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FIGURE 7.2 Psychophysical functions obtained from the 3-, 5-, and 8-year-olds in a temporal bisection task in two anchor duration conditions (1/4 and 2/8 sec) (Droit-Volet and Wearden, 2001), with an example of temporal bisection function obtained from the human adults derived from Wearden (1991). (From Droit-Volet, S. and Wearden, J., J. Exp. Child Psychol, 80, 142-159, 2001.)

phase that maintained the conditions of training, except that the feedback was discontinuous. Furthermore, they received eight or ten blocks of seven trials, two for the two standard durations and five for the intermediate nonstandard durations.

A typical psychophysical function found in human adults in a temporal bisection task, with the mean proportion of long responses (i.e., comparison stimulus durations identified as similar to the long standard duration), plotted against a comparison stimulus duration, is shown in the bottom right panel of Figure 7.2. The slope of this temporal bisection function is steep, indicating a high sensitivity to duration. The Weber ratio (difference limen divided by the bisection point), that is, an index of the steepness of the temporal bisection function, is therefore particularly small (e.g., 0.17 in Wearden's (1991) study). In light of adult temporal bisection performance, several questions can be raised from a developmental perspective. Are children in different age groups capable of duration discrimination in a temporal bisection task? Does the temporal bisection performance in children differ from that in adults? If yes, what might developmental changes in temporal bisection performance look like? And, finally, what are the main causes of these developmental changes?

Until now, the youngest children who have been tested on a temporal bisection task are 3 years old. Figure 7.2 shows their temporal bisection functions (top left), as well as those of older children aged 5 years old (bottom left) and 8 years old (top right). In this figure extracted from Droit-Volet and Wearden's (2001) study, there are two ranges of durations tested, each longer than 1 sec (i.e., 1 to 4 sec and 2 to 8 sec), similar to those generally used in experiments with rats and pigeons. Using these time values without any concurrent distracting task is possible in young children because, unlike adults, they do not spontaneously use counting strategies to time durations up to 10 years (Friedman, 1990a; Wilkening et al., 1987). However, as in studies preventing counting strategies in human adults, Droit-Volet and Wearden (2002) and McCormack et al. (1999) have also used time values shorter than 1 sec with children and have obtained nearly identical temporal bisection functions to those reported in Figure 7.2.

Thus, Figure 7.2 reveals that the temporal bisection task produced orderly data from children as young as 3 years old. At this age, the proportion of long responses increased as the stimulus duration value increased. Therefore, young children are able to discriminate different durations in a temporal bisection task. Furthermore, the use of two ranges of durations allows us to test whether interval timing in children conforms to the scalar property of variance, characteristic of interval timing in animals and human adults. This property is a form of Weber's law (Gibbon, 1977; Gibbon et al., 1984), in which the standard deviation of time judgments grows as a constant fraction of the mean time judgment when different time values are judged. A way to test this scalar property is to examine how well the temporal bisection functions for different time values superimpose when plotted on the same relative time scale (Allan and Gibbon, 1991). Following up on this test in children with both short and long durations, Droit-Volet and Wearden (2001, 2002) found that children's temporal bisection behavior conforms well to the principle of superimposition at all age groups tested. Thus, the scalar property of variance common to the interval timing behavior of animals and human adults is characteristic of interval timing behavior at different levels of the ontogenetic scale, or at least from the age of 3 years in children.

Beyond the similarities, there were also differences in temporal bisection performance between children and adults. In particular, the slope of the psychophysical functions increased with age, being flatter in the 3- and 5-year-olds than in the 8-year-olds, the age at which it was close to the adults'. As a result, the Weber ratio was on average higher in the 3- and 5-year-olds (0.39 and 0.37, respectively) than in the 8-year-olds (0.21), with adults typically showing a Weber ratio of 0.17 (e.g., Wearden, 1991). As the bisection slope and the Weber ratio are two indexes of temporal sensitivity, these data indicate that there was an increase with age in sensitivity for duration in the temporal bisection task.

The question now is: How can we explain these age-related changes in temporal sensitivity in a temporal bisection task? One way is to use the models based on the scalar timing theory accounting for temporal bisection performance in human adults (e.g., Allan and Gibbon, 1991; Wearden, 1991; for more details, see Droit-Volet and Wearden, 2001). More specifically, we used the modified difference model of Wearden (1991). The scalar timing theory proposes that the raw material for time judgments comes from a pacemaker-accumulator system. However, the model also involves memory and decision processes. In the case of bisection, the comparison stimulus duration, t, is assumed to be stored in working memory and reflects the amount of pulses counted in the accumulator of the clock. By contrast, the short and the long standard durations are represented in long-term memory. According to the scalar timing model, the decision to classify the comparison stimulus duration as more similar to the short or the long standard is governed by the difference between the comparison stimulus duration and samples drawn from the long-term memory of the short and the long standard (s*, l*). The memory representations of the short and the long standard are stored as distributions rather than single values, with means equal to the standard values and some coefficient of variation c. The higher this coefficient of variation, the greater is the variability of standard representation in memory, and the flatter the psychophysical function will be. The coefficient of variation of the remembered time is thus a kind of sensitivity parameter controlling the slope of the psychophysical function. The first explanation that we can provide for our developmental data is that the increase in timing sensitivity with age would be related to the decrease in the coefficient of variation of the remembered time. However, psychophysical functions can also differ because of random responses, given regardless of stimulus duration values. Random responding is rare in human adults, but this has been observed in animals. Bridging the gap between animal and human adult timing behavior, we can propose a second hypothesis that the amount of random responses in children would decrease with the increasing age. Interestingly, the probability of random responses is the only parameter that we need to add to the scalar timing model in order to obtain an excellent correspondence between the simulation and our temporal bisection data from young children.

In addition, according to the scalar timing model, responding "short" or "long" depends on a decision threshold adopted by the subject. The model predicts that if the difference between D(s*, t) and D(l*, t) is greater than some threshold value, b, the subject responds short if D(s*, t) < D(l*, t) and long if D(s*, t) > D(l*, t), where D equals the difference. However, facing ambiguous cases, if the differences are not clearly discriminated and are less than the threshold value, b, the model chooses to respond long. The b parameter is thus a kind of bias toward responding long. This bias toward long responses does not affect the slope of the temporal bisection function, but it shifts the psychophysical function laterally. Thus, the different bisection patterns observed at different ages could also be in part due to a developmental change in the bias toward long responses.

This scalar timing model adapted to children's timing behavior fits our data very well (Droit-Volet and Wearden, 2001; Rattat and Droit-Volet, 2001) and has allowed us to identify two main sources of developmental changes in temporal bisection performance. First, the coefficient of variation of the representation of standard durations was the highest in the 3-year-olds and the lowest in the 8-year-olds. Thus, the increase in the sensitivity to time was related to the decrease in the variability of the representation of standard durations in long-term memory. Second, the probability of random responding was between 10 and 20% of responses in the 3- and 5-year-olds and near zero in the 8-year-olds (0.01), as in the adults. Thus, the probability of random responses contaminating timing behavior in temporal bisection decreased with the increasing age of the children. By contrast, the b values were small and constant across the different age groups. In other words, this bias toward responding long did not vary with age. To sum up, temporal sensitivity in temporal bisection is lower in younger children, and the developmental version of the scalar timing model suggests that this is due to the decrease with increasing age in the variability of the long-term memory representation of the standard durations, and the probability of random responding.

7.2.2 Temporal Generalization in Children

Interval timing behavior in children has also been tested with the temporal generalization procedure. In our studies, the children were first presented a standard duration. Then they received a series of comparison stimulus durations shorter than, longer than, or equal to the standard duration. Their task was to indicate whether the just-presented comparison duration was the standard (yes or no response). A correct response resulted in the appearance of a smiling clown, and an incorrect response in a frowning clown (Figure 7.1). Under similar experimental conditions, McCormack et al. (1999) evaluated temporal generalization performance in children from 5 to 10 years using one standard duration that was shorter than 1 sec, and Droit-Volet et al. have evaluated children from 3 to 8 years of age using two ranges of durations, in order to test conformity to the scalar property of variance. In a first study (Droit-Volet et al., 2001), they used two standard durations longer than 1 sec, and in a second study (Droit-Volet, 2002), a standard duration of 400 msec and another ten times as long (i.e., 4.0 sec). The performance obtained from children in this latter study, with an example of generalization gradients obtained from human adults, is shown in Figure 7.3.

As one can see in Figure 7.3, for human adults, the temporal generalization task produces a gradient that peaks at the standard duration, with the proportion of yes responses declining as the deviation from the standard increases. In the present situation, the same orderly gradients were observed in children at the ages of 3, 5, and 8 years old. At the age of 3 years, the children were able to discriminate different durations in the temporal generalization task, as they did in the temporal bisection task. In addition, Droit-Volet et al. found neither a significant effect of the standard durations used nor a significant interaction involving this variable. This lack of effect with the standard duration is consistent with the scalar property of interval timing, according to which the overall proportion of yes responses was not affected by the standard duration. Supporting these results, in all age groups, the generalization gradients for different time values superimposed reasonably well when plotted on the same relative scale, as shown in Figure 7.3. Therefore, the scalar property of interval timing is obtained in children at different ages, as well as in animals and human adults, and this occurred in different temporal discrimination procedures: not only for the temporal bisection task, but also for the temporal generalization task. In short, the ability to exhibit interval timing is a general behavioral property observed at different levels of the ontogenetic scale.

However, in the temporal generalization procedure, there were also clear differences in performance between the children and the adults. Notably, the generalization

3-year-olds

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