Can a Piaget theory of discontinuities in development be investigated using Rasch's theory of a continuous measurement scale? Indeed it can! And in a series of three papers in Archives de Psychologie (1995), Trevor Bond demonstrates the value of a Rasch approach.
If Piaget's stages of development, advancing from concrete to abstract thinking,could only be observed as a series of distinct leaps, then they would produce Guttman response patterns in response data. We would know there were leaps in mental functioning, but we would not know how big they were. Unless they can be placed on a continuous measurement scale, it is impossible to discover how big are the leaps, which leaps are biggest, and how large they are compared with development between the leaps.
In fact, Bond's study shows that the responses do not form a perfect Guttman pattern, but they do show strong ordering. "The overwhelming degree of concurrence of stage allocations derived on the one hand from Piaget's idiosyncratic logical analyses and on the other by rigorous statistical analysis provides an unprecedented validation of this aspect of the Piagetian oeuvre." (Bond p.242)
The plot shows, on the right side, the Piagetian items validated by the measurement system -- observe the advance up from IIB to IIIA to IIIB (indicated to the extreme right). On the left side are the items which challenge Piaget's theory. Observe that the top IIIA is well into the IIIB's, suggesting there is no discontinuity. These items require either refinements to Piagetian theory or revisions to the item classification rules. Simply put, good measurement provokes better theory!
Trevor G. Bond is at the School of Education, James Cook
University of North Queensland, Townsville QLD 4811, Australia.
Bond T.G. (1996) Piaget and Measurement I: The twain really do meet. Archives de Psychologie 63, 71-87.
Bond T.G. (1996) Piaget and Measurement II: Empirical validation of the Piagetian model. Archives de Psychologie 63, 155-185.
Bond T.G. (1996) Piaget and Measurement III: Reassessing the Méthode Clinique. Archives de Psychologie 63, 231-255.
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Bond T.G. (1996) Piaget and Measurement. Rasch Measurement Transactions 10:2
Piaget and Measurement. Bond T.G. Rasch Measurement Transactions, 1996, 10:2 p. 491
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