Encyclopedia of Mathematics Education

2014 Edition
| Editors: Stephen Lerman

Instrumentation in Mathematics Education

  • Luc TroucheEmail author
Reference work entry
DOI: https://doi.org/10.1007/978-94-007-4978-8_80


In order to define instrumentation in the context of mathematics education, it is necessary to define instruments: at this stage of this article, we do not differentiate between instruments and artifacts, i.e., we regard them as things that are created and used by humans to help, assist, support, enlarge, and empower their activity. Instrumentation is the action to give someone an instrument, or the process by which someone acquires an instrument, in order to perform a given activity. The notion of instrumentation is part of a network of concepts; we will focus here on the main dialectical relationships between them.

Instrumentation and Instruction

Contrary to the common perception that mathematics is a pure mental activity, the importance of instruments in mathematical activity has been largely acknowledged: “the development of mathematics has always been dependent upon the material and symbolic tools available for mathematics computations” (Artigue 2002, p. 245). What is...


Appropriation Artifact Document Instrumental genesis Instrumentalization Instrumentation Orchestration Resources System of Instruments 
This is a preview of subscription content, log in to check access.



Thanks to Ghislaine Gueudet and Birgit Pepin for their reading of the preliminary version of this article and their inspiring comments.


  1. Artigue M (2002) Learning mathematics in a CAS environment: the genesis of a reflection about instrumentation and the dialectics between technical and conceptual work. Int J Comput Math Learn 7(3):245–274Google Scholar
  2. Drijvers P, Godino JD, Font V, Trouche L (2012) One episode, two lenses. A reflective analysis of student learning with computer algebra from instrumental and onto-semiotic perspectives. Educ Stud Math 82:23–49. doi 10.1007/s10649-012-9416-8Google Scholar
  3. Drijvers P, Doorman M, Boon P, Reed H, Gravemeijer K (2010) The teacher and the tool: instrumental orchestrations in the technology-rich mathematics classroom. Educ Stud Math 75(2):213–234Google Scholar
  4. Engeström Y, Miettinen R, Punamäki R-L (1999) Perspectives on activity theory. Cambridge University Press, CambridgeGoogle Scholar
  5. Gueudet G, Trouche L (2009) Towards new documentation systems for mathematics teachers? Educ Stud Math 71(3):199–218. doi:10.1007/s10649-008-9159-8Google Scholar
  6. Gueudet G, Pepin B, Trouche L (eds) (2012) From textbooks to ‘lived’ resources: mathematics curriculum materials and teacher documentation. Springer, New YorkGoogle Scholar
  7. Guin D, Ruthven K, Trouche L (eds) (2005) The didactical challenge of symbolic calculators: turning a computational device into a mathematical instrument. Springer, New YorkGoogle Scholar
  8. Guin D, Trouche L (1999) The complex process of converting tools into mathematical instruments. The case of calculators. Int J Comput Math Learn 3(3):195–227Google Scholar
  9. Lagrange J-B, Artigue M, Laborde C, Trouche L (2003) Technology and mathematics education: a multidimensional study of the evolution of research and innovation. In: Bishop AJ, Clements MA, Keitel C, Kilpatrick J, Leung FKS (eds) Second international handbook of mathematics education. Kluwer, Dordrecht, pp 239–271Google Scholar
  10. Maschietto M, Trouche L (2010) Mathematics learning and tools from theoretical, historical and practical points of view: the productive notion of mathematics laboratories. ZDM Int J Math Educ 42(1):33–47. doi:10.1007/s11858-009-0215-3Google Scholar
  11. Noss R, Hoyles C (1996) Windows on mathematical meanings – learning cultures and computers. Kluwer, DordrechtGoogle Scholar
  12. Proust C (2012) Masters’ writings and students’ writings : school material in Mesopotamia. In: Gueudet G, Pepin B, Trouche L (eds) From text to ‘lived’ resources. Mathematics curriculum materials and teacher development. Springer, New York, pp 161–179Google Scholar
  13. Salaün J-M (2012) Vu, lu, su, les architectes de l’information face à l’oligopole du web. La découverte, ParisGoogle Scholar
  14. Trouche L (2004) Managing the complexity of human/machine interactions in computerized learning environments: guiding students’ command process through instrumental orchestrations. Int J Comput Math Learn 9:281–307Google Scholar
  15. Trouche L, Drijvers P (2010) Handheld technology for mathematics education, flashback to the future. ZDM Int J Mathe Educ 42(7):667–681, 10.1007/s11858-010-0269-2Google Scholar
  16. Vergnaud G (1996) The theory of conceptual fields. In: Steffe LP, Nesher P, Cobb P, Goldin GA, Greer B (eds) Theories of mathematical learning. Lawrence Erlbaum Ass, Mahwah, pp 219–239Google Scholar
  17. Verillon P, Rabardel P (1995) Cognition and artifact: a contribution to the study of thought in relation to instrument activity. Eur J Psychol Educ 9(3):77–101Google Scholar
  18. Vygotsky LS (1962) Thought and language. MIT Press, Cambridge, MAGoogle Scholar
  19. Vygotsky LS (1981) The instrumental method in psychology. In: Wertsch JW (ed) The concept of activity in Soviet psychology. M.E Sharpe, ArmonkGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Ecole Normale Supérieure de LyonInstitut Français de l’ÉducationLyon cedex 07France