ZDM

, Volume 48, Issue 6, pp 895–907 | Cite as

Students’ mathematical work on absolute value: focusing on conceptions, errors and obstacles

  • Iliada Elia
  • Serkan Özel
  • Athanasios Gagatsis
  • Areti Panaoura
  • Zeynep Ebrar Yetkiner Özel
Original Article

Abstract

This study investigates students’ conceptions of absolute value (AV), their performance in various items on AV, their errors in these items and the relationships between students’ conceptions and their performance and errors. The Mathematical Working Space (MWS) is used as a framework for studying students’ mathematical work on AV and the obstacles that hinder their work in Turkey and Cyprus. A comparative study between the two countries is undertaken, by which a deeper understanding on students’ personal MWS on AV is gained. Specifically, a survey was carried out in Turkey, following a similar survey in Cyprus, in which secondary school students’ performance was assessed using a test. Findings showed a discrepancy in the conception of AV that was most prevalent in each country, indicating the differences in the reference and suitable MWS between the two countries. For Turkey, the conception of AV as distance from 0, which was the most widely used definition, gave a positive support to the solution of items involving discursive reasoning. This was not the case for Cyprus, in which the most prevalent conception of AV was ‘number without sign’. An analysis of the Turkish students’ errors revealed a distinction between errors in students’ discursive genesis and semiotic genesis, which were a consequence of either didactic or epistemological obstacles that intervened in students’ personal MWS.

Keywords

Absolute value Mathematical Working Space Obstacles Discursive genesis Comparative study 

References

  1. Almog, N., & Ilany, B. (2012). Absolute value inequalities: High school students’ solutions and misconceptions. Educational Studies in Mathematics, 81(3), 347–364.CrossRefGoogle Scholar
  2. Brousseau, G. (1983). Les obstacles épistémologiques et les problèmes en mathématique. Recherches en Didactique des Mathématiques, 4(2), 165–198.Google Scholar
  3. Brousseau, G. (1997). Theory of didactical situations in mathematics. In N. Balacheff, M. Cooper, R. Sutherland, & V. Warfield (Eds.), Mathematics Education Library (Vol. 19). Dordrecht: Kluwer.Google Scholar
  4. Chevallard, Y. (1985). La Transposition Didactique. Du savoir savant au savoir enseigné (2nd edn 1991). Grenoble, France: La Pensée sauvage.Google Scholar
  5. Chevallard, Y., & Bosch, M. (2014). Didactic transposition in mathematics education. In St Lerman (Ed.), Encyclopedia of mathematics education (pp. 170–174). London: Springer.Google Scholar
  6. Cornu, B. (1991). Limits. In A. J. Bishop (Managing Ed.) & D. Tall (Vol. Ed.), Mathematics Education Library: Advanced mathematical thinking (Vol. 11, pp. 153–166). Dordrecht, The Netherlands: Kluwer. doi:10.1007/0-306-47203-1_10.
  7. Duroux, A. (1983). La valeur absolue. Difficultés majeures pour une notion mineure. Petit x, 3, 43–67.Google Scholar
  8. Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61(1–2), 103–131.CrossRefGoogle Scholar
  9. Gagatsis, A., & Panaoura, A. (2014). A multidimensional approach to explore the understanding of the notion of absolute value. International Journal of Mathematical Education in Science and Technology, 45(2), 159–173.CrossRefGoogle Scholar
  10. Gagatsis, A., & Thomaidis, Y. (1995). Eine Studie zur historischen Entwicklung und didaktischen Transposition des Begriffs absoluter Betrag [A study of a historical design, development and didactic transposition of the term “absolute value”]. Journal fur MathematikDidaktik, 16, 3–46.Google Scholar
  11. Gras, R., Suzuki, E., Guillet, F., & Spagnolo, F. (Eds.). (2008). Statistical implicative analysis: Theory and applications. Heidelberg: Springer.Google Scholar
  12. Kuzniak, A., & Richard, P. (2014). Les Espaces de Travail Mathématiques. Points de vue et perspectives. Relime, 17(4-I), 14–27.Google Scholar
  13. Schneider, M. (2014). Epistemological obstacles in mathematics education. In St Lerman (Ed.), Encyclopedia of mathematics education (pp. 214–217). London: Springer.Google Scholar
  14. Stupel, M. (2013). A special application of absolute value techniques in authentic problem solving. International Journal of Mathematical Education in Science and Technology, 44(4), 587–595.CrossRefGoogle Scholar

Copyright information

© FIZ Karlsruhe 2016

Authors and Affiliations

  • Iliada Elia
    • 1
  • Serkan Özel
    • 2
  • Athanasios Gagatsis
    • 1
  • Areti Panaoura
    • 3
  • Zeynep Ebrar Yetkiner Özel
    • 4
  1. 1.Department of EducationUniversity of CyprusNicosiaCyprus
  2. 2.Department of Primary EducationBoğaziçi UniversityİstanbulTurkey
  3. 3.Department of Primary EducationFrederick UniversityNicosiaCyprus
  4. 4.Department of Elementary EducationFatih UniversityİstanbulTurkey

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