NC State
IODE

Overview

Here we provide a list of references that can be used as resources for instructors; they are grouped by role of the instructor / teaching, instructional change, student thinking, mathematics, and general.


Role of the Instructor / Teaching

Johnson, E. (2013). Teachers’ mathematical activity in inquiry-oriented instruction. Journal of Mathematical Behavior, 32(4), 761–775.

Johnson, E., Caughman, J., Fredericks, J., & Gibson, L. (2013). Implementing inquiry-oriented curriculum: From the mathematicians’ perspective. Journal of Mathematical Behavior, 32(4), 743–760.

Johnson, E., & Larsen, S. (2012). Teacher listening: The role of knowledge of content and students. Journal of Mathematical Behavior, 31(1), 117–129.

Kuster, G., Johnson, E., Keene, K. A., & Andrews-Larson, C. (2017). Inquiry-oriented instruction: A conceptualization of the instructional the components and practices. PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 1–18.

Marrongelle, K., & Rasmussen, C. (2008). Meeting new teaching challenges: Teaching strategies that mediate between all lecture and all student discovery. In M. Carlson, & C. Rasmussen (Eds.), Making the connection: Research and teaching in undergraduate mathematics education (pp. 167-178). Washington, DC: The Mathematical Association of America.

Rasmussen, C., & King, K. D. (2000). Locating starting points in differential equations: A realistic mathematics education approach. International Journal of Mathematical Education in Science and Technology, 31(2), 161–172.

Rasmussen, C., & Kwon, O. N. (2007). An inquiry-oriented approach to undergraduate mathematics. Journal of Mathematical Behavior, 26(3), 189–194.

Rasmussen, C., & Marrongelle, K. (2006). Pedagogical content tools: Integrating student reasoning and mathematics in instruction. Journal for Research in Mathematics Education, 37(5), 388–420.

Rasmussen, C., Zandieh, M., & Wawro, M. (2009). How do you know which way the arrows go? The emergence and brokering of a classroom mathematics practice. In W.-M. Roth (Ed.), Mathematical representations at the interface of the body and culture (pp. 171-218). Charlotte, NC: Information Age Publishing.

Stephan, M., & Rasmussen, C. (2002). Classroom mathematical practices in differential equations. Journal of Mathematical Behavior, 21(4), 459–490.

Yackel, E. (2002). What we can learn from analyzing the teacher’s role in collective argumentation. Journal of Mathematical Behavior, 21(4), 423–440.

Yackel, E., Rasmussen, C., & King, K. D. (2000). Social and sociomathematical norms in an advanced undergraduate mathematics course. Journal of Mathematical Behavior, 19, 275–287.

Yoshinobu, S., & Jones, M. G. (2012). The coverage issue. PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 22(4), 303–316.

Instructional Change

Andrews-Larson, C., Peterson, V., & Keller, R. (2016). Eliciting mathematicians’ pedagogical reasoning. In T. Fukawa-Connelly, N. E. Infante, M. Wawro, & S. Brown (Eds.), Proceedings of the 19th Annual Conference on Research in Undergraduate Mathematics Education. Pittsburgh, PA: West Virginia University.

Fortune, N. & Keene, K. A. (2017). Online faculty collaboration to support instructional change. In E. Galindo & J. Newton, (Eds.), Proceedings of the 39th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 543). Indianapolis, IN: Hoosier Association of Mathematics Teacher Educators.

Fortune, N., Keene, K. A., & Hall. W. (2017). Using video in online working groups to support faculty collaboration. In A. Weinberg, C. Rasmussen, J. Rabin, M. Wawro, & S. Brown (Eds.), Proceedings of the 20th Annual Conference on Research in Undergraduate Mathematics Education (pp. 690-697). San Diego, CA: San Diego State University.

Keene, K. A., Fortune, N., & Hall. W. (under review). Supporting mathematics faculty’s instructional change: Using class videos in an online working group. Under review at International Journal of Research in Undergraduate Mathematics Education.

Speer, N. M., & Wagner, J. F. (2009). Knowledge needed by a teacher to provide analytic scaffolding during undergraduate mathematics classroom discussions. Journal for Research in Mathematics Education, 40(5), 530–562.

Wagner, J. F., Speer, N. M., & Rossa, B. (2007). Beyond mathematical content knowledge: A mathematician’s knowledge needed for teaching an inquiry-oriented differential equations course. Journal of Mathematical Behavior, 26(3), 247–266.

Student Thinking

Bouhjar, K., Andrews-Larson, C., Haider, M., & Zandieh, M. (in press). Examining students' procedural and conceptual understanding of eigenvectors and eigenvalues in the context of inquiry-oriented instruction. In S. Stewart, C. Andrews-Larson, A. Berman, & M. Zandieh (Eds.), Challenges in teaching linear algebra. Springer: New York, NY. 

Hall, W., Keene, K. A., & Fortune, N. (2016). Measuring student conceptual understanding: The case of Euler’s method. In T. Fukawa-Connelly, N. E. Infante, M. Wawro, & S. Brown (Eds.), Proceedings of the 19th Annual Conference on Research in Undergraduate Mathematics Education (pp. 837-842). Pittsburgh, PA: West Virginia University.

Keene, K. A. (2007). A characterization of dynamic reasoning: Reasoning with time as parameter. Journal of Mathematical Behavior, 26(3), 230–246.

Keene, K., Rasmussen, C., & Stephan, M. (2012). Gestures and a chain of signification: The case of equilibrium solutions. Mathematics Education Research Journal, 24, 347-369.

Kwon, O. N., Rasmussen, C., & Allen, K. (2005). Students’ retention of mathematical knowledge and skills in differential equations. School Science and Mathematics, 105(5), 227–240.

Rasmussen, C. (2001). New directions in differential equations: A framework for interpreting students’ understandings and difficulties. Journal of Mathematical Behavior, 20(1), 55–87.

Rasmussen, C., & Blumenfeld, H. (2007). Reinventing solutions to systems of linear differential equations: A case of emergent models involving analytic expressions. Journal of Mathematical Behavior, 26(3), 195–210.

Rasmussen, C., Kwon, O. N., Allen, K., Marrongelle, K., & Burtch, M. (2006). Capitalizing on advances in mathematics and K-12 mathematics education in undergraduate mathematics: An inquiry-oriented approach to differential equations. Asia Pacific Education Review, 7(1), 85–93.

Rasmussen, C., Stephan, M., & Allen, K. (2004). Classroom mathematical practices and gesturing. Journal of Mathematical Behavior, 23, 301–323.

Zandieh, M., Wawro, M., & Rasmussen, C. (2016). Symbolizing and brokering in an inquiry oriented linear algebra classroom. In T. Fukawa-Connelly, N. E. Infante, M. Wawro, & S. Brown (Eds.), Proceedings of the 19th Annual Conference on Research in Undergraduate Mathematics Education. Pittsburgh, PA: West Virginia University.

Mathematics

Rasmussen, C., & Keynes, M. (2003). Lines of eigenvectors and solutions to systems of linear differential equations. PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 13(4), 308–320.

Rasmussen, C., & Ruan, W. (2008). Using theorems-as-tools: A case study of the uniqueness theorem in differential equations. In Making the connection: Research and teaching in undergraduate mathematics (pp. 153–164). Washington, DC: Mathematical Association of America.

General

Johnson, E., Keene, K. A., & Andrews-Larson, C. (2015). Inquiry-oriented instruction: What it is and how we are trying to help. American Mathematical Society Blogs On Teaching and Learning. Available at this link.

Rasmussen, C., & Keene, K. A. (2015). Software tools that do more with less. Mathematics Today, (December), 282–285.

Rasmussen, C., & Whitehead, K. (2003). Learning and teaching ordinary differential equations. In A. Selden & J. Selden (Eds.), MAA online research sampler (pp. 1–12). Washington, DC: Mathematical Association of America.

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.

Rota, G. C. (1997). Ten lessons I wish I had learned before I started teaching differential equations. Boston, MA: Mathematical Association of America.

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.