An inquiry-oriented approach to undergraduate mathematics

To improve undergraduate mathematics learning, teachers need to recognize and value characteristics of classroom learning environments that contribute to powerful student learning. The broad goal of this special issue is to share such characteristics and the theoretical and empirical grounding for an innovative approach in differential equations called the Inquiry Oriented Differential Equations (IO-DE) project. We use the IO-DE project as a case example of how undergraduate mathematics can build on theoretical and instructional advances initiated at the K-12 level to create and sustain learning environments for powerful student learning at the undergraduate level. In addition to providing an overview of the five articles in this special issue, we highlight the theoretical background for the IO-DE project and provide a summary of two quantitative studies done to assess the effectiveness of the IO-DE project on student learning.

[1]  James J. Duderstadt,et al.  A Test of Leadership - Charting the Future of U.S. Higher Education , 2006 .

[2]  Chris Larson Rasmussen Qualitative and numerical methods for analyzing differential equations: A case study of students' understandings and difficulties , 1997 .

[3]  Chris Rasmussen,et al.  New directions in differential equations: A framework for interpreting students' understandings and difficulties , 2001 .

[4]  J. Shea National Science Education Standards , 1995 .

[5]  Chris Rasmussen,et al.  Social and sociomathematical norms in an advanced undergraduate mathematics course , 2000 .

[6]  K. Arrow Higher education as a filter , 1973 .

[7]  R. Skemp The psychology of learning mathematics , 1979 .

[8]  Chris Rasmussen,et al.  Advancing Mathematical Activity: A Practice-Oriented View of Advanced Mathematical Thinking , 2005 .

[9]  Ed Dubinsky,et al.  The Concept of Function: Aspects of Epistemology and Pedagogy [MAA Notes, Volume 25] , 1992 .

[10]  Kpe Koeno Gravemeijer How Emergent Models May Foster the Constitution of Formal Mathematics , 1999 .

[11]  Claude Janvier,et al.  The notion of chronicle as an epistemological obstacle to the concept of function , 1998 .

[12]  Slowing the Influence of Flawed Mathematics and Science Education Studies , 2005 .

[13]  Differential equations: a dynamical systems approach, part 1 , by J.H Hubbard and D.H West. Pp 348. DM 78. 1990. ISBN 0-387-97286-2 (Springer). , 1992 .

[14]  Chris Rasmussen,et al.  Students' Retention of Mathematical Knowledge and Skills in Differential Equations. , 2005 .

[15]  E. Yackel,et al.  Beliefs and Norms in the Mathematics Classroom , 2002 .

[16]  Mona Hicks,et al.  Our Underachieving Colleges: A Candid Look at How Much Students Learn and Why They Should Be Learning More , 2006 .

[17]  P. Cobb,et al.  Sociomathematical Norms, Argumentation, and Autonomy in Mathematics. , 1996 .

[18]  E. Glasersfeld Radical constructivism in mathematics education , 2002 .

[19]  Gilah C. Leder,et al.  Beliefs A hidden variable in Mathematics Education , 2002 .

[20]  Chris Rasmussen,et al.  Pedagogical Content Tools: Integrating Student Reasoning and Mathematics in Instruction , 2006 .

[21]  Hans Freudenthal,et al.  Revisiting mathematics education : China lectures , 1991 .

[22]  Chris Rasmussen,et al.  Capitalizing on advances in mathematics and k-12 mathematics education in undergraduate mathematics: An inquiry-oriented approach to differential equations , 2006 .