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Artifact-Centric Activity Theory—A Framework for the Analysis of the Design and Use of Virtual Manipulatives

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International Perspectives on Teaching and Learning Mathematics with Virtual Manipulatives

Part of the book series: Mathematics Education in the Digital Era ((MEDE,volume 7))

Abstract

It is a challenge to analyze the design and the use of Virtual Manipulatives due to their high complexity. As it is possible to create entirely new virtual worlds that can host objects that behave differently than any real objects, allowing for new and unprecedented actions in learning processes, we are in need of tools that enable us to focus on those aspects that are important for our analyses. In this chapter we show how ACAT, Artifact-Centric Activity Theory , can be used to analyze the design and use of a virtual manipulative place value chart.

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Notes

  1. 1.

    We follow the definition of virtual manipulatives by Moyer et al. (2002), but extend it to the category of “apps” on mobile devices (which was unforeseen at the time), that can host virtual manipulatives in a similar way as web sites do.

  2. 2.

    At http://kortenkamps.net/placevalue we provide a screen recording showing the app in action.

  3. 3.

    There is no research so far that could prove or disprove this assumption—this expected help for learning is just hypothetical and based on the theoretic considerations behind the design of the artifact.

References

  • Aebli, H. (1983). Zwölf Grundformen des Lehrens. Eine Allgemeine Didaktik auf psychologischer Grundlage. Medien und Inhalte didaktischer Kommunikation, der Lernzyklus. 13. Auflage, 2006. Stuttgart: Klett-Cotta.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Bartolini, M. B. (2011). Artefacts and utilization schemes in mathematics teacher education: place value in early childhood education. Journal of Mathematics Teacher Education, 14, 93–112.

    Article  Google Scholar 

  • Bruner, J. S., Oliver, R., & Greenfield, P. (1971). Studien zur kognitiven Entwicklung: eine cooperative Untersuchung am “Center for Cognitive Studies” der Harvard-Universität. Stuttgart: Klett.

    Google Scholar 

  • Carroll, J. M., Kellogg, W. A., & Rosson, M. B. (1991). The task-artifact cycle. In J. M. Carroll (Ed.), Designing Interaction: Psychology at the Human-Computer Interface. Cambridge, UK: Cambridge University Press.

    Google Scholar 

  • Clements, D. H. (1999). ‘Concrete’ manipulatives, concrete ideas. Contemporary Issues in Early childhood, 1(1), 45–60.

    Article  Google Scholar 

  • Drijvers, P., Doorman, M., Boon, P., & van Gisbergen, S. (2011). Instrumental orchestration: Theory and practice. In: Durand-Guerrier, V., Soury-Lavergne, S., Arzarello, F. (Eds.), Proceedings of the congress of the European Society for Research in Mathematcis Education (Vol. 6, pp. 1349–1358), January 28–February 1, 2009, Lyon (France).

    Google Scholar 

  • Giest, H., & Lompscher, J. (2004). Tätigkeitstheoretische Überlegungen zu einer neuen Lernkultur. Sitzungsberichte der Leibniz-Sozietät, 72, 101–123.

    Google Scholar 

  • Kaptelinin, V. (2014). Activity theory. In: M. Soegaard & R. F. Dam (Eds.), The encyclopedia of human-computer interaction (2nd Ed.). Aarhus, Denmark: The Interaction Design Foundation. Available online at https://www.interaction-design.org/encyclopedia/activity_theory.html

  • Kortenkamp, U. (2015). Place value chart. Available in the iTunes-Store: https://itunes.apple.com/de/app/stellenwerttafel/id568750442?mt=8. Last opened on September 3, 2015.

  • Kortenkamp, U. & Ladel, S. (2013). Designing a technology based learning environment for place value using artifact-centric Activity Theory. Research Forum Activity Theoretical approaches to mathematics classroom practices with the use of technology. In Proceedings of PME 37. Kiel.

    Google Scholar 

  • Ladel, S. (2009). Multiple externe Repräsentationen (MERs) und deren Verknüpfung durch Computereinsatz. Zur Bedeutung für das Mathematiklernen im Anfangsunterricht. Didaktik in Forschung und Praxis, Bd. 48. Hamburg: Verlag Dr. Kovac.

    Google Scholar 

  • Ladel, S. (2013). Garantierter Lernerfolg “oder” Digitale Demenz? Zum frühen Lernen von Mathematik mit digitalen Medien. In G. Greefrath, F. Käpnick, & M. Stein (Eds.), Beiträge zum Mathematikunterricht (pp. 54–61). Münster.

    Google Scholar 

  • Ladel, S., & Kortenkamp, U. (2013). An activity-theoretic approach to multi-touch tools in early maths learning. In The International Journal for Technology in Mathematics Education, 20(1), 3–8. Plymouth.

    Google Scholar 

  • Ladel, S., & Kortenkamp, U. (2014). Handlungsorientiert zu einem flexiblen Verständnis von Stellenwerten - ein Ansatz aus Sicht der Artifact-Centric Activity Theory. In S. Ladel & C. Schreiber (Hrsg.), Von A udiopodcast bis Z ahlensinn. Band 2 der Reihe Lernen, Lehren und Forschen mit digitalen Medien in der Primarstufe (pp. 151–176). Münster: WTM-Verlag.

    Google Scholar 

  • Ladel, S., & Kortenkamp, U. (2015a). Development of a flexible understanding of place value. In O. Helenius, M. Johansson, T. Lange, T. Meaney, & A. Wernberg (Eds.), Early mathematics learning. Selected papers of the POEM 2014 conference. New York: Springer.

    Google Scholar 

  • Ladel, S., & Kortenkamp, U. (2015b). Dezimalbrüche und Stellenwerttafeln. In Beiträge zum Mathematikunterricht. Münster: WTM-Verlag.

    Google Scholar 

  • Leontiev, A. N. (1978). Activity, consciousness and personality. Englewood Cliffs: Prentice Hall.

    Google Scholar 

  • Moyer, P. S., Bolyard, J. J., & Spikell, M. A. (2002). What are virtual manipulatives? Teaching Children Mathematics, 8(6), 372–377.

    Google Scholar 

  • Rabardel, P. (2002). People and technology: A cognitive approach to contemporary instruments.

    Google Scholar 

  • Ross, S. (1989). Parts, wholes, and place value: A developmental view. Arithmetic Teacher, 36(6), 47–51.

    Google Scholar 

  • Sarama, J. & Clements, D. H. (2009). “Concrete” computer manipulatives in mathematics education. Child Development Perspectives, 3(3), 145–150.

    Google Scholar 

  • Trouche, L. (2004). Managing the complexity of human/machine interactions in computerized learning envirionments: Guiding students’ command process through instrumental orchestrations. International Journal of Computers for Mathematical Learning, 9, 281–307.

    Article  Google Scholar 

  • Van Oers, B., Wardekker, W., Elbers, E., & van der Veer, R. (Eds.). (2008). The transformation of learning: Advances in cultural-historical activity theory. New York: Cambridge University Press.

    Google Scholar 

  • Verillion, P., & Rabardel, P. (1995). Cognition and artifacts: A contribution to the study of thought in relation to instrumented activity. European Journal of Psychology of Education, 10(1).

    Google Scholar 

  • Vom Hofe, R. (1995). Grundvorstellungen mathematischer Inhalte. Heidelberg: Spektrum.

    Google Scholar 

  • Vygotsky, L. S. (1997). The instrumental method in psychology. In R. W. Rieber & J. Wollock (Eds.), The collected works of L.S. Vygotsky. Vol. 3: Problems of the theory and history of psychology (pp. 85–90). New York: Plenum Press.

    Google Scholar 

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Authors and Affiliations

  1. Mathematics Department, University of Saarland, Postfach 151150, 66041, Saarbrücken, Germany

    Silke Ladel

  2. Institute of Mathematics, University of Potsdam, Karl-Liebknecht-Str. 24-25, 14476, Potsdam OT Golm, Germany

    Ulrich Kortenkamp

Authors
  1. Silke Ladel
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  2. Ulrich Kortenkamp
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Correspondence to Silke Ladel .

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Editors and Affiliations

  1. Utah State University, Logan, Utah, USA

    Patricia S. Moyer-Packenham

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Ladel, S., Kortenkamp, U. (2016). Artifact-Centric Activity Theory—A Framework for the Analysis of the Design and Use of Virtual Manipulatives. In: Moyer-Packenham, P. (eds) International Perspectives on Teaching and Learning Mathematics with Virtual Manipulatives. Mathematics Education in the Digital Era, vol 7. Springer, Cham. https://doi.org/10.1007/978-3-319-32718-1_2

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  • DOI: https://doi.org/10.1007/978-3-319-32718-1_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-32716-7

  • Online ISBN: 978-3-319-32718-1

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