Abstract
This paper provides an overview of the Inquiry-Oriented Differential Equations (IO-DE) project and reports on the main results of a study that compared students’ beliefs, skills, and understandings in IO-DE classes to more conventional approaches. The IO-DE project capitalizes on advances within mathematics and mathematics education, including the instructional design theory of Realistic Mathematics Education and the social negotiation of meaning. The main results of the comparison study found no significant difference between project students and comparison students on an assessment of routine skills and a significant difference in favor of project students on an assessment of conceptual understanding. Given these encouraging results, the theoretical underpinnings of the innovative approach may be useful more broadly for undergraduate mathematics education reform.
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References
Artigue, M. (1992). Cognitive difficulties and teaching practices. In G. Harel, & E. Dubinsky (Eds.),The concept of function: Aspects of epistemology and pedagogy (pp.109–132). Washington, DC: The Mathematical Association of America.
Artigue, M. & Gautheron, V. (1983).Systemes differentiels, etude graphique. Paris: CEDIC/F. Nathan.
Blanchard, P., Devaney, R., & Hall, R. (2002).Differential equations. Pacific Grove, CA: Brooks/Cole.
Carlson, M. (1997). Views about mathematics survey: Design and results. In J. A. Dossey, J. O. Swafford, M. Parmantie, & A. E. Dossey (Eds.),Proceedings of the 18 th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 395–402). Columbus, OH: ERIC.
Carlson, M. (1999). The mathematical behavior of six successful mathematics graduate students: Influences leading to mathematical success.Educational Studies in Mathematics, 40, 237–258.
Cobb, P. & Bauersfeld, H. (1995).The emergence of mathematical meaning. Hillsdale, NJ: Lawrence Erlbaum Associates.
Cobb, P., Wood, T., Yackel, E., & McNeal, B. (1992). Characteristics of classroom mathematics traditions: An interactional analysis.American Educational Research Journal, 29, 573–604.
Farlow, J., Hall, J., McDill, J., & West, B. (2002).Differential equations & linear algebra (2nd ed.). Upper Saddle River, NJ: Prentice Hall.
Freudenthal, H. (1991).Revisiting mathematics education. Dordrecht, The Netherlands: Kluwer.
Gravemeijer, K. (1999). How emergent models may foster the constitution of formal mathematics.Mathematical Thinking and Learning, 1, 155–177.
Gravemeijer, K., Cobb, P., Bowers, J., & Whitenack, J. (2000). Symbolizing, modeling, and instructional design. In P. Cobb, E. Yackel, & K. McClain (Eds.),Symbolizing and communication in mathematics classrooms: Perspectives on discourse, tools, and instructional design (pp. 225–273). Mahwah, New Jersey: Lawrence Erlbaum Associates.
Halloun, I., Carlson, M., & Hestenes, D. (1996, September).Views about mathematics. survey. Paper presented at the Research Conference in Collegiate Mathematics Education, Mt. Pleasant, MI.
Holton, D. (Ed.) (2001).The teaching and learning of mathematics at university level. Dordrecht, The Netherlands: Kluwer Academic Publishers.
Huntley, M., Rasmussen, C., Villarubi, R., Sangtong, J., & Fey, J. (2000). Effects of standards-based mathematics education: A study of the Core-Plus Mathematics Project algebra/functions strand.Journal for Research in Mathematics Education, 31, 328–361.
Ju, M. K., & Kwon, O. N. (2003).Perspective mode change in mathematical narrative: Social transformation of view of mathematics in a university differential equations class. Paper presented at the 7 th annual conference on Research in Undergraduate Mathematics Education, Scottsdale, AZ.
Kallaher, M. J. (Ed.) (1999).Revolutions in differential equations: Exploring ODEs with modern technology. Washington, DC: The Mathematical Association of America.
Kaput, J. (1997). Rethinking calculus: Learning and teaching.American Mathematical Monthly, 104, 731–737.
Kwon, O. N. (2003). Guided reinvention of Euler algorithm: An analysis of progressive mathematization in RME-based differential equations course.J. Korea Soc. Math. Ed. Ser. A: The Mathematical Education, 42(3), 387–402.
Kwon, O. N., Rasmussen, C., & Allen, K. (2005). Students’ retention of mathematical knowledge and skills in differential equations.School Science and Mathematics, 105(5), 1–13.
Nagle, R. & Saff, E. (1993).Fundamentals of differential equations (3rd ed.). New York, NY: Addison-Wesley Publishing Company.
Rasmussen, C. (2001). New directions in differential equations: A framework for interpreting students’ understandings and difficulties.Journal of Mathematical Behavior, 20, 55–87.
Rasmussen, C. & Keynes, M. (2003). Lines of eigenvectors and solutions to systems of linear differential equations.PRIMUS, 13(4), 308–320.
Rasmussen, C. & King, K. (2000). Locating starting points in differential equations: A realistic mathematics approach.International Journal of Mathematical Education in Science and Technology, 31, 161–172.
Rasmussen, C. & Marrongelle, K. (in press). Pedagogical content tools: Integrating student reasoning and mathematics into instruction.Journal for Research in Mathematics Education.
Rasmussen, C., Yackel, E., & King, K. (2003). Social and sociomathematical norms in the mathematics classroom. In H. Schoen & R. Charles (Eds.),Teaching mathematics through problem solving: Grades 6–12 (pp. 143–154). Reston, VA: National Council of Teachers of Mathematics.
Rasmussen, C., Zandieh, M., King, K., & Teppo, A. (2005). Advancing mathematical activity: A view of advanced mathematical thinking.Mathematical Thinking and Learning, 7, 51–73.
Richards, J. (1991). Mathematical discussions. In E. von Glasersfeld (Ed.),Radical constructivism in mathematics education (pp. 13–51). Dordrecht, The Netherlands: Kluwer.
Skemp, R. (1987).The psychology of learning mathematics. Hillsdale, NJ: Lawrence Erlbaum Associates.
Stephan, M. & Rasmussen, C. (2002). Classroom mathematical practices in differential equations.Journal of Mathematical Behavior, 21, 459–490.
Treffers, A. (1987).Three dimensions. A model of goal and theory description in mathematics education: The Wiskobas project. Dordrecht, The Netherlands: Kluwer Academic Publishers.
Wagner, J., Speer, N., & Rossa, B. (2006).“How much insight is enough?” What studying mathematicians can reveal about knowledge needed to teach for understanding. Paper presented at the Annual Meeting of the American Educational Research Association, San Francisco, CA.
West, B. (Ed.) (1994). Special issue on differential equations [Special issue].The College Mathematics Journal,25(5).
Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics.Journal for Research in Mathematics Education, 27, 458–477.
Yackel, E. & Rasmussen, C. (2002). Beliefs and norms in the mathematics classroom. In G. Leder, E. Pehkonen, & G. Toerner (Eds.),Beliefs: A hidden variable in mathematics education? (pp. 313–330). Dordrecht, The Netherlands: Kluwer Academic Publishers.
Zandieh, M. & McDonald, M. (1999). Student understanding of equilibrium solution in differential equations. In F. Hitt & M. Santos (Eds.),Proceedings of the 21 st Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 253–258). Columbus, OH: ERIC.
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Rasmussen, C., Kwon, O.N., Allen, K. et al. Capitalizing on advances in mathematics and k-12 mathematics education in undergraduate mathematics: An inquiry-oriented approach to differential equations. Asia Pacific Educ. Rev. 7, 85–93 (2006). https://doi.org/10.1007/BF03036787
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DOI: https://doi.org/10.1007/BF03036787