Abstract
The function is a special kind of dependence, that is, between variables which are distinguished as dependent and independent. (…) This – old fashioned – definition stresses the phenomenologically important element: the directedness from something that varies freely to something that varies under constraint. (Freudenthal, 1983, p. 496).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abels, M. (1996). A shift in algebra, development and implementation: varia-abilities. In M. Kindt, M. Abels & L.M. Doorman (Eds.), Working group 13: Curriculum changes in the secondary school (pp. 3-7). Utrecht: Freudenthal Instituut.
Beth, H.J.E. (1928). Het experimenteel georiënteerde onderwijs in mechanica. [Experiment-oriented mechanics education.] Euclides 5, 49-60.
Boon, P., Doorman, M., Drijvers, P., & Gisbergen, S. van (2008). Pijlenketting en functie. Een experimentele lessenserie over functies met het applet AlgebraPijlen voor klas 2 h/v. [Arrow chain and function. An experimental lesson sequence on function using the applet AlgebraArrows for grade 8]. Retrieved April, 16th, 2010, from http://www.fi.uu.nl/tooluse/en.
Doorman, L.M., & Gravemeijer, K.P.E. (2009). Emergent modeling: discrete graphs to support the understanding of change and velocity. ZDM The International Journal on Mathematics Education 41(1), 199-211.
Doorman, L.M. & Maanen, J. van (2008). A historical perspective on teaching and learning calculus. Australian Senior Mathematics Journal, 22(2), 4-14.
Drijvers, P., Doorman, M., Boon, P., Gisbergen, S. van, & Gravemeijer, K. (2007). Tool use in a technology- rich learning arrangement for the concept of function. In D. Pitta-Pantazi & G. Philippou (Eds.), Proceedings of the V Congress of the European Society for Research in Mathematics Education CERME5 (pp. 1389-1398). Larnaca, Cyprus: University of Cyprus.
Drijvers, P., & Kindt, M. (1998). Differentiaal- en Integraalrekening deel 6: Trillingspatronen. [Differential and integral calculus: oscillation patterns.] Utrecht: Freudenthal Instituut. Retrieved April, 19th, from http://www.fi.uu.nl/wiki/index.php/Profi.
Eves, H. (1990). Foundations and Fundamental Concepts of Mathematics, Third Edition. Mineola, NY: Dover.
Freudenthal, H. (1983).Didactical phenomenology of mathematical structures. Dordrecht, the Netherlands: Reidel.
Janvier, C. (1987). Problems of Representation in the Teaching and Learning Mathematics. Hillsdale NJ: Lawrence Erlbaum Associates.
Janvier, C. (1996). Modelling and Initiation into Algebra. In N. Bednarz, C. Kieran & L. Lee (Eds.), Approaches to Algebra: Perspectives for Research and Teaching (pp. 225-236), Dordrecht: Kluwer Academic Publishers.
Kaput, J.J. (1994). Democratizing Access to Calculus: New Routes to Old Roots. In A.H. Schoenfeld (Ed.), Mathematical Thinking and Problem Solving (pp. 77-156). Washington: Mathematical Association of America.
Kindt, M. (1997). Som en verschil, afstand en snelheid. [Sum and difference, distance and speed]. Utrecht, the Netherlands; Freudenthal Institute.
Oehrtman, M.C., Carlson, M.P., & Thompson, P.W. (2008). Foundational Reasoning Abilities that Promote Coherence in Student’s Function Understanding. 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. Retrieved April, 2nd, fromhttp://www.mathed.asu.edu/media/pdf/pubs/carlson/Oehrtman-Carlson-Thompson_final.pdfPence, B.J. (1995). Relationships between understandings of operations and success in beginning calculus. Paper presented at the North American chapter of the PME, Columbus, Ohio.
Ponce, G. (2007). Critical Juncture Ahead: Proceed with Caution to Introduce the Concept of Function. Mathematics Teacher, 101(2), 136-144.
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://www.math.coe.uga.edu/TME/Issues/v03n2/v3n2.html.
Schoenfeld, A. (2004). The math wars. Educational policy, 18(1), 253-286.
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.
Streun, A. van (2000). Representations in applying functions. International Journal of Mathematical Education in Science and Technology, 31(5), 703-725.
Swan, M. (2008). A Designer Speaks. Educational Designer, 1. Retrieved October, 22nd, 2009
from http://www.educationaldesigner.org/ed/volume1/issue1/article3.
Team W12-16 (1992). Achtergronden van het nieuwe leerplan. Wiskunde 12-16: band 1. [Backgrounds of the new curriculum Math12-16, Vol. I.] Utrecht / Enschede, the Netherlands: Freudenthal Instituut & Stichting LeerplanOntwikkeling.
Vinner, S., & Dreyfuss, T. (1989). Images and definitions for the concept of function. Journal for Research in Mathematics Education, 20(4), 356-366.
Wisconsin Center for Education Research & Freudenthal Institute (Eds.) (2006). Mathematics in context. Chicago: Encyclopaedia Britannica.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Sense Publishers
About this chapter
Cite this chapter
Doorman, M., Drijvers, P. (2011). Algebra in Function. In: Drijvers, P. (eds) Secondary Algebra Education. SensePublishers. https://doi.org/10.1007/978-94-6091-334-1_6
Download citation
DOI: https://doi.org/10.1007/978-94-6091-334-1_6
Publisher Name: SensePublishers
Online ISBN: 978-94-6091-334-1
eBook Packages: Humanities, Social Sciences and LawEducation (R0)
