A set of transitivity tasks was solved on two occasions by 634 2nd through 6th grade
primary school children. Transitivity scales were constructed for both occasions
using Mokken scale analysis. Combining the results, one final scale was constructed
for use in future research. The order of the scale tasks according to their
difficulty level was the same on both occasions. Analysis of the scale scores of one
group retested after 16 weeks and two control groups revealed an absence of effects
due to memorisation or test experience. It was concluded that the final scale is
useful as a transitivity measure in longitudinal research.
Get full access to this article
View all access options for this article.
References
1.
Andrich, D.
(1978).
A rating formulation for ordered response categories
. Psychometrika, 43,
561-573
.
2.
Braine, M.D.
(1959).
The ontogeny of certain logical operations: Piaget's formulation examined
by nonverbal methods
. Psychological Monographs, 73,
1-43
.
3.
Brainerd, CJ.
(1973a).
Order of acquisition of transitivity, conservation, and class inclusion of
length and weight
. Developmental Psychology, 8,
105-116
.
4.
Brainerd, C.J.
(1973b).
Judgments and explanations as criteria for the presence of cognitive structures
. Psychological Bulletin, 79,
172-179
.
5.
Brainerd, C.J.
(1974).
Training and transfer of transitivity, conservation, and class inclusion of length
. Child Development, 45,
324-334
.
6.
Brainerd, C.J.
(1977).
Response criteria in concept development
. Child Development, 48,
360-366
.
7.
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
.
8.
Brainerd, C.J.
, &
Kingma, J.
(1985).
On the independence of short-term memory and working memory in cognitive development
. Cognitive Psychology, 17,
210-247
.
9.
Brainerd, C.J.
, &
Reyna, V.F.
(1990).
Gist is the grist: Fuzzy-Trace theory and the new intuitionism
. Developmental Review, 10,
3-47
.
10.
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
.
11.
Breslow, L.
(1981).
Re-evaluation of the literature on the development of transitive inferences
. Psychological Bulletin, 89,
325-351
.
12.
Bryant, P.E.
, &
Trabasso, T.
(1971).
Transitive inferences and memory in young children
. Nature, 232,
456-458
.
13.
Chapman, M.
, &
Lindenberger, U.
(1988).
Functions, operations, and decalage in the development of transitivity
. Developmental Psychology, 24,
542-551
.
14.
Chapman, M.
, &
Lindenberger, U.
(1992a).
Transitivityjudgments, memory of premises, and models of children's reasoning
. Developmental Review, 12,
124-163
.
15.
Chapman, M.
, &
Lindenberger, U.
(1992b).
How to detect reasoning-remembering dependence (and how not to)
. Developmental Review, 12,
187-198
.
16.
Debets, P.
, &
Brouwer, E.
(1989). User's manual MSP.
Groningen: iec ProGAMMA, Rijksuniversiteit Groningen
.
17.
Debets, P.
,
Sijtsma, K.
,
Brouwer, E.
, &
Molenaar, I.W.
(1989).
MSP: a computer program for item analysis according to a nonparametric IRT approach
. Psychometrika, 54,
534-536
.
18.
DeBoysson-Bardies, B.
, &
O'Regan, K.
(1973).
What children do in spite of adult's hypotheses
. Nature, 246,
531-534
.
19.
Dickson, L.
,
Brown, M.
, &
Gibson, O.
(1984). Children learning mathematics (pp.
79-143).
Oxford: Holt. Rinehart & Winston
.
20.
Foos, P.W.
,
Smith, K.F.
,
Sabol, M.A.
, &
Mynatt, B.T.
(1976).
Cognitive processes in simple linear order problems
. Journal of Experimental Psychology: Human Learning and
Memory, 2,
759-766
.
21.
Geert, van P.L.C.
(1979). De ontwikkeling van het begrijpen (The development
of understanding). In
W. Koops
&
J.J. van der Werff
(Eds.), Overzicht van de ontwikkelingspsychologie (pp.
163-193).
Groningen: Wolters Noordhoff
.
22.
Guttman, L.
(1950). The basis for scalogram analysis. In
S.A. Stouffer
,
L. Guttman
,
E.A. Suchman
,
P.F. Lazarsfeld
,
S.A. Star
, &
J.A. Clausen
(Eds.), Measurement and prediction (pp.
60-90).
Princeton, NJ: Princeton University Press
.
23.
Halford, G.S.
, &
Galloway, W.
(1977).
Children who fail to make transitive inferences can remember comparisons
. Australian Journal of Psychology, 29,
1-5
.
24.
Halford, G.S.
, &
Kelly, M.E.
(1984).
On the basis of early transitive judgments
. Journal of Experimental Child Psychology, 38,
42-63
.
25.
Harris, P.L.
, &
Bassett, E.
(1975).
Transitive inference by four-year-old children
. Developmental Psychology, 11,
875-876
.
26.
Holland, P.W.
, &
Rosenbaum, P.R.
(1986).
Conditional association and unidimensionality in monotone latent trait models
. Annals of Statistics, 14,
1523-1543
.
27.
Kallio, K.D.
(1982).
Developmental change on a five-term transitive inference
. Journal of Experimental Child Psychology, 33,
142-164
.
28.
Keating, D.P.
, &
Caramazza, A.
(1975).
Effects of age and ability on syllogistic reasoning in early adolescence
. Developmental Psychology, 11,
837-842
.
29.
Kingma, J.
, &
Reuvekamp, J.
(1984).
The construction of a developmental scale for seriation
. Educational and Psychological Measurement, 44,
1-23
.
30.
Kingma, J.
, &
TenVergert, E.M.
(1985).
A nonparametric scale analysis of the development of conservation
. Applied Psychological Measurement, 9,
375-387
.
31.
Langer, S.K.
(1967). An introduction to symbolic logic.
New York: Dover
.
32.
Loevinger, J.
(1948).
The technique of homogeneous tests compared with some aspects of "scale
analysis" and factor analysis
. Psychological Bulletin, 45,
507-530
.
33.
Lord, F.M.
, &
Novick, M.R.
(1968). Statistical theories of mental test scores.
Reading, MA: Addison-Wesley
.
34.
McManis, D.L.
(1969).
Conservation and transitivity of length by normals and retardates
. Developmental Psychology, 1,
373-382
.
35.
Meijer, R.R.
,
Sijtsma, K.
, &
Smid, N.G.
(1990).
Theoretical and empirical comparison of the Mokken and the Rasch approach
to IRT
. Applied Psychological Measurement, 14,
283-298
.
36.
Mokken, R.J.
(1971). A theory and procedure of scale analysis.
Den Haag: Mouton
.
37.
Mokken, R.J.
, &
Lewis, C.
(1982).
A nonparametric approach to the analysis of dichotomous item responses
. Applied Psychological Measurement, 6,
417-430
.
38.
Mokken, R.J.
,
Lewis, C.
, &
Sijtsma, K.
(1986).
Rejoinder to "The Mokken scale: A critical discussion"
. Applied Psychological Measurement, 10,
279-285
.
Molenaar, I.W.
(1986). Een vingeroefening in item response theorie voor
drie geordende antwoordcategoriecn [An exercise in item response theory for
three ordered answer categories]. In
G.F. Pikkemaat
&
J.J.A. Moors
(Eds.), Liber amicorum Jaap Muilwijk (pp.
39-57).
Groningen: Econometrisch Instituut
.
41.
Molenaar, I.W.
(1991).
A weighted Loevinger H-coefficient extending Mokken scaling to
multicategory items
. Kwantitatieve Methoden, 37,
97-117
.
42.
Molenaar, I.W.
(in press). Nonparametric methods for polytomous responses.
In
W.J. van der Linden
&
R.K. Hambleton
(Eds.), Handbook of modern psychometrics.
New York: Springer
.
43.
Molenaar, I.W.
, &
Sijtsma, K.
(1988).
Mokken's approach to reliability estimation extended to multicategory items
. Kwantitatieve Methoden, 28,
115-126
.
44.
Murray, J.P.
, &
Youniss, J.
(1968)
Achievement of inferential transitivity and its relation to serial ordering
. Child Development, 39,
1259-1268
.
45.
Perner, J.
, &
Aebi, J.
(1985).
Feedback-dependent encoding of length series
. British Journal of Developmental Psychology, 3,
133-141
.
46.
Perner, J.
, &
Mansbridge, D.G.
(1983).
Developmental differences in encoding length series
. Child Development, 54,
710-719
.
47.
Perner, J.
,
Steiner, G.
, &
Steahelin, C.
(1981).
Mental representation of length and weight series and transitive inferences
in young children
. Journal of Experimental Child Psychology, 31,
177-192
.
48.
Piaget, J. (1942). Classes, relations et nombres: Essai sur les
groupements de la logistique et sur la reversibilite de la pensee. Paris: Collin.
49.
Piaget, J., & Inhelder, B. (1941). Le developpement des quantites
chez lenfant. Neuchatel: Delachaux et Niestle.
50.
Piaget, J., & Szeminska, A. (1941). La genèse du
nombre chex l'enfant. Neuchâtel: Delachaux et Niestlé.
51.
Piaget, J.
,
Grize, J.B.
,
Szeminska, A.
, &
Vinh Bang
. (1977). Epistemology and psychology of functions.
Dordrecht: Reidel
.
52.
Piaget, J., Inhelder, B., & Szeminska, A. (1948). La geometrique
spontanee de lenfant. Paris: Presses Universitaires de France.
53.
Reyna, V.F.
, &
Brainerd, C.J.
(1990).
Fuzzy processing in transitivity development
. Annals of Operations Research, 23,
37-63
.
54.
Riley, C.A.
(1976).
The representation of comparative relations and the transitive inference task
. Journal of Experimental Child Psychology, 22,
1-22
.
55.
Riley, C.A.
, &
Trabasso, T.
(1974).
Comparative, logical structures and encoding in a transitive inference task
. Journal of Experimental Child Psychology, 17,
187-203
.
Russell, J.
(1981).
Children's memory for the premises in a transitive measurement task
assessed by elicited and spontaneous justifications
. Journal of Experimental Child Psychology, 31,
300-309
.
58.
Sijtsma, K.
,
Debets, P.
, &
Molenaar, I.W.
(1990).
Mokken scale analysis for polychotomous items: Theory, a computer program
and an empirical application
. Quality & Quantity, 24,
173-188
.
59.
Sijtsma, K.
. &
Molenaar, I.W.
(1987).
Reliability of test scores in nonparametric item response theory
. Psychometrika, 52,
79-97
.
60.
Smedslund, J.
(1963).
Development of concrete transitivity of length in children
. Child Development, 34,
389-405
.
61.
Sternberg, R.J.
(1980a).
Representation and process in linear syllogistic reasoning
. Journal of Experimental Psychology: General, 109,
119-159
.
62.
Sternberg, R.J.
(1980b).
The development of linear syllogistic reasoning
. Journal of Experimental Child Psychology, 29,
342-356
.
63.
Thayer, E.S.
, &
Collyer, C.E.
(1978).
The development of transitive inference: A review of recent approaches
. Psychological Bulletin, 85,
1327-1343
.
64.
Trabasso, T.
(1975). Representation, memory and reasoning: How do we
make transitive inferences? In
A.D. Pick
(Ed.), Minnesota symposia on child psychology (Vol. 9, pp.
135-172).
Minneapolis, MN: University of Minnesota Press
.
65.
Trabasso, T.
(1977). The role of memory as a system in making
transitive inferences. In
R.V.Kail
&
J.W. Hagen
(Eds.), Perspectives on the development of memory and cognition
(pp.333-336).
Hillsdale, NJ: Lawrence Erlbaum Associates Inc.
