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Abstract
This paper aims to illustrate a design cycle of inquiry-based mathematics activities. We highlight a series of questions that we use when creating inquiry-based materials, testing and evaluating those materials, and revising the materials following this evaluation. These questions highlight the many decisions necessary to find just the right tasks for our students. Throughout the paper the use of multiple representations (graphical, numerical, symbolic, and narrative) and the distinction between facts, skills, methods, and conceptual understanding is explained and illustrated with examples. Additionally, we present evidence of student learning through excerpts from student journals and exam analysis.
ACKNOWLEDGEMENTS
We thank our wonderful colleagues at Rockhust University and Westfield State University, especially Paula Shorter, Volker Ecke, Philip Hotchkiss, and Julian Fleron.
Additional information
Notes on contributors
M. Greene
M. Greene uses an inquiry-focused, active-learning approach in all of her teaching. Her goal is to provide students with a learning environment that encourages them to develop as independent thinkers and problem solvers. She is particularly interested in how to effectively assess the mathematical understanding developed in her classroom. Mairead has a Ph.D. in Algebraic Number Theory. She is now at Rockhurst University in Kansas City, Missouri.
C. von Renesse
C. von Renesse uses open inquiry techniques in all of her teaching. Her passion for music and dancing has been woven into her teaching as part of her inquiry-based approach to mathematics for liberal arts classes. Christine has advanced degrees in Elementary Education, Music and Mathematics from the Technical University Berlin, Germany and a Ph.D. in Algebraic Geometry. She is now at Westfield State University in Massachusetts.