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Entropy reduction in mathematical giftedness

  • Werner Krause
  • Frank Heinrich
Chapter

Abstract

This paper deals with the elementary analysis of cognitive processes in mathematical problem solving for better diagnostics. The present experiment was designed to analyse the internal process and to localize the neural substrates involved in solving mathematical tasks, using EEG-coherence. The internal process is revealed by a sequence of microstates. Microstates are defined here as coherence maps which remain stable over time. The difference in performance between gifted and normal subjects in solving mathematical problems is reflected by the difference between the sequential and topographical properties of microstate sequences. Sequential properties were measured by means of entropy reduction. A higher entropy reduction was found in mathematically gifted subjects in contrast to the normal subjects. Topographical properties were measured by means of difference maps of microstates between mathematically gifted and normal subjects. Gifted subjects exhibit a higher coherence left and right parietal and left frontal. This result corroborates the double representation hypothesis.

Keywords

Mental Rotation Modality Strategy Conditional Entropy Mental Calculation Sequential Property 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Heinrich F (1997) Diskussionsmaterial zur Untersuchung der Doppelrepräsentationshypothese und ein Bemerkungen aus mathematikdidaktischer Sicht. (unveröffentlicht).Google Scholar
  2. Jäncke L, Kleinschmidt A, Mirzazade S, Specht K, Freund HJ (1998) Mental rotation ability determines the activity in posterior cortical areas during the imagination, palpation and construction of 3D objects. Neurolmage 7: 119CrossRefGoogle Scholar
  3. Jasper HH (1958) The ten-twenty electrode system of the International Federation. Electroencephalography and Clinical Neurophysiology 10: 371–375Google Scholar
  4. Klix F (1992) Die Natur des Verstandes. Hogrefe, GöttingenGoogle Scholar
  5. Krause W (2000) Denken und Gedächtnis aus naturwissenschaftlicher Sicht. Hogrefe, GöttingenGoogle Scholar
  6. Krause W, Seidel G, Schack B (2001) Ordnungsbildung. Z. Psychol. 209: 376–401CrossRefGoogle Scholar
  7. Lautsch E, Weber S (1995) Methoden und Anwendungen der Konfigurationsfrequenzanalyse (KFA). Belz Psychologie Verlags Union, WeinheimGoogle Scholar
  8. Schack B, Krause W (1995) Dynamic power and coherence analysis of ultra short-term cognitive processes a methodical study. Brain Topogr 8: 127–136CrossRefGoogle Scholar
  9. Schack B, Grieszbach G, Krause W (1999) The sensitivity of instantaneous coherence for considering elementary comparison processing. Part I: the relationship between mental activities and instantaneous EEG coherence. Int. J. Psychophysiol. 31: 219–240Google Scholar
  10. Schack B, Seidel G, Krause W, Heinrich F (2001) Coherence Analysis of the Ongoing EEG by Means of Microstates of Synchronous Oscillations. Proceedings-23rd Annual Conference-IEEE/EMBS Oct 25–28, IstanbulGoogle Scholar
  11. Seidel G. (2000) Ordnungsbildung und Doppelrepräsentation im Denken mathematisch, Hochbegabter. Sequentielle und topologische Eigenschaften von Mikrozustandssequenzen. Doctoral thesis, University of Jena.Google Scholar
  12. Zargo L, Pesenti M, Mellet E, Crivello F, Mazoyer B, Tourio-Mazoyer N (2001) Neural Correlates of Simple and Complex Mental Calculation. Neurolmage 13: 314–327Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Werner Krause
    • 1
  • Frank Heinrich
    • 2
  1. 1.Gundula Seidel University of JenaGermany
  2. 2.University of BambergGermany

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