On the emergence of the discriminative mode for transitive-inference

Abstract

Transitive-inference tasks play increasing roles in many areas of cognitive science. However, discrepancies between the two competing paradigms (classical-Piagetian and IP-paradigm) imply that one paradigm fails to index its target (deductive) competence. Here, potential flaws of one were addressed using considerations from the other. Children of 5 Á7 years (N 0/216) solved 3-term transitive problems, some implying a single largest item, and some not. Findings indicate a discriminative competence (a Transitive-Switch) at least 2 years before competence in actually deducing correct solutions. Interestingly, although the transitive-switch was constant across age with both memory and inference increasing with age, it was nevertheless a much stronger predictor of transitive performance than either memory or age. A predictive relationship between memory and inference held for the 5-and 6-year-olds but not the 7-year-olds; suggesting as it approaches maturity, transitive-inference becomes independent of memory. Coincidental with this latter finding, only the 7-year-olds' transitive performance approximated a deductive competence. As the initial validation of the IP-paradigm rested on acceptance of its age estimate of 4 years, its claim to index deduction must now be revisited.You might notice on one day that a friend jogs faster than yourself; and then on a different day notice that you jog faster than another friend. If you then deduce the fastest, without needing to measure jogging speeds or to wait for an occasion where all three are jogging together, you have demonstrated a particular form of relational reasoning called ''transitive-inference'' (TI). As a second example, a transitive-inference might permit the reasoner to decide whether different objects bear particular size or spatial relationships within a scene (e.g., are expected to be to the left or right of certain other objects even Correspondence should be addressed to

Transitivity for height versus speed: To what extent do the under-7s really have a transitive capacity?

“…A similar test for 5 year-olds showed that they were reliably above chance (t (65) = 3.566, p = 0.001), as were the 6 year-olds (t (82) = 9.119, p < 0.001). Wright (2006a) suggests that the notion of a competence threshold might be useful in developmental research on transitive reasoning. Borrowing the concept from general psychophysical designs, he asserted that the competence threshold should be defined as that level laying as close to perfect performance as it is to chance performance.…”

“…This finding is in close agreement with three-term studies (e.g., Markovits & Dumas, 1999; cf. Oakhill, 1984;Wright, 2006a).…”

“…This finding is in close agreement with three-term studies (e.g., Markovits & Dumas, 1999; cf. Oakhill, 1984;Wright, 2006a).What was essentially a simplified variant on Kallio's design was subsequently employed by Pears and Bryant (1990). The main difference was the use of three-dimensional blocks which could be manipulated by the children, instead of them having to reason about drawings of rockets/planes as in the Kallio study.…”

“…In one three-term study, Wright (2006a) showed 5 to 7 year-olds objects (rods, spheres & cubes) with such small differences in size that their relative sizes were quite hard to discern when two Transitivity for Height v Speed 7 objects were held at arms length (around 2m apart but also around 3m away from the child). Once children correctly encoded which was bigger within each of two pairs, they were asked to restate the two premises for themselves and then deduce and report the biggest object.…”

“…4, Finally, we wanted to use a paradigm offering specifically 4 year-olds every opportunity to show their transitive deductive capacity but which did not risk giving them "non-logical" cues to the correct answers (Riley & Trabasso, 1974;Wright & Dowker, 2002). Additionally, we wanted to assess the view emerging from virtually every relevant study of the past 20 years, that deductive transitive reasoning does not reach a level indicative of competence until after 6 years (Ameel et al, 2007;Artman & Cahan, 1993;Markovits et al, 1995;Markovits & Dumas, 1999;Rabinowitz et al, 1994;Wright, 2006a). …”