Visualization of relationship between a function and Its derivative

Year 2015, Volume: 5 Issue: 1, 205 - 213, 01.04.2015

Karmelita Pjanıć , Edin Lıđan , Admir Kurtanovıć

Abstract

The first and second derivatives of a function provide an enormous amount of useful
information about function itself as well as of the shape of the graph of the function.
Mathematics curriculum in Bosnia and Herzegovina emphasises algebraic representation of
a function ant its derivatives. That implies that concept of a derivative of a function is only
partialy developed. On the other hand, an important skill to develop is that of producing the
graph of the derivative of a function, given the graph of the function and conversely, to
producing the graph of a function, given the graph of its derivative. In this paper we
describe one possibility of enhancing pupils understanding of relationship between function
and its derivative using specially designed Wolfram Mathematica applet. Preliminary results
of implementation of the applet during the topic Examination of functions using its
derivatives, indicate that visualization support better understanding of concept of function
and its derivative.

Keywords

Function, Derivative, Graphical representation

References

• Cunningham, S. (1994). Some strategies for using visualisation in mathematics teaching. Zentralblattfur Didaktik der Mathematik, ZDM, 94 (3), 83-85.
• Eisenberg, T. & Dreyfus, T. (1991). On the reluctance to visualize in mathematics. Visualization in teaching and learning mathematics (Eds: W. Zimmerman & S.
• Cunningham). Washington DC: Mathematical Association of America. pp. 25-37.
• Evangelidou, A., Spyrou, P., Elia, I. & Gagatsis, A. (2004). University students' conceptions of function. Proceedings of the 28th conference of the international group for the psychology of mathematica education Vol 2 (Eds: M. J. Hoines & A. B. Fuglestad). Norway: Bergen University College. pp. 351-358.
• Hadžibegović, Z. & Pjanić, K. (2011). Obrazovanje budućih nastavnika tehničke kulture: razmatranje stupnja uzajamnog integriranja znanja u matematici i fizici. Pedagogija 3/ 2011 God. LXVI, Belgrad, pp. 468-480.
• Hadžibegović, Z. & Pjanić, K. (2011). Studija o rezultatima uzajamnog integriranja znanja u matematici i fizici studenata tehničkog obrazovanja na Univerzitetu u Sarajevu , Naša škola, LVII, 56/226, Sarajevo. pp. 153-170.
• Hitt Espinosa, F. (1997). Researching a problem of convergence with mathematica: history and visualisation of a mathematical idea. International Journal of Mathematical Education in Science and Technology, 28 (5), 697-706.
• Mariotti, M. A. & Pesci, A. (1994). Visualization in teaching - learning situations. Proceedings of PME, 18 (1), 22.
• Mason, J. (1992). Towards a research programme for mental imagery. Proceedings of the November Conference of BSRLM. pp. 24-29.
• Michelsen, C. (2005). Expanding the domain – variables and functions in an interdisciplinary context between mathematics and physics. Proceedings of the 1st International Symposium of Mathematics and its Connections to the Arts and Sciences (Eds: A. Beckmann, C. Michelsen, B. Shriraman). Germany: The University of Education, Schwabisch Gmund. pp. 201-214.
• Pjanić, K. (2011). Pojam funkcije i njegovo razumijevanje – slučaj studenata razredne nastave. Zbornik radova sa Naučnog skupa Nauka i politika. Univerzitet u Istočnom Sarajevu. pp. 131-140.
• Pjanić, K. & Nesimović, S. (2012). Algebarska i grafička reprezentacija pojma funkcije. Zbornik radova sa Naučnog skupa “Nauka i identitet”, Prva matematička konferencija Republike Srpske, Knjiga 6, Tom 3, Univerzitet u Istočnom Sarajevu. pp. 263-269.
• Presmeg, N. (1995). Preference for Visual Methods: An International Study. Proceedings of PME, 19 (3), 58-65.
• Presmeg, N. (1986). Visualisation and mathematical giftedness. Educational Studies in Mathematics, 17, 297-311.
• Sierpinska, A. (1992). On understanding the notion of function. The concept of function: aspects of epistemology and pedagogy (Eds: G. Harel & E. Dubinsky). United States: Mathematical Association of America. pp. 25-58.
• Tall, D. (1991). Intuition and rigour: The role of visualization in the calculus. Visualisation in teaching and learning mathematics (Eds: W. Zimmerman & S. Cunningham). Washington DC: Mathematical Association of America. pp. 105-119.
• Vinner, S. & Dreyfus, T. (1989). Images and definitions for the concept of function, Journal for Research in Mathematics Education, 20 (4), 356-366.
• Zimmerman, W. & Cunningham, S. (1991). What is mathematical visualisation? Visualisation in teaching and learning mathematics (Eds: W. Zimmerman & S. Cunningham). Washington DC: Mathematical Association of America. pp. 1-9.