Skip to main content
SpringerLink
Log in

Measuring the ability of transitive reasoning, using product and strategy information

  • Application Reviews And Case Studies
  • Published:
Psychometrika Aims and scope Submit manuscript

Abstract

Cognitive theories disagree about the processes and the number of abilities involved in transitive reasoning. This led to controversies about the influence of task characteristics on individuals' performance and the development of transitive reasoning. In this study, a computer test was constructed containing 16 transitive reasoning tasks having different characteristics with respect to presentation form, task format, and task content. Both product and strategy information were analyzed to measure the performance of 6- to 13-year-old children. Three methods (MSP, DETECT, and Improved DIMTEST) were used to determine the number of abilities involved and to test the assumptions imposed on the data by item response models. Nonparametric IRT models were used to construct a scale for transitive reasoning. Multiple regression was used to determine the influence of task characteristics on the difficulty level of the tasks. It was concluded that: (1) the qualitatively distinct abilities predicted by Piaget's theory could not be distinguished by means of different dimensions in the data structure; (2) transitive reasoning could be described by one ability, and some task characteristics influenced the difficulty of a task; and (3) strategy information provided a stronger scale than product information.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Bouwmeester, S., & Aalbers, T. (2002).Tranred. Tilburg: Tilburg University.

    Google Scholar 

  • Bouwmeester, S., Sijtsma, K., & Vermunt, J.K. (2004). Latent class regression analysis to describe cognitive developmental phenomena: an application to transitive reasoning.European Journal of Developmental Psychology, 1, 67–86.

    Google Scholar 

  • Braine, M.D.S. (1959). The onthogeny of certain logical operations: Piaget's formulation examined by nonverbal methods.Monographs for the Society for Research in Child Development, 27, 41–63.

    Google Scholar 

  • Brainerd, C.J. (1977). Response criteria in concept development research.Child Development, 48, 360–366.

    Google Scholar 

  • Brainerd, C.J., & Kingma, J. (1984). Do children have to remember to reason? A fuzzy-trace theory of transitivity development.Developmental Review, 4, 311–377.

    Google Scholar 

  • Brainerd, C.J., & Kingma, J. (1985). On the independence of short-term memory and working memory in cognitive development.Cognitive Psychology, 17, 210–247.

    Google Scholar 

  • Brainerd, C.J., & Reyna, V.F. (1992). The memory independence effect: What do the data show? What do the theories claim?Developmental Review, 12, 164–186.

    Google Scholar 

  • Bryant, P.E., & Trabasso, T. (1971). Transitive inferences and memory in young children.Nature, 232, 456–458.

    Google Scholar 

  • Chapman, M., & Lindenberger, U. (1988). Functions, operations, and decalage in the development of transitivity.Developmental Psychology, 24, 542–551.

    Google Scholar 

  • Chapman, M., & Lindenberger, U. (1992). Transitivity judgments, memory for premises, and models of children's reasoning.Developmental Review, 12, 124–163.

    Google Scholar 

  • Clark, H.H. (1969). Linguistic processes in deductive reasoning.Journal of Educational Psychology, 76, 387–404.

    Google Scholar 

  • DeSoto, C.B., London, M., & Handel, S. (1965). Social reasoning and spatial paralogic.Journal of Social Psychology, 2, 513–521.

    Google Scholar 

  • Fischer, G.H. (1973). The linear logistic test model as an instrument in educational research.Acta Psychologica, 37, 359–374.

    Google Scholar 

  • Fischer, G.H. (1995). The linear logistic test model. In G.H. Fischer and I.W. Molenaar (Eds.),Rasch Models, Foundations, Recent Developments, and Applications (pp. 131–155). New York: Springer-Verlag.

    Google Scholar 

  • Grayson, D.A. (1988). Two-group classification in latent trait theory: Scores with monotone likelihood ratio.Psychometrika, 53, 383–392.

    Google Scholar 

  • Green, K.E., & Smith, R.M. (1987). A comparison of two methods of decomposing item difficulties.Journal of Educational Statistics, 12, 369–381.

    Google Scholar 

  • Hatti, J., Krakowski, K., Rogers, H.J., & Swaminathan, H. (1996). An assessment of Stout's index of essential unidimmensionality.Applied Psychological Measurement, 20, 1–14.

    Google Scholar 

  • Hemker, B.T., Sijtsma, K., & Molenaar, I.W. (1995). Selection of unidimensional scales from a multidimensional item bank in the polytomous Mokken IRT model.Applied Psychological Measurement, 19, 337–352.

    Google Scholar 

  • Hemker, B.T., Sijtsma, K., Molenaar, I.W., & Junker, B.W. (1997). Stochastic ordering using the latent trait and the sumscore in polytomous IRT models.Psychometrika, 62, 331–348.

    Google Scholar 

  • Hosenfield, B., Van der Maas, H. L.J., & van den Boom, D.C. (1997). Detecting bimodality in the analogical reasoning performance of elementary schoolchildren.International Journal of Behavioral Development, 20, 529–547.

    Google Scholar 

  • Huttenlocher, J. (1968). Constructing spatial images.Psychological Review, 75, 550–560.

    Google Scholar 

  • Huttenlocher, J., & Higgens, E.T. (1971). Adjectives, comparatives and syllogisms.Psychological Review, 78, 487–504.

    Google Scholar 

  • Junker, B.W. (1993). Conditional association, essential independence, and monotone unidimensional item response models.The Annals of Statistics, 21, 1359–1378.

    Google Scholar 

  • Kelderman, H., & Rijkes, C. P.M. (1994). Loglinear multidimensional IRT models for polytomously scores items.Psychometrika, 59, 149–176.

    Google Scholar 

  • McDonald, R.P. (1985). Linear versus nonlinear models in item response theory.Applied Psychological Measurement, 6, 379–396.

    Google Scholar 

  • Mokken, R.J. (1971).A Theory and Procedure of Scale Analysis. The Hague: Mouton.

    Google Scholar 

  • Mokken, R.J., Lewis, C., & Sijtsma, K. (1986). Rejoinder to “the Mokken scale: A critical discussion.”Applied Psychological Measurement, 10, 279–285.

    Google Scholar 

  • Molenaar, I.W., & Sijtsma, K. (2000).User's manual MSP5 for Windows. A program for Mokken Scale analysis for Polytomous items [software manual]. Groningen, The Netherlands: iecProGamma.

    Google Scholar 

  • Murray, J.P., & Youniss, J. (1968). Achievement of inferential transitivity and its relation to serial ordering.Child Development, 39, 1259–1268.

    Google Scholar 

  • Nandakumar, R., & Stout, W. (1993). Refinements of Stout's procedure for assessing latent trait unidimensionality.Journal of Educational Statistics, 18, 41–68.

    Google Scholar 

  • Nandakumar, R., Yu, F., Li, H.H., & Stout, W. (1998). Assessing unidimensionality of polytomous data.Applied Psychological Measurement, 22, 99–115.

    Google Scholar 

  • Piaget, J. (1961).Les Méchanicismes Perceptives. Paris: Presses Universitaires de France.

    Google Scholar 

  • Piaget, J., & Inhelder, B. (1941).Le Développement des Quantités Chez l'Enfant. Neuchatel: Delachaux et Niestlé.

    Google Scholar 

  • Piaget, J., Inhelder, B., & Szeminska, A. (1948).La Géométric Spontanée de l'Enfant. Paris: Presses Universitaires de France.

    Google Scholar 

  • Piaget, J., & Szeminska, A. (1941).La Genèse du Nombre Chez l'Enfant. Neuchatel: Delachaux et Niestlé.

    Google Scholar 

  • Quinton, G., & Fellows, B. (1975). “Perceptual” strategies in the solving of three-term series problems.British Journal of Psychology, 66, 69–78.

    Google Scholar 

  • Reckase, M.A. (1997). A linear logistic multidimensional model for dichotomous item response data. In W.J. van der Linden, & R.K. Hambleton (Eds.),Handbook of Modern Item Response Theory (pp. 271–286). New York: Springer-Verlag.

    Google Scholar 

  • Reyna, V.F., & Brainerd, C.J. (1990). Fuzzy processing in transitivity development.Annals of Operations Research, 23, 37–63.

    Google Scholar 

  • Roussos, L.A., Stout, W., & Marden, J. (1998). Using new proximity measures with hierarchical cluster analysis to detect multidimensionality.Journal of Educational Measurement, 35, 1–30.

    Google Scholar 

  • Scheiblechner, H. (1972). Das lernen un lösen complexer Denkaufgaben (Learning and solving complex thought problems).Zeitschrift für experimentelle und angewandte Psychologie, 19, 481–520.

    Google Scholar 

  • Sijtsma, K., & Meijer, R.R. (1992). A method for investigating the intersection of item response functions in Mokken's nonparametric IRT model.Applied Psychological Measurement, 16, 149–157.

    Google Scholar 

  • Sijtsma, K., & Molenaar, I.W. (2002).Introduction to Nonparametric Item Response Theory. Thousand Oaks, CA: Sage Publications.

    Google Scholar 

  • Smedslund, J. (1963). Development of concrete transitivity of length in children.Child Development, 34, 389–405.

    Google Scholar 

  • Smedslund, J. (1969). Psychological diagnostics.Psychological Bulletin, 71, 237–248.

    Google Scholar 

  • Sternberg, R.J. (1980a). Representation and process in linear syllogistic reasoning.Journal of Experimental Psychology, 109, 119–159.

    Google Scholar 

  • Sternberg, R.J. (1980b). The development of linear syllogistic reasoning.Journal of Experimental Child Psychology, 29, 340–356.

    Google Scholar 

  • Sternberg, R.J., & Weil, E.M. (1980). An aptitude × strategy interaction in linear syllogistic reasoning.Journal of Educational Psychology, 72, 226–239.

    Google Scholar 

  • Stout, W. (1993).DIMTEST. Urbana-Champaign, IL: The William Stout Institute for Measurement.

    Google Scholar 

  • Stout, W. (1996).DETECT. Urbana-Champaign, IL: The William Stout Institute for Measurement.

    Google Scholar 

  • Stout, W., Froelich, A.G., & Gao, F. (2001). Using resampling methods to produce an improved DIMTEST procedure. In A. Boomsma, M.A.J. van Duijn, & T.A.B. Snijders (Eds.),Essays on Item Response Theory (pp. 357–375). New York: Springer.

    Google Scholar 

  • Stout, W., Habing, B., Douglas, J., Kim, H.R., Roussos, L.A., & Zhang, J. (1996). Conditional covariance-based non-parametric multidimensionality assessment.Applied Psychological Measurement, 20, 331–354.

    Google Scholar 

  • Thomas, H., Lohaus, A., & Kessler, T. (1999). Stability and change in longitudinal water-level task performance.Developmental Psychology, 35, 1024–1037.

    Google Scholar 

  • Trabasso, T. (1977). The role of memory as a system in making transitive inferences. In R.V. Kail, J.W. Hagen, & J.M. Belmont (Eds.),Perspectives on the Development of Memory and Cognition (pp. 333–366). Hillsdale, NJ: Erlbaum.

    Google Scholar 

  • Trabasso, T., Riley, C.A., & Wilson, E.G. (1975). The representation of linear order and spatial strategies in reasoning: a developmental study. In R.J. Falmagne (Ed.),Reasoning: Representation and Process in Children and Adults (pp. 201–229). Hillsdale, NJ: Erlbaum.

    Google Scholar 

  • Van Abswoude, A. A.H., Van der Ark, L.A., & Sijtsma, K. (2004). A comparative study on test dimensionality assessment procedures under nonparametric IRT models.Applied Psychological Measurement, 28, 3–24.

    Google Scholar 

  • Verweij, A.C. (1999).Scaling transitive inference in 7–12 years old children. Unpublished doctoral dissertation, Vrÿe Universiteit Amsterdam, the Netherlands.

    Google Scholar 

  • Verweij, A.C., Sijtsma, K., & Koops, W. (1999). An ordinal scale for transitive reasoning by means of a deductive strategy.International Journal of Behavioral Development, 23, 241–264.

    Google Scholar 

  • Wright, B.C. (2001). Reconceptualizing the transitive inference ability: A framework for existing and future research.Developmental Review, 21, 375–422.

    Google Scholar 

  • Zhang, J., & Stout, W. (1999a). Conditional covariance structure of generalized compensatory multidimensional items.Psychometrika, 64, 129–152.

    Google Scholar 

  • Zhang, J., & Stout, W. (1999b). The theoretical DETECT index of dimensionality and its application to approximate simple structure.Psychometrika, 64, 213–249.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Methodology and Statistics FSW, Tilburg University, P.O. Box 90153, 5000 LE, Tilburg, The Netherlands

    Samantha Bouwmeester & Klaas Sijtsma

Authors
  1. Samantha Bouwmeester
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Klaas Sijtsma
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Samantha Bouwmeester.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bouwmeester, S., Sijtsma, K. Measuring the ability of transitive reasoning, using product and strategy information. Psychometrika 69, 123–146 (2004). https://doi.org/10.1007/BF02295843

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02295843

Key words

Search

Navigation