Learning two-variable functions using 3D dynamic geometry

References

• Alves, F. R. V. (2012). Transição interna do Cálculo:uma discussão do uso do GeoGebra no contexto do Cálculo a Várias Variáveis [Internal calculation transition: A discussion of the use of GeoGebra in the context of calculus of several variables]. Revista Do Instituto GeoGebra de São Paulo, 1(2), 5–19.
   Google Scholar
• Arnon, I., Cottrill, J., Dubinsky, E., Oktaç, A., Roa Fuentes, S., Trigueros, M., & Weller, K. (2014). APOS theory: A framework for research and curriculum development in mathematics education. Springer. https://doi.org/10.1007/978-1-4614-7966-6
   Google Scholar
• Artigue, M. (2002). Learning mathematics in a CAS environment: The genesis of a reflection about instrumentation and the dialectics between technical and conceptual work. International Journal of Computers for Mathematical Learning, 7(3), 245–274. https://doi.org/10.1023/A:1022103903080
   Google Scholar
• Artigue, M., & Trouche, L. (2021). Revisiting the French didactic tradition through technological lenses. Mathematics, 9(6), 629. https://doi.org/10.3390/math9060629
   Web of Science ®Google Scholar
• Borji, V., Martínez-Planell, R., & Trigueros, M. (2022). Student understanding of functions of two variables: A reproducibility study. The Journal of Mathematical Behavior, 66, Article 100950. https://doi.org/10.1016/j.jmathb.2022.100950
   Web of Science ®Google Scholar
• Buteau, C., Muller, E., Mgombelo, J., Sacristán, A. I., & Dreise, K. (2020). Instrumental genesis stages of programming for mathematical work. Digital Experiences in Mathematics Education, 6(3), 367–390. https://doi.org/10.1007/s40751-020-00060-w
   Google Scholar
• Cuevas-Vallejo, A., Orozco-Santiago, J., & Paz-Rodríguez, S. (2023). A learning trajectory for university students regarding the concept of vector. Journal of Mathematical Behavior, 70, Article 101044. https://doi.org/10.1016/j.jmathb.2023.101044
   Web of Science ®Google Scholar
• Dorko, A., & Weber, E. (2014). Generalising calculus ideas from two dimensions to three: How multivariable calculus students think about domain and range. Research in Mathematics Education, 16(3), 269–287. https://doi.org/10.1080/14794802.2014.919873
   Google Scholar
• Hughes, J. (2005). The role of teacher knowledge and learning experiences in forming technology-integrated pedagogy. Journal of Technology and Teacher Education, 13(2), 277–302. Retrieved March 17, 2023, from https://www.learntechlib.org/primary/p/26105/
   Google Scholar
• Martínez-Planell, R., & Gaisman, M. T. (2013). Graphs of functions of two variables: Results from the design of instruction. International Journal of Mathematical Education in Science and Technology, 44(5), 663–672. https://doi.org/10.1080/0020739X.2013.780214
   Google Scholar
• Martínez-Planell, R., & Trigueros, M. (2012). Students’ understanding of the general notion of a function of two variables. Educational Studies in Mathematics, 81(3), 365–384. https://doi.org/10.1007/s10649-012-9408-8
   Web of Science ®Google Scholar
• Martínez-Planell, R., & Trigueros, M. (2019). Using cycles of research in APOS: The case of functions of two variables. Journal of Mathematical Behavior, 55, Article 100687. https://doi.org/10.1016/j.jmathb.2019.01.003
   Web of Science ®Google Scholar
• Martínez-Planell, R., & Trigueros, M. (2021). Multivariable calculus results in different countries. ZDM – Mathematics Education, 53(3), 695–707. https://doi.org/10.1007/s11858-021-01233-6
   Google Scholar
• Rabardel, P. (2002). People and technology: A cognitive approach to contemporary instruments. Armand Colin. https://hal.science/hal-01020705v1
   Google Scholar
• Rojas Flórez, L. C., Mejía Velasco, H. R., & Esteban Duarte, P. V. (2019). Conceptualización de la derivada direccional a partir de la pendiente de una recta en el espacio [Conceptualization of directional derivative as the slope of a line in space]. El Cálculo y su enseñanza, 12(1), 13–26. https://doi.org/10.61174/recacym.v12i1.31
   Google Scholar
• Roschelle, J., Noss, R., Blikstein, P., & Jackiw, N. (2017). Technology for learning mathematics. In J. Cai (Ed.), Compendium for research in mathematics education (pp. 853–876). National Council of Teachers of Mathematics.
   Google Scholar
• Şefik, Ö., & Dost, Ş. (2019). The analysis of the understanding of the three-dimensional (Euclidian) space and the two-variable function concept by university students. Journal of Mathematical Behavior, 57(1), 100697. https://doi.org/10.1016/j.jmathb.2019.03.004
   Google Scholar
• Soury-Lavergne, S. (2020). La géométrie dynamique pour l’apprentissage et l’enseignement des mathématiques [Dynamic geometry for learning and teaching mathematics]. Cnesco. https://hal.science/hal-03853287/
   Google Scholar
• Trigueros, M., & Martínez-Planell, R. (2010). Geometrical representations in the learning of two-variable functions. Educational Studies in Mathematics, 73(1), 3–19. https://doi.org/10.1007/s10649-009-9201-5
   Web of Science ®Google Scholar
• Trouche, L. (2004). Managing the complexity of human/machine interactions in computerized learning environments: Guiding students’ command process through instrumental orchestrations. International Journal of Computers for Mathematical Learning, 9(3), 281–307. https://doi.org/10.1007/s10758-004-3468-5
   Google Scholar
• Vergnaud, G. (1998). Towards a cognitive theory of practice. In A. Sierpinska & J. Kilpatrick (Eds.), Mathematics education as a research domain: A search for identity (pp. 227–240). Springer. https://doi.org/10.1007/978-94-011-5194-8_15
   Google Scholar
• Weber, E., & Thompson, P. W. (2014). Students’ images of two-variable functions and their graphs. Educational Studies in Mathematics, 87(1), 67–85. https://doi.org/10.1007/s10649-014-9548-0
   Web of Science ®Google Scholar