Development of cognitive averaging: when light and light make dark.

In two experiments we studied developmental changes in reasoning about intensive quantities. In contrast to previous studies, color--an intensive quantity that is readily perceivable--was chosen as stimulus material. Children between 6 and 12 years of age and adults predicted the mixture intensity of pairs of liquids with different intensities of red color, the liquid volumes in the two source glasses either being the same (Experiment 1) or different (Experiment 2). The data show that cognitive averaging in this domain develops late and slowly. An extensitivity bias, a strong tendency to use rules (adding in particular) that hold for extensive but not for intensive quantities, predominated up to the age of 12 years and was not totally absent in adults. Contrary to common expectation, children's use of the correct averaging rule became more likely when an extensive quantity, volume, was also varied and thus the task increased in complexity.

Learning categories by touch: on the development of holistic and analytic processing.

The development of holistic and analytic processing often studied in the visual domain was investigated in haptics. Children 3 to 9 years of age and adults had to categorize haptic exemplars that varied systematically in four attributes (size, shape, surface texture, and weight). The subjects could learn the categories either analytically--that is, by focusing on a single attribute--or holistically--that is, in terms of overall similarity. The data show that even the youngest children learned the haptic categories far more often in an analytic mode than in a holistic mode. Nevertheless, an age trend was observed, referring to the attributes that the analytic learners used for their categorization. The children preferred substance-related attributes, especially surface texture, whereas the adults preferred structure-related attributes, especially shape. Thus, it appears that analytic and/or holistic processing in category learning develops in a similar manner in the visual and haptic domains.

Children's construction of fair chances: adjusting probabilities.

A probability-adjustment task was presented to 6-14-year-old children. In 2 experiments, children had to generate equal probabilities by completing the missing beads in a target urn with 1 type of beads presented beside a full urn with both winning and losing beads. The task was embedded in a competitive game. This relevant-involvement method secured optimal understanding and motivation. The analysis was based on number of matches with, and sum of distances from, the correct response and the predictions of other strategies. The results indicate that only at around the age of 13 did most children proportionally integrate the 2 dimensions (i.e., the numbers of winning and losing beads). The youngest sometimes relied on 1 dimension, and 9- and 10-year-olds partly combined the 2 types of quantities additively. The cognition involved in probability adjustment was analytic rather than global or intuitive. The ability to generate equal probabilities is discussed in terms of the many faces of probability.

Children's analogical reasoning about natural phenomena.

This report investigates children's analogical reasoning in a physics task, using an analogy generated by the children rather than by the experimenter. A total of 127 elementary school children took part in three related studies. Children learned to predict the behavior of a balance scale. Later, they were asked to solve a force interaction problem. Two versions of the balance scale training were devised: version A suggested an incorrect solution to the target problem (negative analogy), and version B suggested a correct solution to the target problem (positive analogy). In Study 1, 9- to 10-year-olds showed spontaneous transfer in both training conditions. In Study 2, 7-year-olds did not show any transfer in the positive analogy condition. Study 3 revealed that the lack of transfer in younger children was not due to a failure either to notice the analogy or to perform the mapping. Instead, 7-year-olds transferred only selected aspects of the correct solution.

Development of time quantification: integration and nonintegration of beginnings and endings in comparing durations.

This study investigated how children handle time information when deducing durations of events. In an elaboration of the commonly used choice paradigm to study children's time concepts, pairs of durations were presented in a 4 beginning lags X 4 ending lags design in 2 different problem series. Children's task was to equalize the durations of the 2 events by restarting 1 event for a certain time. The normative rule, quantification of duration differences in beginnings and endings and their integration by addition or subtraction, began to predominate at the age of 10 years and was the only rule employed by 13-year-olds. In contrast, almost all 7-year-olds simplified the task to an ordinal level. 4 different nonalgebraic rules were identified, each placing more importance on endings than on beginnings. Neither young children's tendency to simplify nor older children's capacity to quantify could be detected in previous studies, because they investigated time concepts on an ordinal level only. In light of the present findings, previous notions on the development of time concepts in children have to be reevaluated.