References
- 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.
- Asiala, M., Brown, A., DeVries, D., J., Dubinsky, E., Mathews, D., & Thomas, K. (1996). A framework for research and development in undergraduate mathematics education. In J. Kaput, E. Dubinsky, & A. H. Schoenfeld (Eds.), Research in collegiate mathematics education II (pp. 1–32). Providence, RI: American Mathematical Society.
- Bernard, H. (1994). Research methods in anthropology (2nd ed.). Thousand Oaks, CA: Sage.
- Borwein, J. M., & Bailey, D. H. (2003). Experiments in mathematics: Computational paths to discovery. Natick, MA: AK Peters.
- Boyatzis, R. (1998). Transforming qualitative information: Thematic analysis and code development. Thousand Oaks, CA: Sage.
- Caglayan, G. (2015). Making sense of eigenvalue-eigenvector relationships: Math majors’ linear algebra – geometry connections in a dynamic environment. Journal of Mathematical Behavior, 40, 131–153.
- Caglayan, G. (2018). Visualizing the inner product space R(mxn) in a MATLAB-assisted linear algebra classroom. International Journal of Mathematical Education in Science and Technology, 49(4), 616–628.
- Caglayan, G. (in press). Coordinating analytic and visual approaches: Math majors' understanding of orthogonal Hermite polynomials in the polynomial inner product space in a technology-assisted learning environment. The Journal of Mathematical Behavior. doi:10.1016/j.jmathb.2018.03.006.
- Carlson, D., Johnson, C. R., Lay, D. C., & Porter, A. D. (1993). The linear algebra curriculum study group recommendations for the first course in linear algebra. College Mathematics Journal, 24(1), 41–46.
- Dogan-Dunlap, H. (2010). Linear algebra students’ modes of reasoning: Geometric representations. Linear Algebra and its Applications, 432(8), 2141–2159.
- Dorier, J.-L. (1991). Sur l'enseignement des concepts élémentaires d'algèbre linéaire à l'université [On the teaching of elementary concepts of linear algebra at the university]. Recherches en Didactique des Mathématiques, 11(2/3), 325–364.
- Dorier, J.-L. (1995). Meta level in the teaching of unifying and generalizing concepts in mathematics. Educational Studies in Mathematics, 29(2), 175–197.
- Dorier, J.-L., Robert, A., Robinet, J., & Rogalski, M. (2000). On a research programme concerning the teaching and learning of linear algebra in first year of French science university. International Journal of Mathematical Education in Science and Technology, 31(1), 27–35.
- Dorier, J.-L., & Sierpinska, A. (2001). Research into the teaching and learning of linear algebra. In D. Holton, M. Artigue, U. Krichgraber, J. Hillel, M. Niss, & A. Schoenfeld (Eds.), The teaching and learning of mathematics at university level: An ICMI study (pp. 255–273). Dordrecht, The Netherlands: Kluwer.
- Dubinsky, E., & McDonald, M. (2001). APOS: A constructivist theory of learning in undergrad mathematics education. In D. Holton (Ed.), The teaching and learning of mathematics at university level: An ICMI study (pp. 273–280). Dordrecht, The Netherlands: Kluwer.
- Glaser, B. G., & Strauss, A. L. (1967). The discovery of grounded theory: Strategies for qualitative research. Chicago, IL: Aldine.
- Gol Tabaghi, S., & Sinclair, N. (2013). Using dynamic geometry software to explore eigenvectors: The emergence of dynamic-synthetic-geometric thinking. Technology, Knowledge and Learning, 18(3), 149–164.
- Gueudet-Chartier, G. (2006). Using geometry to teach and learn linear algebra. In F. Hitt, G. Harel, & A. Selden (Eds.), Research in collegiate mathematics education (Vol. 6, pp. 171–195). Washington, DC: American Mathematical Society.
- Harel, G. (1990). Using geometric models and vector arithmetic to teach high-school students basic notions in linear algebra. International Journal for Mathematics Education in Science and Technology, 21(3), 387–392.
- Harel, G. (2000). Principles of learning and teaching mathematics, with particular reference to the learning and teaching of linear algebra: Old and new observations. In J. Dorier (Ed.), On the teaching of linear algebra (pp. 177–189). Dordrecht, The Netherlands: Kluwer.
- Harel, G., & Kaput, J. (1991). The role of conceptual entities in building advanced mathematical concepts and their symbols. In D. Tall (Ed.), Advanced mathematical thinking (pp. 82–94). Dordrecht, The Netherlands: Kluwer.
- Hannah, J., Stewart, S., & Thomas, M. O. J. (2013). Emphasising language and visualization in teaching linear algebra. International Journal of Mathematical Education in Science and Technology, 44(4), 475–489.
- Hillel, J. (2000). Modes of description and the problem of representation in linear algebra. In J. Dorier (Ed.), On the teaching of linear algebra (pp. 191–207). Dordrecht, The Netherlands: Kluwer.
- Kvale, S. (2007). Doing interviews. London, UK: Sage.
- Lapp, D. A., Nyman, M. A., & Berry, L. S. (2010). Student connections of linear algebra concepts: An analysis of concept maps. International Journal of Mathematical Education in Science and Technology, 41(1), 1–18.
- Larson, R. (2013). Elementary linear algebra (7th ed.). Boston, MA: Cengage.
- Parraguez, M., & Oktac, A. (2010). Construction of the vector space concept from the viewpoint of APOS theory. Linear Algebra and Its Applications, 432(8), 2112–2124.
- Patton, M. Q. (2002). Qualitative research and evaluation methods. Thousand Oaks, CA: Sage.
- Piaget, J. (1977). Epistemology and psychology of functions. Dordrecht, The Netherlands: D. Reidel Publishing.
- Sinclair, N., & Gol Tabaghi, S. (2010). Drawing space: Mathematicians’ kinetic conceptions of eigenvectors. Educational Studies in Mathematics, 74(3), 223–240.
- Thomas, M. O. J., & Stewart, S. (2011). Eigenvalues and eigenvectors: Embodied, symbolic and formal thinking. Mathematics Education Research Journal, 23(3), 275–296.
- Wawro, M., Sweeney, G., & Rabin, J. M. (2011). Subspace in linear algebra: Investigating students’ concept images and interactions with the formal definition. Educational Studies in Mathematics, 78(1), 1–19.
- Wawro, M., Rasmussen, C., Zandieh, M., Sweeney, G., & 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.
- 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.