiou.edu/ This material is based upon the work supported by the National Science Foundation Under Grant No. 0119679. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. Mathematics Teaching and Learning in Rural Contexts: A Social Systems Perspective Michael L. Arnold McREL Mid-continent Research for Education and Learning 2550 S. Parker Road, Suite 500 Aurora, CO 80014 303-632-5501 [email protected]
1 MATHEMATICS TEACHING AND LEARNING IN RURAL CONTEXTS: A SOCIAL SYSTEMS PERSPECTIVE Michael L. Arnold McREL The notion that mathematics teaching and learning is somehow different in rural contexts than in urban and suburban ones is strange to most people. After all, 2 + 2 = 4 whether you live in Buffalo, New York, or Buffalo, Wisconsin (population 1,040). A triangle has three angles that add up to 180° whether you live in Detroit, Michigan, or Detroit, Texas (population 718). And the square root of 1,936 is still 44 whether you are in Minneapolis, Minnesota, or Minneapolis, North Carolina (population 250). Among those of us who attended or taught in a rural school, however, experience suggests that meaningful differences do exist. Although much anecdotal evidence exists about these differences, there is not yet a comprehensive body of empirical literature upon which to draw definitive conclusions about the effects of rurality on mathematics teaching and learning. There is, however, substantial research about how organizations function, and that literature can enlighten us about which aspects of rural schools might influence the teaching and learning of mathematics in rural schools. This paper examines some of this research and suggests ways it can be applied to rural schools. The discussion begins with a brief consideration of an open social systems model of schools in order to provide a framework for thinking about how the contexts of rural communities and schools might influence student achievement in mathematics. Schools as Social Systems Figure 1 illustrates the open systems model selected to illuminate the issues, especially for readers unused to thinking about the organizational contexts of curriculum and instruction. In this model schools are social systems comprised of interdependent subsystems that function together to transform inputs into outcomes. Although they do have recognizable boundaries that separate them from their wider environment, they are open rather than closed systems. That is, external forces in the environment beyond the school influence the internal components of the school. At the same time, however, the school affects the environment in a reciprocal relationship in which the school relies on the community for the provision of inputs, while the community relies on the school to transform those inputs into something of value (e.g., student achievement). At the heart of the school is a transformation process where the school converts inputs (e.g., human resources) into outcomes. This process involves four subsystems: the structural system, the political system, the individual system, and the cultural system. The structural system comprises the organizational hierarchy and the bureaucratic rules and regulations that organize the work of teachers, administrators and other staff. The political system represents the informal power relationships that occur within schools that can have significant influence on the workings of the organization. The individual system consists of the beliefs and needs of individuals within the system, while the cultural system represents the shared beliefs and expectations of participants in the system. These subsystems support the technical core of the organization, which is “where the actual ‘product’ of the organization is produced” (Hoy ?encourage all students to learn for understanding; ?foster healthy skepticism; ?allow for, recognize, and build on differences in learning styles, multiple intelligences, and abilities; ?carefully align curriculum, assessment, and high standards; ?conduct interim assessments of students’ progress and use the results to improve instruction; ?measure instructional effectiveness through student performance and achievement; and ?use a problem-solving approach (Sutton 16(3), 193-201. Kannapel, P. J., & DeYoung, A. J. (1999). The rural school problem in 1999: A review and critique of the literature. Journal of Research in Rural Education, 15, 67-79. Khattri, N., Riley, K. W., & Kane, M. B. (1997). Students at risk in poor, rural areas: A review of the research. Journal of Research in Rural Education, 13 (2), 79-100. Kusmin, L. D. (2000). “Skilled metro workers get highest payoffs for using a computer at work.“ Rural America, 15 (2), 24-30. Lewis, K. S., Toole, J., & Hargreaves, A. (1999). Rethinking school improvement. In Murphy, J., & Louis, K. S. (eds.) Handbook of research on educational administration. San Francisco: Jossey-Bass. Marzano, R. J. (1998). A theory-based meta-analysis of research on instruction. Aurora, CO: Mid-continent Research for Education and Learning. Available online at //www.mcrel.org/products/learning/meta.asp Marzano, R. J., Pickering, D. J., & Pollock, J. E. (2001). Classroom instruction that works: Research-based strategies for increasing student achievement. Alexandria, VA: Association for Supervision and Curriculum Development. Mintzbert, H. (1983). Power in and around organizations. Englewood Cliffs, NJ: Prentice Hall. 15 Murphy, P. J., & Angelski, K. (1997). Rural teacher mobility: A report from British Columbia. Rural Educator, 18 (2), 5-11. National Research Council. (1996). National science education standards. Washington, DC: National Academy Press. (ERIC Document Reproduction Service No. ED391690) Perrault, M. (October 26, 2002). Dental gap widening: State’s rural poor often go without care. Denver, CO: Rocky Mountain News, (1C & 4C). Sanders, N. E. (2000). Standards and local curriculum: A zero-sum game? Journal of Research in Rural Education, 16 (3), 193-201. Scott, R.W. (1998). Organizations: Rational, natural, and open systems (4th ed). Englewood Cliffs, NJ: Prentice Hall. Smylie, M., & Smart, J. (1990). Teacher support for career enhancement initiatives: program characteristics and effects on work. Educational Evaluation and Policy Analysis, 12(2), 9-55. Stauber, K. N. (2001). Why invest in Rural America—and how? A critical public policy question for the 21st century. In Exploring Policy Options for A New Rural America, 9-28. Kansas City, MO: Center for the Study of Rural America, Federal Reserve Bank of Kansas City. Sutton, J., & Krueger, A. (2002). EdThoughts: What we know about mathematics teaching and learning. Aurora, CO: Mid-continent Research for Education and Learning. Theobald, P., & Nachtigal, P. (1995). Culture, community, and the promise of rural education. Phi Delta Kappan, 77(2), 132-35. Van Secker, C. E., & Lissitz, R. W. (1999). Estimating the impact of instructional practices on student achievement in science. Journal of Research in Science Teaching 36 (10), 1110-1126).