Skip to Main Content

Experimental Psychology (Russia)
2012. Vol. 5, no. 4, 75–98
ISSN: 2072-7593 / 2311-7036 (online)

Mathematical foundations of a new approach to the construction of testing procedures

715

L.S. Kuravsky, P.A. Marmalyuk, V.I. Alkhimov, G.A. Yuryev

PDF (RUS)
Online translation in english
GS
Information
in Google Scholar

Abstract

In this paper the authors propose to consider a new approach to the construction of intelligent and competency tests, based on a new technology of eye tracking of the subject on the surface of the test stimulus with the application of one of the most common varieties of random processes and methods of the subsequent analysis of the obtained data. Special attention is given to the mathematical substantiation of the proposed methods. An example of practical application of the obtained results for determining of the level of mathematical education of pupils and students is an illustration of the adaptation of the methods to the decision of applied problems of an estimation of the level of intelligence and competence.

General Information

Keywords: testing, Markov process, the Fokker-Planck-Kolmogorov equation, Kolmogorov equations

Journal rubric: Mathematical Psychology

Article type: scientific article

For citation: Kuravsky L.S., Marmalyuk P.A., Alkhimov V.I., Yuryev G.A. Mathematical foundations of a new approach to the construction of testing procedures . Eksperimental'naâ psihologiâ = Experimental Psychology (Russia), 2012. Vol. 5, no. 4, pp. 75–98. (In Russ., аbstr. in Engl.)

References

  1. Barabanshhikov V. A. Okulomotornye struktury vosprijatija. M.: IP RAN, 1997.
  2. Barabanshhikov V. A. Vosprijatie vyrazhenij lica. M.: IP RAN, 2009.
  3. Barabanshhikov V. A. Jekspressii lica i ih vosprijatie. M.: IP RAN, 2012.
  4. Barabanshhikov V. A. Vosprijatie individual'no-psihologicheskih osobennostej cheloveka po izobrazheniju celogo i chastichno otkrytogo lica // Jeksperimental'naja psihologija. 2008. T. 1. № 1. S. 62–83.
  5. Barabanshhikov V. A., Anan'eva K. I., Haritonov V. N. Organizacija dvizhenij glaz pri vosprijatii izobrazhenij lica // Jeksperimental'naja psihologija. 2009. T. 2. № 2. S. 31–60.
  6. Barabanshhikov V. A., Demidov A. A. Jeksperimental'naja psihologija v Rossii: sovremennoe sostojanie i perspektivy razvitija // Jeksperimental'naja psihologija. 2011. T. 4. № 1. S. 134–140.
  7. Barabanshhikov V. A., Majnina I. N. Ocenka «glubinnyh» individual'no-psihologicheskih osobennostej cheloveka po fotoizobrazheniju ego lica // Jeksperimental'naja psihologija. 2010. T. 3. № 4. S. 50–71.
  8. Bezrukih M. M., Demidov A. A., Ivanov V. V. Vozrastnye osobennosti okulomotornoj aktivnosti detej v processe chtenija // Psihologija cheloveka v sovremennom mire. T. 2: Mater. Vseross. jubil. nauch. konf., posvjashh. 120-letiju so dnja rozhdenija S. L. Rubinshtejna. M.: IP RAN. 2009. S. 151–155.
  9. Demidov A. A., Zhegallo A. V. Oborudovanie SMI dlja registracii dvizhenij glaz: test-drajv // Jeksperimental'naja psihologija. 2008. T. 1. № 1. S. 149–159.
  10. Zhegallo A. V. Sistema registracii dvizhenij glaz SMI High Speed: osobennosti ispol'zovanija // Jeksperimental'naja psihologija. 2009. T. 2. № 4. S. 111–117.
  11. Kramer G. Matematicheskie metody statistiki. M.: Mir, 1976.

  12. Kuravskij L. S., Baranov S. N. Primenenie nejronnyh setej dlja diagnostiki i prognozirovanija ustalostnogo razrushenija tonkostennyh konstrukcij // Nejrokomp'jutery: razrabotka i primenenie. 2001. № 12. S. 47–63.

  13. Kuravskij L. S., Baranov S. N. Sintez setej Markova dlja prognozirovanija ustalostnogo razrushenija // Nejrokomp'jutery: razrabotka i primenenie. 2002. № 11. S. 29–40.

  14. Kuravskij L. S., Baranov S. N., Malyh S. B. Nejronnye seti v zadachah prognozirovanija, diagnostiki i analiza dannyh: Ucheb. posobie. M.: RUSAVIA, 2003.

  15. Kuravskij L. S., Baranov S. N., Kornienko P. A. Obuchaemye mnogofaktornye seti Markova i ih primenenie dlja issledovanija psihologicheskih harakteristik // Nejrokomp'jutery: razrabotka i primenenie. 2005. № 12. S. 65–76.

  16. Kuravskij L. S., Baranov S. N., Jur'ev G. A. Sintez i identifikacija skrytyh markovskih modelej dlja diagnostiki ustalostnogo razrushenija // Nejrokomp'jutery: razrabotka i primenenie. 2010. № 12. s. 20–36.

  17. Kuravskij L. S., Margolis A. A., Jur'ev G. A., Marmaljuk P. A. Koncepcija sistemy podderzhki prinjatija reshenij dlja psihologicheskogo testirovanija // Psihologicheskaja nauka i obrazovanie. 2012. № 1. S. 56–65.

  18. Kuravskij L. S., Jur'ev G. A. Adaptivnoe testirovanie kak markovskij process: modeli i ih identifikacija // Nejrokomp'jutery: razrabotka i primenenie. 2011 a. № 2. S. 21–29.

  19. Kuravskij L. S., Jur'ev G. A. Ispol'zovanie markovskih modelej pri obrabotke rezul'tatov testirovanija // Voprosy psihologii. 2011 b. № 2. S. 98–107.

  20. Kuravskij L. S., Jur'ev G. A. Ob odnom podhode k adaptivnomu testirovaniju i ustraneniju ego artefaktov // Nejrokomp'jutery: razrabotka i primenenie. 2012 a. № 1. S. 54–66.

  21. Kuravskij L. S., Jur'ev G. A. Verojatnostnyj metod fil'tracii artefaktov pri adaptivnom testirovanii // Jeksperimental'naja psihologija. 2012 b. T. 5. № 1. S. 119–131.

  22. Marmaljuk P. A., Zvonkina O. M. Opornye pokazateli glazodvigatel'noj aktivnosti pri prohozhdenii testa Ravena i avtomatizacija ih rascheta // Molodye uchenye – nashej novoj shkole. Mater. XI Mezhvuz. nauch.prakt. konf. s mezhd. uchastiem. M.: MGPPU, 2012. S. 350–352.

  23. Panfilova A. S. Sistema testirovanija intellekta na baze faktornyh modelej i samoorganizujushhihsja kart Kohonena // Nejrokomp'jutery: razrabotka i primenenie. 2012. № 9 (v pechati).

  24. Tihonov V. I., Shahtarin B. I., Sizyh V. V. Sluchajnye processy. Primery i zadachi. T. 5. Ocenka signalov, ih parametrov i spektrov. Osnovy teorii informacii. M.: Gorjachaja linija-Telekom, 2009.

  25. Tjumeneva Ju. A. Psihologicheskoe izmerenie. M.: Aspekt-Press, 2007.

  26. Hohlova A. A. Issledovanie glazodvigatel'noj aktivnosti pri prohozhdenii matrichnogo testa intellekta Ravena // Molodye uchenye – nashej novoj shkole: Mater. X Nauch.-prakt. mezhvuz. konf. M.: MGPPU. 2011. S. 343–345.

  27. Shahtarin B. I. Sluchajnye processy v radiotehnike. T. 1. Linejnye preobrazovanija. M.: Gorjachaja linija- Telekom, 2010.

  28. Baker F. B. The Basics of Item Response Theory. ERIC Clearinghouse on Assessment and Evaluation. University of Maryland, College Park, MD, 2001.
  29. Brandt S. A., Stark L. W. Spontaneous eye movements during visual imagery reflect the content of the visual scene // Journal of Cognitive Neuroscience.1997. № 9. Р. 27–38.
  30. Cagli R. C., Coraggio P., Napoletano P., Boccignone G. What the draughtsman’s hand tells the draughtsman’s eye: A sensorimotor account of drawing // International Journal of Pattern Recognition and Artificial Intelligence. 2008. № 22. Р. 1015–1029.
  31. Dayan P. Improving generalization for temporal difference learning: The successor representation // Neural Computation. 1993. № 5. Р. 613–624.
  32. Ellis S. R., Stark L. Statistical dependency in visual scanning // Human Factors. 1986. № 28. Р. 421–438.
  33. Gregory R. J. Psychological testing: History, principles, and applications (5th edition). N.Y.: Pearson, 2007.
  34. Gulliksen H. Theory of Mental Tests. John Wiley & Sons Inc., 1950.
  35. Hayes Т. R., Petrov A. A., Sederberg P. B. A novel method for analyzing sequential eye movements reveals strategic influence on Raven’s Advanced Progressive Matrices // Journal of Vision. 2011. № 10. Р. 1–11.
  36. Jansen A. R., Marriott K., Yelland G. W. Parsing of algebraic expressions by experienced users of mathematics // European Journal of Cognitive Psychology. 2007. № 19. Р. 286–320.
  37. Kuravsky L. S., Baranov S. N. Condition monitoring of the structures suffered acoustic fatigue failure and forecasting their service life // Proc. Condition Monitoring 2003, Oxford, United Kingdom, July 2003. Р. 256–279.
  38. Kuravsky L. S., Malykh S. B. On the application of queuing theory for analysis of twin data // Twin Research. 2000. № 3. Р. 92–98.
  39. Kuravsky L. S., Baranov S. N. Neural networks in fatigue damage recognition: diagnostics and statistical analysis // Proc. 11th International Congress on Sound and Vibration, St.-Petersburg, Russia, July 2004. Р. 2929–2944.
  40. Kuravsky L. S., Baranov S. N. The concept of multifactor Markov networks and its application to forecasting and diagnostics of technical systems // Proc. Condition Monitoring 2005, Cambridge, United Kingdom, July 2005. Р. 111–117.
  41. Kuravsky L. S., Baranov S. N., Yuryev G. A. Synthesis and identification of hidden Markov models based on a novel statistical technique in condition monitoring // Proc. 7th International Conference on Condition Monitoring & Machinery Failure Prevention Technologies, Stratford-upon-Avon, England, June 2010.
  42. Myers C. W., Schoelles M. J. ProtoMatch: A tool for analyzing high-density, sequential eye gaze and cursor protocols // Behavior Research Methods. 2005. № 37. Р. 256–270.
  43. Patalano A. L., Juhasz B. J., Dicke О. The Relationship Between Indecisiveness and Eye Movement Patterns in a Decision Making Informational Search Task // Journal of Behavioral Decision Making. 2010. № 23. Р. 353–368.
  44. Ponsoda V., Scott D., Findlay J. M. A probability vector and transition matrix analysis of eye movements during visual search // Acta Psychologica. 1995. № 88. Р. 167–185.
  45. Rabiner L. R. A tutorial on hidden Markov models and selected applications in speech recognition // Proceedings of the IEEE. 1989. № 77. Р. 257–286.
  46. Rasch G. Probabilistic models for some intelligence and attainment tests / Еxpanded edition with foreword and afterword by B. D. Wright. Chicago: The University of Chicago Press. 1980.
  47. Rayner K. Eye movements in reading and information processing: 20 years of research // Psychological Bulletin. 1998. № 124. P. 372–422.
  48. Salvucci D. D., Anderson J. R. Automated eye-movement protocol analysis // Human-Computer Interaction. 2001. № 16. Р. 39–86.
  49. Simola J., Salojarvi, Kojo I. Using hidden Markov model to uncover processing states from eye movements in information search tasks // Cognitive Systems Research. 2008. № 9. Р. 237–251.
  50. Van der Lans R., Pieters R., Wedel M. Eyemovement analysis of search effectiveness // Journal of the American Statistical Association. 2008. № 103. Р. 452–461.
  51. Vigneau F., Caissie A., Bors D. Eye-movement analysis demonstrates strategic influences on intelligence // Intelligence. 2006. № 34. P. 261–272.
  52. Wright B. D., Masters G. N. Rating scale analysis. Rasch measurements. Chicago: MESA Press, 1982.
  53. Wright B. D., Stone M. N. Best Test Design. Chicago: MESA Press, 1979.

Information About the Authors

Lev S. Kuravsky, Doctor of Engineering, professor, Dean of the Computer Science Faculty, Moscow State University of Psychology and Education, Moscow, Russia, ORCID: https://orcid.org/0000-0002-3375-8446, e-mail: l.s.kuravsky@gmail.com

Pavel A. Marmalyuk, PhD in Engineering, Head of the Laboratory of Psychology and Applied Software, Moscow State University of Psychology & Education, associate professor, Department of Information Technologies, Moscow State University of Psychology & Education, Moscow, Russia, e-mail: ykk.mail@gmail.com

Valery I. Alkhimov, Doctor of Physics and Matematics, Professor, Department of Applied Mathematics, Faculty of Information Technologies, Moscow State University of Psychology and Education, Moscow, Russia, e-mail: alvaliv@list.ru

Grigory A. Yuryev, PhD in Physics and Matematics, Associate Professor, Head of Department of the Computer Science Faculty, Leading Researcher, Youth Laboratory Information Technologies for Psychological Diagnostics, Moscow State University of Psychology and Education, Moscow, Russia, ORCID: https://orcid.org/0000-0002-2960-6562, e-mail: g.a.yuryev@gmail.com

Metrics

Views

Total: 2026
Previous month: 8
Current month: 6

Downloads

Total: 715
Previous month: 4
Current month: 1