Number Presented

FIGURE 6.2 (a) The probability of signaling response completion as a function of the number of responses the rat made and the number that was required to obtain reward. Data from Platt and Johnson (1971). (b) The mean number of responses made (left axis, circles) and the standard deviation (right axis, squares) of the response distributions shown in panel (a), and the coefficient of variation (CV), which is the ratio of the standard deviation to the mean, as a function of the number required. (c) The mean (left axis, circles), standard deviation (right axis, squares), and CV (lower panel) as a function of the number of button responses required obtained by Whalen et al. (1999). The constant CV shown for rats in panel (b) and humans in panel (c) demonstrates that both species represent number with scalar variability.

In another version of a number production paradigm, Xia et al. (2000) trained pigeons to flexibly produce one to six responses cued by specific visual symbols. The pigeons' accuracy decreased with increasing number; however, four of six birds were above chance on all six numerosities, and nine of nine were above chance when only the numerosities 1 to 4 were tested (see also Rumbaugh and Washburn,

1993). Collectively, these studies suggest that animals can be trained to make a given number of responses; however, the very nature of these experimental designs makes it difficult to determine whether the animals were basing their judgments on the number of their own responses or instead some correlated attribute of the trials, such as the duration of responding or effort expended. To address this problem, some researchers have manipulated the rate of responding by using pharmacological manipulations or food restriction (e.g., Mechner and Guevrekian, 1962); other researchers have turned to different experimental designs altogether.

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