Advertisement

What Is Or What Might Be the Benefit of Using Computer Algebra Systems in the Learning and Teaching of Calculus?

  • Hans-Georg WeigandEmail author
Chapter
Part of the Mathematics Education in the Digital Era book series (MEDE, volume 9)

Abstract

Advantages and disadvantages of the use of Digital Technologies (DT) and especially of Computer Algebra Systems (CAS) in mathematics lessons are worldwide discussed controversially. Many empirical studies show the benefit of the use of DT in classrooms and there are also many useful examples concerning their use. However, despite these inspiring results and the countless ideas, classroom suggestions, lesson plans and research reports, the use of DT—and especially CAS—has not succeeded, as many had expected during the last decades see Hoyles & Lagrange, (2010). The thesis of this article is that we have not been able to convince teachers, lecturers at university and parents of the benefit of CAS in the classrooms in a sufficient way. What are the arguments that justify the use of CAS in the classroom? The article gives examples of a fruitful use of CAS with regard to the generally accepted goals or standards of mathematics education—like fostering students’ abilities in problem solving, modelling, proving or communicating—and to the subjects taught in high school. The basis of the argumentation is a competence model which classifies the relation between contents or topics: sequences and limits, functions and equations; representations of DT or CAS: static isolated, static multiple, dynamic isolated and dynamic multiple representations; and classroom activities: calculate, consult, control, communicate and discover.

References

  1. Ainsworth, S. (1999). The functions of multiple representations. Computers & Education, 33, 131–152.CrossRefGoogle Scholar
  2. Aldon, G., Artigue, M., Bardini, C., & Trouche, L. (Eds.). (2008). Une étude sur la conception et les usages didactiques d’une nouvelle plate-forme mathématique, potentialité, complexité. http://educmath.inrp.fr/Educmath/dossier-parutions/experimentation-collaborative-de-laboratoires-mathematiques. Accessed May 29, 2016.
  3. 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
  4. Bauer A. (2013). Reasoning with multiple and dynamic representations. In E. Faggione & A. Montone (Eds.), Proceedings of the ICTMT 11, Bari. (pp. 327–329). http://www.dm.uniba.it/ictmt11/download/ICTMT11_Proceedings.pdf
  5. Clark-Wilson, A. (2008). Evaluating TI-Nspire in secondary mathematics classrooms. Chichester: The Mathematics Centre of University of Chichester. Research report. www.chiuni.ac.uk. Accessed May 29, 2016.
  6. Drijvers, P. et.al. (2010). Integrating technology into mathematics education: Theoretical perspectives. In C. Hoyles & B. Lagrange (Eds.), Mathematics education and technology-rethinking the terrain. The 17th ICMI study (pp. 89–132). Dordrecht: Springer.Google Scholar
  7. Drijvers, P., & Weigand, H.-G. (Eds.). (2010). Handheld technology in the mathematics classroom—theory and practice. ZDMThe International Journal on Mathematics Education, (7).Google Scholar
  8. Guin, D., Ruthven, K., & Trouche, L. (Eds.). (2005). The didactical challenge of symbolic calculators. New York: Springer.Google Scholar
  9. Hoyles, C., & Lagrange, J.-B. (Eds.). (2010). Mathematics education and technology—Rethinking the terrain. The 17th ICMI Study. New York: Springer.Google Scholar
  10. Ingelmann, M., & Bruder, R (2007). Appropriate CAS-use in class 7 and 8. In J.-H. Woo et al. (Ed.), Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education. PME. Seoul: The Korea Society of Educational Studies in Mathematics.Google Scholar
  11. Kieran, C., & Drijvers, P. (2006). The Co-emergence of machine techniques, paper-and-pencil techniques, and theoretical reflection, A study of CAS use in secondary school algebra. International Journal of Computers for Mathematical Learning, 11, 205–263.CrossRefGoogle Scholar
  12. Kultusministerkonferenz (KMK). (2004). Bildungsstandards im Fach Mathematik für den mittleren Schulabschluss. München: Wolters Kluwer.Google Scholar
  13. Kultusministerkonferenz (KMK). (2012). Bildungsstandards im Fach Mathematik für die Allgemeine Hochschulreife. München: Wolters Kluwer.Google Scholar
  14. Ng, O.-L. (2016). Comparing calculus communication across static and dynamic environments using a multimodal approach. Digital Experiences in Mathematics Education, 1–27.Google Scholar
  15. Niss, M. (2004). Mathematical competencies and the learning of mathematics: The Danish KOM project. In A. Gagtsis & S. Papastavridis (Eds.), 3rd Mediterranean Conference on mathematical education, 3–5 January 2003, Athens, Greece (pp. 115–124). Athens: The Hellenic mathematical society, 2003.Google Scholar
  16. OECD: Organisation for Economic Co-operation and Development (Ed.). (1999). Measuring student knowledge and skills. A new framework for assessment. Paris: OECD Publication Service. http://www.pisa.oecd.org, http://www.pisa.oecd.org/document/58/0,2340,en_32252351_32236159_33688954_1_1_1_1,00.html
  17. OECD: Organisation for Economic Co-operation and Development (Ed.). (2003). The PISA 2003 Assessment frmework: Mathematics, reading, science and problem solving knowledge and skills. Paris: OECD Publication Service. http://www.pisa.oecd.org, http://www.pisa.oecd.org/document/29/0,3343,en_32252351_32236173_33694301_1_1_1_1,00.html
  18. Pierce, R., & Stacey, K. (2004). A framework for monitoring progress and planning teaching towards the effective use of computer algebra systems. International Journal of Computers for Mathematical Learning, 9, 59–93.CrossRefGoogle Scholar
  19. Tonisson, E. (2015). Differences between expected answers and the answers given by computer algebra systems to school equations. The International Journal for Technology in Mathematics Education, 22(2), 71–77.Google Scholar
  20. Vollrath, H.-J. (1989). Funktionales Denken. Journal für Mathematikdidaktik, 10, 3–37.CrossRefGoogle Scholar
  21. Weigand, H.-G. (2008). Teaching with a symbolic calculator in 10th grade—Evaluation of a one year project. International Journal for Technology in Mathematics Education, 15(1), 19–32.Google Scholar
  22. Weigand, H.-G. (2010). Book review of C. Hoyles & J.-B. Lagrange (Eds.). (2010). Mathematics education and technology—Rethinking the terrain. The 17th ICMI Study, Springer: New York. ZDM—The International Journal on Mathematics Education 42(7), 801–808.Google Scholar
  23. Weigand, H.-G., & Bichler, E. (2010a). Towards a competence model for the use of symbolic calculators in mathematics lessons—The case of functions. ZDM—The International Journal on Mathematics Education, 42(7), 697–713.CrossRefGoogle Scholar
  24. Weigand, H.-G., & Bichler, E. (2010b). Symbolic calculators in mathematics lessons—The case of calculus. International Journal for Technology in Mathematics Education, 17(1), 3–15.Google Scholar
  25. Weigand, H.-G., & Bichler, E. (2010c). The long-term project “Integration of symbolic calculator in mathematics lessons”—The case of Calculus. In V. Durand-Guerrier, S. Soury-Lavergne, & F. Arzarello (Eds.), Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education. 2009, Lyon (France) (pp. 1191–1200). http://ife.ens-lyon.fr/publications/edition-electronique/cerme6/wg7-15-weigand-bichler.pdf
  26. Weigand, H.-G. (2013). Looking back and flashing ahead—Didactical implications for the use of digital technologies in the next decade. In E. Faggione & A. Montone (Eds.), Proceedings of the ICTMT 11, Bari (pp. 298–303). http://www.dm.uniba.it/ictmt11/download/ICTMT11_Proceedings.pdf
  27. Zbiek, R. M., Heid, M. K., Blume, G. W., & Dick, Th P. (2007). Research on technology in mathematics education. In F. K. Lester (Ed.), Second Handbook of Research (pp. 1169–1206). Charlottte, NC: Information Age Publishing.Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.University of WuerzburgWürzburgGermany

Personalised recommendations