The Importance Of Interval Timing In Cognitive Development

Interest in comparative cognition, mental processes subserving thought without language, and the development of temporal knowledge have contributed to the recent excitement surrounding studies of interval timing and counting in preverbal infants and young children (see Brannon and Roitman, this volume; Droit-Volet, this volume). One of the central issues is whether children are able to time with the same accuracy and precision as adults or whether there are developmental transitions in their timing abilities (e.g., Droit-Volet and Wearden, 2001; McCormack et al., 1999). Other issues are concerned with the way in which children understand and abstract knowledge of duration from other stimulus attributes such as force and deal with attentional distraction during a timing task (e.g., Droit-Volet, 1998, this volume; Gautier and Droit-Volet, 2002). For example, when 3- and 51/2-year-old children are asked to carry out a response duration task in which they are instructed to press longer or harder than in a previous session, the results indicate that 3-year-olds rely on a certain amount of force to produce the correct response duration. In contrast, the 51/2-year-olds are able to dissociate force and duration; i.e., when they are asked to press harder, they do not press longer (Droit-Volet, 1998, this volume). These findings indicate that a marked dissociation between force and duration only emerges between the ages of 3 and 51/2 and suggest different conceptualizations of time as a function of experience and maturation.

Analog representations of stimulus magnitudes have also been explored using mode-control models of temporal integration as a guide for understanding nonsym-bolic counting and timing processes in animals, nonverbal infants, young children, and adults (see Brannon and Roitman, this volume; Clement and Droit-Volet, 2001; Dehaene et al., 1999; Gallistel and Gelman, 1992; Meck and Church, 1983; Meck et al., 1985; Wynn, 1995, 1998). The mode-control model posits that magnitude estimations of time and number are mediated by the same pacemaker-accumulator system, but operated in different pulse accumulation modes (e.g., a run mode for time and an event mode for number). This unified model of temporal integration has become influential in the debate surrounding the foundations of numerical thinking and the evidence for nonverbal counting ability in a variety of animals, including monkeys and human infants (e.g., Brannon and Roitman, this volume; Brannon and Terrace, 1998; Brannon et al., 2001; Breukelaar and Dalrymple-Alford, 1999; Broadbent et al., 1993; Church and Meck, 1984; Dehaene et al., 1999; Gallistel, 1990; Gallistel and Gelman, 1992; Grondin et al., 1999; Roberts, 1995; Roberts and Mitchell, 1994; Starkey et al., 1990; Whalen et al., 1999; Wynn, 1992, 1995, 1998; Wynn and Chiang, 1998).

In order to illustrate, it is sometimes helpful to count only when a certain condition occurs. For example, if timing pulses are counted when a machine is running (i.e., the ON signal is true), you can calculate the percentage of time the machine is in use just by comparing the total count with the elapsed time. This calculation is simple even though the machine may start and stop many times during the monitoring. In order to do this, the counter must have a switch input, as well as its normal count input. You connect the machine's ON signal to the switch and a source of clock pulses to the normal count input, making the measurements within the counter. The way that this mechanism is applied in the mode-control model is that at the onset of a relevant stimulus, pulses are directed into an accumulator so that they can be integrated over time. This is accomplished by a mode switch that allows pulses to flow into the accumulator in one of three different modes, depending on the nature of the stimulus (see Brannon and Roitman, this volume; Meck, 1997; Meck and Church, 1983; Meck et al., 1985). In this model numerosity is represented by the linear magnitude of an internal variable (e.g., pulse accumulation), and it is this value that is remembered and entered into calculation. The mode-control model is assumed to be a model of counting when the switch is set to the event mode. In this condition discreet stimuli are marked by a fixed increment in the accumulator. It is this temporal integration process that represents the numerosity of events or objects and thus constitutes this model's proposed numeron, just as this same temporal integration process represents duration when pulses are gated through the switch in the run or stop mode.

The mode-control model provides a unified theory of counting and timing by positing the existence of an isomorphism between number and duration. The model incorporates the idea that the nervous system inverts the representational convention whereby numbers are used to represent linear magnitudes. Instead of using number to represent magnitude, it is proposed that the nervous system uses magnitude to represent number (see Carey, 2001; Gallistel and Gelman, 2000; Gelman and Cordes, 2001).

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