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No abstract

Functional measurement methodology was used to assess children's attention to the total number of alternative outcomes as well as the number of target outcomes when making probability estimates. In Study 1, first-, third-, and fifth-grade children were given the task of estimating on a simple, continuous but nonnumeric scale the probability of drawing a particular color of jelly bean from a bag containing either 1, 2, or 3 jelly beans of that color, and either 6, 8, or 10 jelly beans total. In Study 2, first- through fifth-grade children were given the task of estimating the likelihood that a bug would fall on a pot containing a flower when presented displays of planters containing either 2, 3, 4, or 5 pots with flowers, and 6, 8, or 10 pots total. In both studies, the children were exposed to each of the combinations of numerator and denominator across 3 replications. The results indicate that all age groups attend to variations in the denominator as well as to variations in the numerator, and, furthermore, that they attend to the interaction between these variables. This finding contrasts sharply with research that requires children to choose which of 2 containers offers the greater chance of yielding a target item in a blind draw. It is suggested that children possess the skill to make accurate probability estimates, but they are unaware that these estimates should always be made and used when comparing the probability of an event across trials. The findings are discussed in relation to the broader issue of the limitations of the choice paradigm as a means of investigating children's thinking.

Uncertainty surely plays an important role in promoting and directing cognitive growth, but most investigations of children’s reasoning and problem solving have relied on procedures that are poorly suited to reveal the degree to which individuals are certain of the answers they endorse. We examine research on children’s reasoning in the context of obvious indeterminacy in order to assess whether simple modifications of the standard assessment procedures would allow us to monitor subjective certainty more reliably. It is concluded that when we set as our goal the measurement of judgment certainty, major changes in our testing methods are required. Two promising alternatives are considered, and it is hypothesized that once these new procedures are perfected and applied, we will discover that uncertainties are both prevalent and prolonged – that most of what seems to be known at any one time is actually understood only partially and therefore with some degree of uncertainty. It is argued that this is a natural and acceptable situation. Progress requires only a relative degree of confidence and not complete certainty. Persistent, vague uncertainties, on the other hand, provide continuous motivation and sensitization for further discoveries, growth, and development.

First-, third-, fifth-, and sixth-grade children were administered 20 relational reasoning problems in which they had to deduce the possible sizes of one item relative to two others on the basis of a visual comparison of the sizes of the two other items and a written clue concerning the location(s) of the biggest or smallest of the three items. Some problems had single solutions, whereas others had multiple solutions. Although a high frequency of flawless performance on the single-solution problems was not seen until sixth grade, reasoning errors were less frequent than would be expected by chance even among the first-grade children. A ready facility for detecting the possibility of more than one correct solution to multiple-solution problems also did not emerge until sixth grade. Corrective feedback substantially improved the frequency with which first-through fifth-grade children detected multiple solutions on reassessment; however, this training failed to raise their performance to the level displayed spontaneously by the sixth-grade children.