Graphs of functions of two variables: results from the design of instruction

References

• Yerushalmy M. Designing representations: reasoning about functions of two variables. J Res Math Educ. 1997;28:431–466.
   Web of Science ®Google Scholar
• Kabael T. The effects of the function machine on students’ understanding levels and their image and definition for the concept of function. In: Swars SL, Stinson DW, Lemons-Smith S, editors. Proceedings of the 31st Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Atlanta, GA: Georgia State University; 2009. p. 58–64.
   Google Scholar
• Kabael T. Generalizing single variable functions to two-variable functions, function machine and APOS. Kuram ve Uygulamada Egilim Bilimleri [Educ Sci: Theory & Practice]. 2011;11(1):484–499.
   Web of Science ®Google Scholar
• Montiel M, Wilhelmi M, Vidakovic D, Elstak I. Using the onto-semiotic approach to identify and analyze mathematical meaning when transiting between different coordinate systems in a multivariate context. Educ Stud Math. 2009;72:139–160.
   Web of Science ®Google Scholar
• Martínez-Planell R, Trigueros Gaisman M. Students’ ideas on functions of two variables: domain, range, and representations. In: Swars SL, Stinson DW, Lemons-Smith S, editors. Proceedings of the 31st Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Atlanta, GA: Georgia State University; 2009. p. 73–80.
   Google Scholar
• Martínez-Planell R, Trigueros Gaisman M. Students’ understanding of the general notion of a function of two variables. Educ Stud Math. 2012;81(3):365–384.
   Web of Science ®Google Scholar
• Trigueros M, Martínez-Planell R. Visualization and abstraction: geometric representation of functions of two variables. In: Lamberg T, Wiest LR, editors. Proceedings of the 29th Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education. Reno, NV: University of Nevada; 2007. p. 100–107.
   Google Scholar
• Trigueros M, Martínez-Planell R. Geometrical representations in the learning of two variable functions. Educ Stud Math. 2010;73:3–19.
   Web of Science ®Google Scholar
• Trigueros M, Martínez-Planell R. How are graphs of two variable functions taught?. In: Wiest LR, Lamberg T, editors. Proceedings of the 33rd Annual Meeting of the North America Chapter of the International Group for the Psychology of Mathematics Education. Reno, NV: University of Nevada at Reno; 2011. Available from: http://www.allacademic.com/meta/p512583_index.html.
   Google Scholar
• Asiala M, Brown A, DeVries DJ, Dubinsky E, Mathews D, Thomas K. A framework for research and development in undergraduate mathematics education. In: Kaput J, Dubinsky E, Schoenfeld AH, editors. Research in collegiate mathematics education II. Providence, RI: AMS; 1996. p. 1–32.
   Google Scholar
• Dubinsky E. Reflective abstraction in advanced mathematical thinking. In: Tall D, editor. Advanced mathematical thinking. Dordrecht: Kluwer Academic Press; 1991. p. 95–123.
   Google Scholar
• Dubinsky E, McDonald M. APOS: a constructivist theory of learning in undergraduate mathematics education. In: Holton D, editor. The teaching and learning of mathematics at the university level: an ICMI study. Dordrecht: Kluwer Academic Press; 2001. p. 273–280.
   Google Scholar
• Duval R. Representation, vision and visualization: cognitive functions in mathematical thinking. In: Hitt F, Santos M, editors. Proceedings of the XXI Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Columbus, OH: ERIC; 1999. p. 3–26.
   Google Scholar
• Duval R. A cognitive analysis of problems of comprehension in a learning of mathematics. Educ Stud Math. 2006;61:103–131.
   Google Scholar
• McGee D. Visualization tools for 3D Mayaguez, Puerto Rico: University of Puerto Rico at Mayaguez; 2009 [ cited 2013 Mar 9]. Available from: http://quiz.uprm.edu/visual3d/.
   Google Scholar
• Martínez-Planell R, Trigueros Gaisman M. Actividades para el cálculo multivariable [Activities for multivariable calculus]. Mayaguez, Puerto Rico: University of Puerto Rico at Mayaguez; 2012 [ cited 2013 Mar 9]. Available from: http://pegasus.uprm.edu/rmplanell.
   Google Scholar