Friedrich Wilkening

Integrating velocity, time, and distance information: A developmental study ☆ ☆☆

Abstract The development of understanding the relationships between velocity, time, and distance was investigated in three tasks. In each task, values of two dimensions were given, and 5-year-olds, 10-year-olds, and adults had to infer values of the third dimension. These inferences were made in all age groups. The integration rules were found to depend upon age and task. In the distance = time × velocity task, all age groups obeyed the normative multiplication rule. In the time = distance ÷ velocity task, the two older age groups obeyed the normative division rule, but the 5-year-olds shifted to a simpler subtraction rule. In the velocity = distance ÷ time task, which was the most difficult, the two older age groups simplified to use of a subtraction rule, and the 5-year-olds simplified even further to use of a distance-only rule. The knowledge level revealed for young children contrasts sharply with results from previous studies using Piagetian choice tasks, which apparently investigate selective attention to one dimension rather than conceptual understanding of relations.

Intuitive physics in action and judgment: The development of knowledge about projectile motion.

This article contrasts intuitive knowledge about projectile motion expressed in action with knowledge expressed in explicit judgments. In the action condition of Experiment 1 children and adults threw a ball horizontally from different heights to hit targets on the floor; in the judgment condition the same subjects rated the respective launch speeds required. All age groups appropriately varied the launch speed with respect to both height of release and target distance in the action condition. In the judgment condition, however, kindergartners failed to integrate the relevant dimensions and even fourth graders and adults showed misconceptions of the speed-height relation. Experiment 2 established that the speed gradations in the action condition did not critically depend on visual flight feedback or the availability of outcome information

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 and adolescents' intuitive judgements about distributive justice: Integrating need, effort, and luck

This study investigated the principles that children and adolescents rely on when allocating a resource fairly. In a series of three experiments, 51 Swiss children (aged 7 and 9 years) and 309 German children (aged 6, 9, and 15 years) participated. A different situational context was presented in each experiment, where luck, need and effort of two protagonists were systematically varied. Primary-school children relied mainly on need when making distributive justice judgements. Effort became more prominent as the allocation principle in adolescence. Equality occurred rarely in all age groups. Integrational capacity and the ability to differentiate between the three situational contexts increased from childhood to adolescence. The data suggest the conclusion that the development of distributive justice decisions has both generalized and context-specific components.

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.

Judgment and action knowledge in speed adjustment tasks: experiments in a virtual environment

Two experiments were conducted to investigate childrens and adults’ knowledge of time and speed in action and judgment tasks. Participants had to set the speed of a moving car to a new speed so that it would reach a target line at the same time as a reference car moving at a higher speed and disappearing in a tunnel at the midway point. In Experiment 1 (24 10-year-olds, 24 adults), childrens and adults’ speed adjustments followed the normative pattern when responses had to be graded linearly as a function of the cars initial speed. In a non-linear condition, only adults’ action responses corresponded with the normative function. Simplifying the task by shortening the tunnel systematically in Experiment 2 (24 10-year-olds, 24 adults) enabled children to grade the speeds adequately in the action conditions only. Adults now produced normative response patterns in both judgment and action. Whether people show linearization biases was thus shown to depend on the interaction of age, task demands and response mode.

How to speed up to be in time: Action-judgment dissociations in children and adults

Children 6 and 10 years of age and adults were asked how fast a toy car had to be to catch up with another car, the latter moving with a constant speed throughout. The speed change was required either after half of the time (linear condition) or half of the distance (nonlinear condition), and responses were given either on a rating scale (judgment condition) or by actually producing the motion (action condition). In the linear condition, the data patterns for both judgments and actions were in accordance with the normative rule at all ages. This was not true for the nonlinear condition, where children’s and adults’ judgment and also children’s action patterns were linear, and only adults’ action patterns were in line with the nonlinearity principle. Discussing the reasons for the misconceptions and for the action-judgment dissociations, a claim is made for a new view on the development of children’s concepts of time and speed.

Chapter 3 Measuring Time via Counting: The Development of Children's Conceptions of Time as a Quantifiable Dimension

Publisher Summary This chapter explores the questions of when children come to treat time as a quantifiable dimension and what strategies they invent on their own when trying to measure the duration of short events. Children as young as 5 years can conceive of time as a quantitative entity. They can also quantify durations on the basis of “pure” time information in events that do not involve speed and distance information. Childrens quantification of time comes out most clearly in the algebraic addition rules for the integration of successive events. The quantification can be read off directly from the factorial plots of the judgments. Not only did these children discriminate different levels of durations, but they also integrated them as prescribed by the normative adding rule. The adding rule can be used to yield validated scales of subjective time, according to the logic of functional measurement. The quality of childrens time judgments—and of their integration rules—did not only vary with the problem structure but also with the strategies they used to measure the passage of time.

A misrepresentation of knowledge representation

Abstract D. D. Kerkman and J. C. Wrights comparison (1988, Developmental Review, 8, 323–360) of two theories of problem-solving development rests on a fundamental misunderstanding. Contrary to Kerkman and Wright, nonalgebraic rules, including centration and sequential decision rules, are theoretically allowed and have been empirically demonstrated in a number of studies of information integration theory. Moreover, the hybrid model proposed by Kerkman and Wright, namely, a development from sequential decision rules to algebraic integration rules, does not contradict information integration theory but instead conforms with what has already explicitly been demonstrated in its empirical applications.

Children's recognition of the usefulness of a record: Distinguishing deterministic and probabilistic events

Children aged six, eight, and ten years were asked to decide which of two devices—one deterministically functioning and the other probabilistically functioning—they wanted to keep a record of in order to find out whether or not the device worked properly. The devices were a ball-dropping device (deterministic) and a spinner (probabilistic). To investigate the devices, the children were asked to observe—and potentially record—only as many events as necessary in order to determine the function of each device with sufficient certainty. Children investigated both devices first in a rigged and then in a natural state. In Experiment 1, only the ten year olds showed a good understanding of a records relative usefulness for investigating the functioning of the probabilistic in preference to the deterministic device. Younger children did not adapt the record keeping to the different kinds of functioning. This might have been related to their difficulties in understanding the deterministic character of the ball-dropping device, therefore its deterministic character was made more salient in Experiment 2. However, this manipulation did not change the results. In both experiments, only the ten year olds appeared to have a good understanding of the fact that a decision about the probabilistic nature of an event sequence requires a relatively large number of observations and therefore, if faced with a choice, a record is more useful for the investigation of probabilistic than deterministic phenomena.