Display options
Cite
Hansen SM, Haider H, Eichler A, et al. Fostering Formal Commutativity Knowledge with Approximate Arithmetic. PLoS One. 2015;10(11):e0142551doi: 10.1371/journal.pone.0142551.
Hansen, S. M., Haider, H., Eichler, A., Godau, C., Frensch, P. A., & Gaschler, R. (2015). Fostering Formal Commutativity Knowledge with Approximate Arithmetic. PloS one, 10(11), e0142551. https://doi.org/10.1371/journal.pone.0142551
Hansen, Sonja Maria, et al. "Fostering Formal Commutativity Knowledge with Approximate Arithmetic." PloS one vol. 10,11 (2015): e0142551. doi: https://doi.org/10.1371/journal.pone.0142551
Hansen SM, Haider H, Eichler A, Godau C, Frensch PA, Gaschler R. Fostering Formal Commutativity Knowledge with Approximate Arithmetic. PLoS One. 2015 Nov 11;10(11):e0142551. doi: 10.1371/journal.pone.0142551. eCollection 2015. PMID: 26560311; PMCID: PMC4652602.
Copy Download .nbib Format: NLM
Share it on

PLoS One. 2015 Nov 11;10(11):e0142551. doi: 10.1371/journal.pone.0142551. eCollection 2015.

Fostering Formal Commutativity Knowledge with Approximate Arithmetic.

PloS one

Sonja Maria Hansen, Hilde Haider, Alexandra Eichler, Claudia Godau, Peter A Frensch, Robert Gaschler

Affiliations

  1. University of Cologne, Department of Psychology, Cologne, Germany.
  2. Humboldt-Universität zu Berlin, Exzellenzcluster Bild Wissen Gestaltung, Berlin, Germany.
  3. FernUniversität in Hagen, Department of Psychology, Hagen, Germany.

PMID: 26560311 PMCID: PMC4652602 DOI: 10.1371/journal.pone.0142551

Abstract

How can we enhance the understanding of abstract mathematical principles in elementary school? Different studies found out that nonsymbolic estimation could foster subsequent exact number processing and simple arithmetic. Taking the commutativity principle as a test case, we investigated if the approximate calculation of symbolic commutative quantities can also alter the access to procedural and conceptual knowledge of a more abstract arithmetic principle. Experiment 1 tested first graders who had not been instructed about commutativity in school yet. Approximate calculation with symbolic quantities positively influenced the use of commutativity-based shortcuts in formal arithmetic. We replicated this finding with older first graders (Experiment 2) and third graders (Experiment 3). Despite the positive effect of approximation on the spontaneous application of commutativity-based shortcuts in arithmetic problems, we found no comparable impact on the application of conceptual knowledge of the commutativity principle. Overall, our results show that the usage of a specific arithmetic principle can benefit from approximation. However, the findings also suggest that the correct use of certain procedures does not always imply conceptual understanding. Rather, the conceptual understanding of commutativity seems to lag behind procedural proficiency during elementary school.

References

  1. J Exp Child Psychol. 2006 Apr;93(4):285-303 - PubMed
  2. Atten Percept Psychophys. 2012 Jan;74(1):163-73 - PubMed
  3. Dev Psychol. 1998 Sep;34(5):882-91 - PubMed
  4. J Exp Child Psychol. 2009 Aug;103(4):469-79 - PubMed
  5. Nature. 2007 May 31;447(7144):589-91 - PubMed
  6. J Exp Psychol Gen. 1998 Dec;127(4):377-97 - PubMed
  7. PLoS One. 2013 Sep 23;8(9):e74972 - PubMed
  8. Nature. 1992 Aug 27;358(6389):749-50 - PubMed
  9. J Exp Child Psychol. 2010 Dec;107(4):394-406 - PubMed
  10. J Vis. 2010 Jun 01;10(6):20 - PubMed
  11. Psychon Bull Rev. 1994 Dec;1(4):476-90 - PubMed
  12. Child Dev. 2006 Jan-Feb;77(1):1-15 - PubMed
  13. Cognition. 2010 Jun;115(3):394-406 - PubMed
  14. Dev Psychol. 2010 Jan;46(1):178-92 - PubMed
  15. Am Psychol. 1995 Jan;50(1):24-37 - PubMed
  16. Trends Cogn Sci. 2004 Jul;8(7):307-14 - PubMed
  17. J Exp Child Psychol. 1999 Nov;74(3):157-93 - PubMed
  18. J Exp Child Psychol. 2009 Sep;104(1):1-21 - PubMed
  19. Cognition. 2014 Apr;131(1):92-107 - PubMed
  20. Proc Natl Acad Sci U S A. 2005 Sep 27;102(39):14116-21 - PubMed
  21. J Exp Child Psychol. 2005 Nov;92(3):220-46 - PubMed
  22. Dev Psychol. 2011 Nov;47(6):1525-38 - PubMed
  23. PLoS One. 2011;6(9):e23749 - PubMed
  24. Cognition. 2000 Jan 10;74(1):B1-B11 - PubMed
  25. Front Hum Neurosci. 2014 Jan 06;7:924 - PubMed
  26. Cognition. 1992 Aug;44(1-2):43-74 - PubMed
  27. Atten Percept Psychophys. 2009 May;71(4):803-21 - PubMed
  28. Behav Res Methods Instrum Comput. 1999 Feb;31(1):137-49 - PubMed
  29. Cognition. 2008 Jun;107(3):932-45 - PubMed
  30. Trends Cogn Sci. 2010 Dec;14(12):542-51 - PubMed
  31. J Exp Child Psychol. 2012 Dec;113(4):552-68 - PubMed
  32. Trends Cogn Sci. 2009 Feb;13(2):83-91 - PubMed

MeSH terms

Publication Types