Ainley, J., Bills, L. & Wilson, K. E. (2005). Designing spreadsheet-based tasks for purposeful algebra. International Journal of Computers for Mathematical Learning, 10
(3), 191–215.CrossRefGoogle Scholar
Akkus, R., Hand, B. & Seymour, J. (2008). Understanding students’ understanding of functions. Mathematics Teaching, 207
, 10–13.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
, 245–274.CrossRefGoogle Scholar
Bereiter, C. (1985). Towards a solution of the learning paradox. Review of Educational Research, 55
(2), 201–226.Google Scholar
Bloch, I. (2003). Teaching functions in a graphic milieu: What forms of knowledge enable students to conjecture and prove? Educational Studies in Mathematics, 52
(1), 3–28.CrossRefGoogle Scholar
Boon, P. (2008). AlgebraArrows
. Retrieved at June 9th, 2008, from http://www.fi.uu.nl/wisweb/en/welcome.html
Breidenbach, D., Dubinsky, E., Hawks, J. & Nichols, D. (1992). Development of the process conception of function. Educational Studies in Mathematics, 23
, 247–285.CrossRefGoogle Scholar
Carlson, M., Jacobs, S., Coe, E., Larsen, S. & Hsu, E. (2002). Applying covariational reasoning while modeling dynamic events: A framework and a study. Journal for Research in Mathematics Education, 33
, 352–378.CrossRefGoogle Scholar
Cobb, P. (2002). Reasoning with tools and inscriptions. The Journal of the Learning Sciences, 11
(2&3), 187–215.Google Scholar
Cobb, P. & Yackel, E. (1996). Constructivist, emergent, and sociocultural perspectives in the context of developmental research. Educational Psychologist, 31 (3/4), 175–190.
Doorman, L. M. & Gravemeijer, K. P. E. (2009). Emergent modeling: discrete graphs to support the understanding of change and velocity. ZDM-International Journal on Mathematics Education, 41, 199–211.
Drijvers, P., Doorman, M., Boon, P., Van Gisbergen, S. & Gravemeijer, K. (2007). Tool use in a technology-rich learning arrangement for the concept of function. In Pitta-Pantazi, D., & Philippou, G., Proceedings of CERME 5, 1389–1398.
Dubinsky, E. (1991). Reflective abstraction in advanced mathematical thinking. In D. O. Tall (Ed.), Advanced mathematical thinking
(pp. 95–123). Dordrecht: Kluwer.Google Scholar
Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61
, 103–131.CrossRefGoogle Scholar
Elia, I., Panaoura, A., Eracleous, A. & Gagatsis, A. (2007). Relations between secondary pupils’ conceptions about functions and problem solving in different representations. International Journal of Science and Mathematics Education, 5
, 533–556.CrossRefGoogle Scholar
Even, R. (1998). Factors involved in linking representations of functions. The Journal of Mathematical Behavior, 17
, 105–121.CrossRefGoogle Scholar
Falcade, R., Laborde, C. & Mariotti, M. A. (2007). Approaching functions: Cabri tools as instruments of semiotic mediation. Educational Studies in Mathematics, 66
, 317–333.CrossRefGoogle Scholar
Freudenthal, H. (1983). Didactical phenomenology of mathematical structures
. The Netherlands: Reidel: Dordrecht.Google Scholar
Freudenthal, H. (1991). Revisiting mathematics education—China lectures
. Dordrecht: Kluwer Academic Publishers.Google Scholar
Gravemeijer, K. (1999). How emergent models may foster the constitution of formal mathematics. Mathematical Thinking and Learning, 1, 155–177.
Gravemeijer, K. (2007). Emergent modelling as a precursor to mathematical modelling. In W. Blum, P. L. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education. The 14th ICMI Study (pp 137–144). New York: Springer.
Gravemeijer, K. P. E., Lehrer, R., van Oers, B., & Verschaffel, L. (Eds.). (2002). Symbolizing, modeling and tool use in mathematics education. Dordrecht, the Netherlands: Kluwer Academic Publishers.
Gravemeijer, K., & Cobb, P. (2006). Design research from the learning design perspective. In J. van den Akker, K. Gravemeijer, S. McKenney, & N. Nieveen (Eds.), Educational design research (pp. 17–51). London: Routledge.
Hennessy, S., Ruthven, K. & Brindley, S. (2005). Teacher perspectives on integrating ICT into subject teaching: commitment, constraints, caution and change. Journal of Curriculum Studies, 37(2), 155–192.
Hoyles, C. & Noss, R. (2003). What can digital technologies take from and bring to research in mathematics education? In A. J. Bishop, M. A. Clements, C. Keitel, J. Kilpatrick & F. K. S. Leung (Eds.), Second international handbook of mathematics education
(pp. 323–349). Dordrecht: Kluwer Academic Publishers.CrossRefGoogle Scholar
Janvier, C. (1987). Translation processes in mathematics education. In C. Janvier (Ed.), Problems of representation in teaching and learning mathematics
(pp. 27–32). Hillsdale: Lawrence Erlbaum Associates.Google Scholar
Kalchman, M. & Koedinger, K. (2005). Teaching and learning functions. In S. Donovan & J. Bransford (Eds.), How students learn mathematics
(pp. 351–392). Washington DC: National Academy of Sciences.Google Scholar
Kaput, J. & Schorr, R. (2007). Changing representational infrastructures changes most everything: The case of SimCalc, algebra and calculus. In G. W. Blume & M. K. Heid (Eds.), Research on technology and the learning and teaching of mathematics: Vol. 2 cases and perspectives
(pp. 211–253). Charlotte: Information Age Publishing.Google Scholar
Kuchemann, D. (1981). Algebra. In K. Hart (Ed.), Children’s understanding of mathematics:11–16 (pp. 102–119). London: Murray.
Lehrer, R. & Schauble, L. (2002). Symbolic communication in mathematics and science: Constituting inscription and thought. In E. D. Amsel & J. Byrnes (Eds.), Language, literacy, and cognitive development. The development and consequences of symbolic communication. (pp. 167–192). Mahwah, NJ: Lawrence Erlbaum Associates.
Malle, G. (2000). Zwei Aspekte von Funktionen: Zuordnung und Kovariation. Mathematik Lehren, 103, 8–11.
Meel, D. (1998). Honors students’ calculus understandings: Comparing Calculus&Mathematica and traditional calculus students. In Shoenfeld, A., J. Kaput, & E. Dubinsky (Eds.) CBMS Issues in Mathematics Education 7: Research in Collegiate Mathematics Education III. pp. 163–215.
Meira, L. (1995). The microevolution of mathematical representations in children’s activity. Cognition and Instruction, 13
, 269–313.CrossRefGoogle Scholar
Oehrtman, M. C., Carlson, M. P. & Thompson, P. W. (2008). Foundational reasoning abilities that promote coherence in students’ understandings of function. In M. P. Carlson & C. Rasmussen (Eds.), Making the connection: Research and practice in undergraduate mathematics
(pp. 27–42). Washington DC: Mathematical Association of America.CrossRefGoogle Scholar
Pirie, S. E. B. & Kieren, T. E. (1989). A recursive theory of mathematical understanding. For the Learning of Mathematics, 9
(3), 7–11.Google Scholar
Ponce, G. (2007). Critical juncture ahead: Proceed with caution to introduce the concept of function. Mathematics Teacher, 101
(2), 136–144.Google Scholar
Ponte, J.P. (1992). The history of the concept of function and some educational implications. The Mathematics Educator, 3
(2), 3–8. Retrieved April, 2nd, from http://math.coe.uga.edu/TME/Issues/v03n2/v3n2.html
Rasmussen, C. & Blumenfeld, H. (2007). Reinventing solutions to systems of linear differential equations: A case of emergent models involving analytic expressions. The Journal of Mathematical Behavior, 26
, 195–210.CrossRefGoogle Scholar
Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22
, 1–36.CrossRefGoogle Scholar
Sfard, A. & McClain, K. (2002). Special issue: Analyzing tools: Perspective on the role of designed artifacts in mathematics learning. The Journal of the Learning Sciences, 11
, 153–388.Google Scholar
Sherin, M. G. (2002). A balancing act: Developing a discourse community in a mathematics community. Journal of Mathematics Teacher Education, 5
, 205–233.CrossRefGoogle Scholar
Skaja, M. (2003). A secondary school student’s understanding of the concept of function—A case study. Educational Studies in Mathematics, 53
(3), 229–254.CrossRefGoogle Scholar
Slavit, D. (1997). An alternate route to the reification of function. Educational Studies in Mathematics, 33
, 259–281.CrossRefGoogle Scholar
Stein, M. K., Engle, R. A., Smith, M. S. & Hughes, E. K. (2008). Orchestrating productive mathematical discussions: Five practices for helping teachers move beyond show and tell. Mathematical Thinking and Learning, 10
(4), 313–340.CrossRefGoogle Scholar
Tall, D. (1996). Functions and calculus. In A. J. Bishop, K. Clements, C. Keitel, J. Kilpatrick & C. Laborde (Eds.), International handbook on mathematics education
(pp. 289–325). Dordrecht: Kluwer Academic Publishers.Google Scholar
Trouche, L. (2004). Managing complexity of human/machine interactions in computerized learning environments: Guiding students’ command process through instrumental orchestrations. International Journal of Computers for Mathematical Learning, 9
, 281–307.CrossRefGoogle Scholar
van den Heuvel-Panhuizen, M. H. A. M. (2003). The learning paradox and the learning miracle: Thoughts on primary school mathematics education. ZDM-International Journal on Mathematics Education, 24
, 96–121.Google Scholar
van Nes, F. T. & Doorman, L. M. (2010). The interaction between multimedia data analysis and theory development in design research. Mathematics Education Research Journal 22(1), 6–30.
Vinner, S. & Dreyfuss, T. (1989). Images and definitions for the concept of function. Journal for Research in Mathematics Education, 20
(4), 356–366.CrossRefGoogle Scholar
Vygotsky, L. S. (1986). Thought and language—Rev’d edition
. Cambridge: A. Kozulin. The MIT Press.Google Scholar
Wertsch, J. V. (1998). Mind as action
. New York: Oxford University Press.Google Scholar