Investigating the influence of body movements on children's mental arithmetic performance.

Several lines of research have demonstrated spatial-numerical associations in both adults and children, which are thought to be based on a spatial representation of numerical information in the form of a mental number line. The acquisition of increasingly precise mental number line representations is assumed to support arithmetic learning in children. It is further suggested that sensorimotor experiences shape the development of number concepts and arithmetic learning, and that mental arithmetic can be characterized as "motion along a path" and might constitute shifts in attention along the mental number line. The present study investigated whether movements in physical space influence mental arithmetic in primary school children, and whether the expected effect depends on concurrency of body movements and mental arithmetic. After turning their body towards the left or right, 48 children aged 8 to 10 years solved simple subtraction and addition problems. Meanwhile, they either walked or stood still and looked towards the respective direction. We report a congruency effect between body orientation and operation type, i.e., higher performance for the combinations leftward orientation and subtraction and rightward orientation and addition. We found no significant difference between walking and looking conditions. The present results suggest that mental arithmetic in children is influenced by preceding sensorimotor cues and not necessarily by concurrent body movements.

Thinking about time and number: An application of the dual-systems approach to numerical cognition.

Based on the notion that time, space, and number are part of a generalized magnitude system, we assume that the dual-systems approach to temporal cognition also applies to numerical cognition. Referring to theoretical models of the development of numerical concepts, we propose that children's early skills in processing numbers can be described analogously to temporal updating and temporal reasoning.

Young children understand the normative force of standards of equal resource distribution.

Much recent research has shown that children are sensitive to basic principles of fair distribution of resources much earlier than previously assumed. Under appropriate circumstances, toddlers and sometimes even infants both expect that others will follow principles of equal distribution of resources and do so themselves. But from these findings it remains unclear whether young children understand and follow such principles of fairness as normative rules. The current study tested for such an understanding of the normative force of principles of resource distribution with a novel method. In the study, 3- and 5-year-olds witnessed how a (puppet) agent distributed resources jointly earned by herself and a fellow agent in equal or unequal ways. In one condition, the child herself or himself was this fellow agent, and in another condition it was an unrelated third party. Children spontaneously protested frequently against unfair distributions both when they themselves were affected and when another third party was affected (and never did so after fair distributions), with 5-year-olds doing so in more explicitly normative terms than 3-year-olds. These findings suggest that young children indeed understand principles of fair distribution as normatively binding regardless of whether they are personally affected or not.

The development of reasoning about the temporal and causal relations among past, present, and future events.

Children's capacity to reason about temporal and causal relations among past, present, and future events was investigated. In two studies, 4- and 6-year-olds (N=160) received structurally analogous search and planning tasks that required retrospective or prospective temporal-causal reasoning, respectively. The search task was compared with a closely matched control task that did not require temporal-causal reasoning. Results revealed that (a) both age groups solved the control task, (b) 6-year-olds mastered both retrospective and prospective tasks, and (c) 4-year-olds showed limited competence in both retrospective and prospective tasks. The current study, thus, suggests that flexible temporal-causal reasoning develops in parallel for past- and future-directed reasoning, is qualitatively different from simpler forms of temporal cognition, and develops during the late preschool years.

Young children understand the normative implications of future-directed speech acts.

Much recent research has shown that the capacity for mental time travel and temporal reasoning emerges during the preschool years. Nothing is known so far, however, about young children's grasp of the normative dimension of future-directed thought and speech. The present study is the first to show that children from age 4 understand the normative outreach of such future-directed speech acts: subjects at time 1 witnessed a speaker make future-directed speech acts about/towards an actor A, either in imperative mode ("A, do X!") or as a prediction ("the actor A will do X"). When at time 2 the actor A performed an action that did not match the content of the speech act at time 1, children identified the speaker as the source of a mistake in the prediction case, and the actor as the source of the mistake in the imperative case and leveled criticism accordingly. These findings add to our knowledge about the emergence and development of temporal cognition in revealing an early sensitivity to the normative aspects of future-orientation.

Young children share the spoils after collaboration.

Egalitarian behavior is considered to be a species-typical component of human cooperation. Human adults tend to share resources equally, even if they have the opportunity to keep a larger portion for themselves. Recent experiments have suggested that this tendency emerges fairly late in human ontogeny, not before 6 or 7 years of age. Here we show that 3-year-old children share mostly equally with a peer after they have worked together actively to obtain rewards in a collaboration task, even when those rewards could easily be monopolized. These findings contrast with previous findings from a similar experiment with chimpanzees, who tended to monopolize resources whenever they could. The potentially species-unique tendency of humans to share equally emerges early in ontogeny, perhaps originating in collaborative interactions among peers.