### 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.

### Inquiry Based Mathematics Education

Laursen, S. & Rasmussen, C. (2019). I on the prize: Inquiry approaches in undergraduate mathematics. *International Journal of Research in Undergraduate Mathematics Education*, *5*(1), 129–146. https://doi.org/10.1007/s40753-019-00085-6

### 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. (2018). Inquiry-oriented instruction: A conceptualization of the instructional the components and practices. *PRIMUS*, *28*(1), 13–30.

Kuster, G., Johnson, E., Rupnow, R., & Wilhelm, A. G. (2019). The Inquiry-Oriented Instructional Measure. *International Journal of Research in Undergraduate Mathematics Education*, *5*(2), 183–204. https://doi.org/10.1007/s40753-019-00089-2

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., Marrongelle, K., Kwon, O.N., & Hodge, A. (2017). Four goals for instructors using inquiry-based learning. *Notices of the American Mathematical Society, 64*(11), 1308-1311*.*

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. (2019). A mathematician’s instructional change endeavors: Pursuing students’ mathematical thinking. In *Proceedings of the 22nd Annual Conference on the Research in Undergraduate Mathematics Education* (pp. TBA). Oklahoma City, OK: Oklahoma State University and the University of Oklahoma.

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.

Hall, W. L., Fortune, N., & Keene., K. A. (under review). Unpacking the talk: A framework for conversation in an online working group of university mathematicians sharing classroom videos. Under review at the *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. A., & Rasmussen, C. (2013). Sometimes less is more: Examples of student-centered technology as boundary objects in differential equations. In S. Habre (Ed.), *Enhancing mathematics understanding through visualization: The role of* *dynamical software* (pp. 12-36). Hershey, PA: IGI Global.

Keene, K. A., 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.

Marrongelle, K. (2007). The function of graphs and gestures in algorithmatization. *The Journal of Mathematical Behavior*, *26*(3), 211-229.

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. & Keene, K. A. (2019). Knowing solutions to differential equations with rate of change as a function: Waypoints in the journey. *The Journal of Mathematical Behavior. *In press.

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

Dunmyre, J., Fortune, N., Bogart, T., Rasmussen, C., & Keene, K. (2019). Climate change in a differential equations course: Using bifurcation diagrams to explore small changes with big effects. *Community of Ordinary Differential Equation Educators Special Issue Linking Differential Equations to Social Justice and Environmental Concerns*, *12*(1), 1–10.

Oremland, L., Dunmyre, J., & Fortune, N. (under review). Reinventing the Salty Tank through guided inquiry. Under review at *PRIMUS*.

Rasmussen, C., Dunmyre, J., Fortune, N., & Keene, K. (2019). Modeling as a means to develop new ideas: The case of reinventing a bifurcation diagram. *PRIMUS*, *29*(6), 509–526. https://doi.org/10.1080/10511970.2018.1472160

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.

Fortune, N., Rasmussen, C., Keene, K. A., Bogart, T., & Dunmyre, J. (under review). Bringing social justice topics to differential equations via a climate change problem: Identity, power, access, and achievement. Under review at the *MathAMATYC Educator Special Issue on Research in Undergraduate Mathematics Education*.

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.