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 ScholarAkkus, R., Hand, B. & Seymour, J. (2008). Understanding students’ understanding of functions.

*Mathematics Teaching, 207*, 10–13.

Google ScholarArtigue, 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 ScholarBereiter, C. (1985). Towards a solution of the learning paradox.

*Review of Educational Research, 55*(2), 201–226.

Google ScholarBloch, 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 ScholarBoon, 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 ScholarCarlson, 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 ScholarCobb, P. (2002). Reasoning with tools and inscriptions.

*The Journal of the Learning Sciences, 11*(2&3), 187–215.

Google ScholarCobb, 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., P*roceedings 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 ScholarDuval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics.

*Educational Studies in Mathematics, 61*, 103–131.

CrossRefGoogle ScholarElia, 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 ScholarEven, R. (1998). Factors involved in linking representations of functions.

*The Journal of Mathematical Behavior, 17*, 105–121.

CrossRefGoogle ScholarFalcade, R., Laborde, C. & Mariotti, M. A. (2007). Approaching functions: Cabri tools as instruments of semiotic mediation.

*Educational Studies in Mathematics, 66*, 317–333.

CrossRefGoogle ScholarFreudenthal, H. (1983).

*Didactical phenomenology of mathematical structures*. The Netherlands: Reidel: Dordrecht.

Google ScholarFreudenthal, H. (1991).

*Revisiting mathematics education—China lectures*. Dordrecht: Kluwer Academic Publishers.

Google ScholarGravemeijer, 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 ScholarJanvier, 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 ScholarKalchman, 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 ScholarKaput, 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 ScholarKuchemann, 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 ScholarOehrtman, 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 ScholarPirie, S. E. B. & Kieren, T. E. (1989). A recursive theory of mathematical understanding.

*For the Learning of Mathematics, 9*(3), 7–11.

Google ScholarPonce, G. (2007). Critical juncture ahead: Proceed with caution to introduce the concept of function.

*Mathematics Teacher, 101*(2), 136–144.

Google ScholarPonte, 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 ScholarSfard, 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 ScholarSfard, 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 ScholarSherin, M. G. (2002). A balancing act: Developing a discourse community in a mathematics community.

*Journal of Mathematics Teacher Education, 5*, 205–233.

CrossRefGoogle ScholarSkaja, 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 ScholarSlavit, D. (1997). An alternate route to the reification of function.

*Educational Studies in Mathematics, 33*, 259–281.

CrossRefGoogle ScholarStein, 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 ScholarTall, 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 ScholarTrouche, 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 Scholarvan 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 Scholarvan 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 ScholarVygotsky, L. S. (1986).

*Thought and language—Rev’d edition*. Cambridge: A. Kozulin. The MIT Press.

Google ScholarWertsch, J. V. (1998).

*Mind as action*. New York: Oxford University Press.

Google Scholar