Linear independence from a perspective of connections

References

• Altieri, M., & Schirmer, E. (2019). Learning the concept of eigenvalues and eigenvectors: A comparative analysis of achieved concept construction in linear algebra using APOS theory among students from different educational backgrounds. Journal of ZDM: Mathematics Education. Springer, 51(7), 1125–1140. https://doi.org/https://doi.org/10.1007/s11858-019-01074-4
   Web of Science ®Google Scholar
• Dogan, H. (2004). Visual instruction of abstract concepts for non-major students. International Journal of Engineering Education, 2, 671.
   Google Scholar
• Dogan, H. (2006). Lack of Set Theory-Relevant Prerequisite Knowledge. International Journal of Mathematics Education in Science and Technology, 37, 41–41.
   Google Scholar
• Dogan-Dunlap, H. (2010). Linear Algebra students' modes of reasoning: Geometric Representations. Linear Algebra and Its Applications, 432, 2141–2159.
   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. (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.
   Google Scholar
• Dogan, H. (2019). Some aspects of linear independence schemas. In S. Stewat, C. Andrews-Larson, & M. Zandieh (Eds.), Research on teaching and learning in linear algebra. Springer Journal of ZDM: Mathematics Education, 51(7), 1169–1181.
   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. doi:https://doi.org/10.1007/s11858-019-01101-4
   Web of Science ®Google Scholar
• Dorier, J., Robert, A., Robinet, J., & Rogalski, M. (2000). The obstacle of formalism in linear algebra. In J.-L. Dorier (Ed.), On the teaching of linear algebra, mathematics education library, vol.23 (pp. 85–124). Kluwer Academic Publishers.
   Google Scholar
• Dorier, J., & Sierpinska, A. (2001). Research into the teaching and learning of linear algebra. In D. Holton (Ed.), The teaching and learning of mathematics of university level (pp. 255–273). Kluwer Academic Publishers.
   Google Scholar
• Glaser, B. (1992). Emergence vs. forcing: Basics of grounded theory analysis. Sociology Press.
   Google Scholar
• Harel, G. (1997). The linear algebra curriculum study group recommendations: Moving beyond concept definition. Resources for Teaching Linear Algebra, MAA Notes, 42, 107–126.
   Google Scholar
• Harel, G. (2000). Principles of learning and teaching mathematics, with particular reference to the learning and teaching of linear algebra. In J. Dorier (Ed.), On the teaching of linear algebra (pp. 177–189). Kluwer.
   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/https://doi.org/10.1007/s11858-018-01015-7
   Web of Science ®Google Scholar
• Hillel, J. (2000). Modes of description and the problem of representation in linear algebra. In J.-L. Dorier (Ed.), On the teaching of linear algebra (pp. 191–207). Kluwer.
   Google Scholar
• Johnson, W. L., Riess, D. R., & Arnold, T. J. (2002). Introduction to linear algebra. 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/https://doi.org/10.1007/s11858-019-01061-9
   Web of Science ®Google Scholar
• Kazunga, C., & Bansilal, S. (2018). Misconceptions about determinants. In S. Stewart, C. Andrews-Larson, A. Berman, & M. Zandieh (Eds.), Challenges and strategies in teaching linear algebra. ICME-13 monographs series part II (pp. 127–146). Springer.
   Google Scholar
• Oktac, A. (2019). Mental constructions in linear algebra. Journal of ZDM: Mathematics Education, 51(7), 1043–1054. doi:https://doi.org/10.1007/s11858-019-01037-9
   Web of Science ®Google Scholar
• Payton, S. (2019). Fostering mathematical connections in introductory linear algebra through adapted inquiry. Journal of ZDM: Mathematics Education, 51(7), 1239–1252. https://doi.org/https://doi.org/10.1007/s11858-019-01029-9
   Web of Science ®Google Scholar
• Selinski, E. N., Rasmussen, C., Wawro, M., & Zandieh, M. (2014). A method for using adjacency matrices to analyze the connections students make within and between concepts: The case of linear algebra. Journal for Research in Mathematics Education, 45(5), 550–583. https://doi.org/https://doi.org/10.5951/jresematheduc.45.5.0550
   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). Kluwer Academic Publishers.
   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/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 inR2: A semiotic mediation perspective in a dynamic geometry environment. Journal of ZDM: Mathematics Education, 51(7), 1199–1214. https://doi.org/https://doi.org/10.1007/s11858-019-01032-0
   Web of Science ®Google Scholar
• Wawro, M. (2014). Student reasoning about the invertible matrix theorem in linear algebra. ZDM Mathematics Education, 46(3), 389–406. doi:https://doi.org/10.1007/s11858-014-0579-x
   Google Scholar
• Zandieh, M., Adiredja, A., & Knapp, J. (2019). Exploring everyday examples to explain basis: Insights into student understanding from students in Germany. Journal of ZDM: Mathematics Education. Springer, 51(7), 1153–1168. https://doi.org/https://doi.org/10.1007/s11858-019-01033-z
   Web of Science ®Google Scholar