Publications


Below is a list of publications resulting from the research done into the teaching and learning of linear algebra and/or inquiry-oriented teaching in undergraduate mathematics. References that are in bold are directly related to the IOLA materials.



Andrews-Larson, C. (2015). Roots of Linear Algebra: An historical exploration of linear systems. PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 25(6), 507-528.

Andrews-Larson, C., & Kasper, V. (2015). Variations in Implementation of Student-Centered Instructional Materials in Undergraduate Mathematics Education. In T. Fukawa-Connely, N. Infante, K. Keene, & M. Zandieh (Eds.), Proceedings of the 18th Annual Conference on Research in Undergraduate Mathematics Education, Pittsburgh (pp. 74-88). Pittsburgh, PA.

Andrews-Larson, C., Peterson, V., & Keller, R. (2016). Eliciting mathematicians' pedagogical reasoning. In T. Fukawa-Connelly, N. Infante, M. Wawro, & S. Brown (Eds.), Proceedings of the 19th Annual Conference on Research in Undergraduate Mathematics Education (pp. 61-75). Pittsburgh, PA. Retrieved from http://sigmaa.maa.org/rume/RUME19v3.pdf

Andrews-Larson, C., Wawro, M., & Zandieh, M. (2017). A hypothetical learning trajectory for conceptualizing matrices as linear transformations.International Journal of Mathematical Education in Science and Technology, 48(6), 809-829.

Bagley, S., Rasmussen, C., & Zandieh, M. (2015). Inverse, composition, and identity: The case of function and linear transformation. The Journal of Mathematical Behavior, 37, 36-47.

Haider, M., Bouhjar, K., Findley, K., Quea, R., Keegan, B., & Andrews-Larson, C. (2016). Using student reasoning to inform assessment development in linear algebra. In T. Fukawa-Connelly, N. Infante, M. Wawro, & S. Brown (Eds.), Proceedings of the 19th Annual Conference on Research in Undergraduate Mathematics Education (pp. 163-177). Pittsburgh, PA. Retrieved from http://sigmaa.maa.org/rume/RUME19v3.pdf

Henderson, F., Rasmussen, C., Sweeney, G., Wawro, M, & Zandieh, M. (2010). Symbol sense in linear algebra: A start toward eigen theory. Proceedings of the 13th Annual Conference on Research in Undergraduate Mathematics Education, Raleigh, NC. Retrieved from http://sigmaa.maa.org/rume/crume2010

Johnson, E., Keene, K., & Andrews-Larson, C. (2015). Inquiry-Oriented Instruction: What It Is and How We are Trying to Help. [Web log post.]. American Mathematical Society, Blog On Teaching and Learning Mathematics. Retrieved from http://blogs.ams.org/matheducation/2015/04/10/inquiry-oriented-instruction-what-it-is-and-how-we-are-trying-to-help/

Kuster, G., Johnson, E., Keene, K., & Andrews-Larson, C. (submitted). Inquiry-oriented instruction: A conceptualization of the instructional components and practices. Manuscript submitted for publication.

Larsen, S. (2013). A local instructional theory for the guided reinvention of the group and isomorphism concepts. The Journal of Mathematical Behavior, 32(4), 712-725.

Larsen, S., & Lockwood, E. (2013). A local instructional theory for the guided reinvention of the quotient group concept. The Journal of Mathematical Behavior, 32(4), 726-742.

Larson, C. & Zandieh, M. (2013). Three interpretations of the matrix equation Ax=b. For the Learning of Mathematics, 33(2), 11-17.

Lockwood, E., Johnson, E., & Larsen, S. (2013). Developing instructor support materials for an inquiry-oriented curriculum. The Journal of Mathematical Behavior, 32(4), 776-790.

Plaxco, D., & Wawro, M. (2015). Analyzing student understanding in linear algebra through mathematical activity. The Journal of Mathematical Behavior, 38, 87-100.

Rasmussen, C. L., & 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. (2007). An inquiry oriented approach to undergraduate mathematics. Journal of Mathematical Behavior, 26, 189-194.

Rasmussen, C., Wawro, M. & Zandieh, M. (2015). Examining individual and collective level mathematical progress. Educational Studies in Mathematics, 88(2), 259-281.

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.

Selinski, N., Rasmussen, C., Wawro, M., & Zandieh, M. (2014). A methodology for using adjacency matrices to analyze the connections students make between concepts: The case of linear algebra. Journal for Research in Mathematics Education, 45(5), 550-583.

Wawro, M. (2014). Student reasoning about the invertible matrix theorem in linear algebra. ZDM The International Journal on Mathematics Education, 46(3), 1-18.

Wawro, M. (2015). Reasoning about solutions in linear algebra: The case of Abraham and the Invertible Matrix Theorem. International Journal of Research in Undergraduate Mathematics Education, 1(3), 315-338.

Wawro, M., Larson, C., Zandieh, M., & Rasmussen, C. (2012). A hypothetical collective progression for conceptualizing matrices as linear transformations. Proceedings from Fifteenth Conference on Research in Undergraduate Mathematics Education, Portland, OR.

Wawro, M., Rasmussen, C., Zandieh, M., & Larson, C. (2013). Design research within undergraduate mathematics education: An example from introductory linear algebra. In T. Plomp, & N. Nieveen (Eds.), Educational design research – Part B: Illustrative cases (pp. 905-925). Enschede, the Netherlands: SLO.

Wawro, M., Rasmussen, C., Zandieh, M., Sweeney, G. F., & Larson, C. (2012). An inquiry-oriented approach to span and linear independence: The case of the magic carpet ride sequence. PRIMUS, 22(8), 577-599.

Wawro, M., Sweeney, G., & Rabin, J. (2011). Subspace in linear algebra: Investigating students’ concept images and interactions with the formal definition. Educational Studies in Mathematics, 78, 1-19.

Zandieh, M., & Rasmussen, C. (2010). Defining as a mathematical activity: A framework for characterizing progress from informal to more formal ways of reasoning. Journal of Mathematical Behavior, 29, 57-75.

Zandieh, M., Wawro, M., & Rasmussen, C. (2017). An example of inquiry in linear algebra: The roles of symbolizing and brokering. PRIMUS, 27(1), 96-124. DOI 10.1080/10511970.2016.1199618