Coordinated topics as transitional enablers towards higher-level conceptualisations of the range concept

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. https://doi.org/10.1080/0020739X.2016.1276225
   Web of Science ®Google Scholar
• Arnon, I., Cottrill, J., Dubinsky, E., Oktac, A., Fuentes, S. R., Trigueros, M., & Weller, K. (2014). APOS theory: A framework for research and curriculum development in mathematics education. Springer.
   Google Scholar
• Caglayan, G. (2019). Is it a subspace or not? Making sense of subspaces of vector spaces in a technology-assisted learning environment. Journal of ZDM: Mathematics Education, 51(7), 1215–1238. https://doi.org/10.1007/s11858-019-01101-4
   Web of Science ®Google Scholar
• Dogan, H. (2004). Visual instruction of abstract concepts for non-major students. International Journal of Engineering Education, 20(4), 671–676.
   Web of Science ®Google Scholar
• Dogan, H. (2018a). Mental schemes of linear algebra: Visual constructs. In S. Stewart, C. Andrews-Larson, A. Berman, & M. Zandieh (Eds.), Challenges and strategies in teaching linear algebra. ICME-13 Monographs Series Part III (pp. 219–240). Springer.
   Google Scholar
• Dogan, H. (2018b). Differing instructional modalities and cognitive structures: Linear algebra. Linear Algebra and its Applications, 542, 464–483. https://doi.org/10.1016/j.laa.2017.07.007
   Web of Science ®Google Scholar
• Dogan, H. (2019). Some aspects of linear independence schemas. Journal of ZDM: Mathematics Education, 51(7), 1169–1181. https://doi.org/10.1007/s11858-019-01082-4
   Google Scholar
• Dogan, H., Shear, E., Garcia Contreras, F. A., & Hoffman, L. (2022). Linear independence from a perspective of connections. International Journal of Mathematical Education in Science and Technology, 53(1), 190–205. https://doi.org/10.1080/0020739X.2021.1961031
   Web of Science ®Google Scholar
• Dogan-Dunlap, H. (2006). Lack of set theory-relevant prerequisite knowledge. International Journal of Mathematics Education in Science and Technology, 37(4), 401–410. https://doi.org/10.1080/00207390600594853
   Google Scholar
• Dogan-Dunlap, H. (2010). Linear algebra students’ modes of reasoning: Geometric representations. Linear Algebra and Its Applications, 432(8), 2141–2159. https://doi.org/10.1016/j.laa.2009.08.037
   Web of Science ®Google Scholar
• Harel, G. (2018). The learning and teaching of linear algebra through the lenses of intellectual need and epistemological justification and their constituents. In S. Stewart, C. Andrews-Larson, A. Berman, & M. Zandieh (Eds.), Challenges and strategies in teaching linear algebra. ICME-13 Monographs Series Part I (pp. 3–28). Springer.
   Google Scholar
• Harel, G. (2019). Variations in the use of geometry in the teaching of linear algebra. Journal of ZDM: Mathematics Education, 51(7), 1031–1042. https://doi.org/10.1007/s11858-018-01015-7
   Web of Science ®Google Scholar
• Johnson, W. L., Riess, R. D., & Arnold, T. J. (2002). Intro. to linear algebra (5th ed., pp. 15). Pearson Education.
   Google Scholar
• Karakok, G. (2019). Making connections among representations of eigenvector: What sort of a beast is it? Journal of ZDM: Mathematics Education, 51(7), 1141–1152. https://doi.org/10.1007/s11858-019-01061-9
   Web of Science ®Google Scholar
• Oktaç, A. (2019). Mental construction in linear algebra. ZDM: Mathematics Education, 51(1), 1043–1055. https://doi.org/10.1007/s11858-019-01037-9
   Google Scholar
• Oktaç, A., Padilla, R. V., Sandoval, O. R., & Millán, D. V. (2021). Transitional points in constructing the preimage concept in linear algebra. International Journal of Mathematics Education in Science and Technology, 53(5), 1170–1189. https://doi.org/10.1080/0020739X.2021.1968523
   Web of Science ®Google Scholar
• Sierpinska, A. (2000). On some aspects of students’ thinking in linear algebra. In J.-L. Dorier (Ed.), On the teaching of linear algebra (pp. 209–246). Springer.
   Google Scholar
• Stewart, S., Troup, J., & Plaxco, D. (2019). Reflection on teaching linear algebra: Examining one instructor’s movements between the three worlds of mathematical thinking. Journal of ZDM: Mathematics Education, 51(7), 1253–1266. https://doi.org/10.1007/s11858-019-01086-0
   Web of Science ®Google Scholar
• Trigueros, M. (2018). Learning linear algebra using models and conceptual activities. In S. Stewart, C. Andrews-Larson, A. Berman, & M. Zandieh (Eds.), Challenges and strategies in teaching linear algebra. ICME-13 Monographs Series Part I (pp. 29–50). Springer.
   Google Scholar
• Turgut, M. (2019). Sense-making regarding matrix representation of geometric transformations in R2; a semiotic mediation perspective in a dynamic geometry environment. ZDM: Mathematics Education, 51(1), 1199–1214. https://doi.org/10.1007/s11858-019-01032-0
   Google Scholar
• Villabona, D., Camacho, G., Vazquez, R., Ramirez, O., & Oktac, A. (2020, September). Process conception of linear transformations from a functional perspective. In INDRUM 2020, Universite de Carthage, Universite de Montpellier, Cyberspace (virtually from Bizerte), hal-03113850.
   Google Scholar
• Zandieh, M., Ellis, J., & Rasmussen, C. (2017). A characterization of a unified notion of mathematical function: The case of high school function and linear transformation. Educational Studies in Mathematics, 95(1), 21–38. https://doi.org/10.1007/s10649-016-9737-0
   Web of Science ®Google Scholar