The development of children's understanding of intensive quantities

Researchers have been aware for some time of the differences between extensive and intensive quantities but the significance of these differences has not been recognized in mathematics curricula. In England children are provided with many opportunities in their first few years in school to manipulate, measure and reason about extensive quantities but have virtually no opportunity to do the same with intensive quantities. This paper contrasts extensive and intensive quantities and describes the obstacles to primary school children's understanding of intensive quantities: the need to consider two variables simultaneously and the difficulty of understanding inverse relations between variables. Study 1 shows that children have considerable difficulty in using inverse relations reasoning. Study 2 shows that this form of reasoning is more difficult in the context of intensive than extensive quantities problems. Implications for education are considered and examples of experiences with intensive quantities that could provided in school are presented.     

The development of children's art

Pupils transferring to secondary school are positive about science and look forward to practical work. The research reported here explored Y6 and Y7 pupils' perceptions of practical science in school and the world of work.

Pupils at both ages saw practical work as a natural and enjoyable consequence of scientific endeavour and of use to society. They made a number of links between school science and the work of scientists. Y6 pupils were more likely than Y7 pupils to link practical science with product testing and to future careers. The findings of the research and further thinking about KS2/3 transition are used to point out useful features that might help design bridging work in science.     

Young children's understanding of random phenomena

2 experiments on the development of the understanding of random phenomena are reported. Of interest was whether children understand the characteristic uncertainty in the physical nature of random phenomena as well as the unpredictability of outcomes. Children were asked, for both a random and a determined phenomenon, whether they knew what its next outcome would be and why. In Experiment 1, 4-, 5-, and 7-year-olds correctly differentiated their responses to the question of outcome predictability; the 2 older groups also mentioned appropriate characteristics of the random mechanism in explaining why they did not know what its outcome would be. Although 3-year-olds did not differentiate the random and determined phenomena, neither did they treat both phenomena as predictable. This latter result is inconsistent with Piaget and Inhelder's characterization of an early stage of development. Experiment 2 was designed to control for the possibility that children in Experiment 1 learned how to respond on the basis of pretest experience with the 2 different phenomena. 5- and 7-year-olds performed at a comparable level to the same-aged children in Experiment 1. Results suggest an earlier understanding of random phenomena than previously has been reported and support results in the literature indicating an early understanding of causality.     

Exploring children's understanding of death concepts

This study is an investigation of the effects of death education on children and their understanding of death. The participants of this study were eighty 5- and 6-year-olds who were enrolled in a suburban kindergarten in Korea. To examine the level of children's understanding of death, researchers interviewed each child in both the control and experimental groups. After the interview, researchers provided an intervention (11 educational activities) to the experimental group. No educational intervention was provided to the control group. Researchers re-interviewed children in both groups after the treatment. The overall mean score of the experimental group was significantly higher than that of the control group on all five categories of the death concept: causality, old age, irreversibility, finality, and inevitability. Implications regarding how death education can be approached in early childhood settings are also discussed.     

Deaf children's understanding of beliefs and desires

Twenty-two children (5-12 year old) who were profoundly, prelingually deaf were given two tests designed to tap their 'theory of mind', that is, their ability to attribute independent mental states to other people. The tests were versions of Baron-Cohen, Leslie, and Frith's Sally-Anne task and of Baron-Cohen's breakfast task. Seventy percent of the children were successful on all questions requiring belief attribution, a considerably and significantly larger percentage than the 29% obtained by Peterson and Siegal for a similar sample, though it is still lower than would be expected on the basis on chronological age. Children were universally successful on questions requiring the attribution of desire. We discuss implications of the findings.     

Young children's understanding of counting and cardinality

4-year-old's knowledge of counting and cardinality--the last count word reached represents the numerosity of the set--was tested in 2 experiments. Experiment 1 investigated the nature of early cardinality responses by presenting different forms of the cardinality question before, after, and before and after the child counted. Both type and time of question has large effects. Experiment 2 examined whether children of this age could recognize errors in 4 counting procedures and whether they would reject a cardinality response arrived at through a mistaken counting procedure. The children were very good at recognizing a standard counting procedure as correct. They had only limited success at treating procedures that violated the stable order of count words or violated the one-one correspondence between count word and object as incorrect. They lacked an understanding of the order irrelevance in that they judged valid, nonstandard counting orders as incorrect. The children did not seem to link their evaluation of a cardinality response with their evaluation of the counting procedure used to reach that response. The results do not indicate that counting principles initially govern the child's acquisition of counting knowledge. They are consistent with the suggestion that early cardinality responses are last-word responses.     

Settling into school: The importance of early friendships for the development of children's social understanding and communicative competence

This paper reports an exploratory study of 37 children (aged 4–5 years) throughout their first term of formal schooling. Children in two different schools were included in the study. Four pairs of friends and four isolated children were targeted for in‐depth observation every week throughout the term. The behaviour and speech of these 12 children were coded systematically in various activities and settings to assess their level of social involvement and their adjustment to school. Sociometric interviews were carried out with all 37 children. These were used to examine the pattern of social relationships in the two classes and to investigate Children's understanding of concepts such as ‘friendship’. The target children also took part in a communication game with other children from their classes, matched in age and verbal ability, but who were not friends. It was predicted that children who started school in the company of a friend or friends would have better developed social and communicative skills than children who began school without the support of existing friendships. As predicted, children who had well established friendships on entry to school gave more sophisticated reasons as to why children liked and disliked each other. These children were also more effective communicators than the isolated children. The results suggest that friendship not only plays an important part in developing young Children's social competencies, but also that it influences children'sperformance on a range of classroom‐based learning activities, particularly those which involve mutual collaboration and co‐operation.     

The use of narrative to promote primary school children's understanding of evolution

This study explores learning about evolution when information is presented in either a narrative or an expository text (ET). Narratives engage the imagination, and consequently may allow children to overcome conceptual constraints that make evolution difficult to comprehend. Participants were 16 Year One, 21 Year Two and 25 Year Three pupils from a British primary school. Expository and narrative texts about evolution were read with children before assessing participants' understanding. Those reading the narrative showed a greater understanding of the book's contents about evolution than those reading the ET. Implications for using the imagination and narrative in the science classroom are discussed.     

Mothers' time with infant and time in employment as predictors of mother-child relationships and children's early development

This study tested predictions from economic and developmental theories that maternal time with an infant is important for mother-child relationships and children's development, using time-use diaries for mothers of 7- to 8-month-old infants from the National Institute of Child Health and Human Development Study of Early Child Care (N = 1,053). Employment reduced time with infants, but mothers compensated for some work time by decreasing time in other activities. With family and maternal characteristics controlled, time with infants predicted high Home Observation for Measurement of the Environment (HOME) scores and maternal sensitivity, but bore little relation to children's engagement with mothers, secure attachment, social behavior, or cognitive performance from 15 to 36 months. Mothers who spent more time at work had higher HOME scores. Maternal time with infants may reflect maternal characteristics that affect both time allocation and maternal behavior.     

The development of children's knowledge of temporal structure

Adults have a rich understanding of a number of time systems, but little is known about how this knowledge develops. 3 experiments were conducted to test a model in which the first representations of the days of the week and months of the year have verbal-list properties, and these are later supplemented by image representations. In Experiments 1 and 2, fourth or fifth graders could judge forward relative order for these contents, but not until adolescence could backward order judgments be made accurately. In Experiment 3, fourth graders used a serial process to solve a categorical distance judgment task, whereas older groups shifted to a process with more rapid access to information about the position of remote items. The results are interpreted as supporting the 2-stage model and appear inconsistent with a number of alternative models.     

Almost thinking counterfactually: children's understanding of close counterfactuals

Saying something "almost happened" indicates that one is considering a close counterfactual world. Previous evidence suggested that children start to consider these close counterfactuals at around 2 years of age (P. L. Harris, 1997), substantially earlier than they pass other tests of counterfactual thinking. However, this success appears to result from false positives. In Experiment 1 (N = 41), 3- and 4-year-olds could identify a character who almost completed an action when the comparison did not complete it. However, in Experiments 1 and 2 (N = 98), children performed poorly when the comparison character completed the action. In Experiment 3 (N = 28), 5- and 6-year-olds consistently passed the task, indicating that they made appropriate counterfactual interpretations of the "almost" statements. This understanding of close counterfactuals proved more difficult than standard counterfactuals.     

Sociocultural input facilitates children's developing understanding of extraordinary minds

Three- to 5-year-old (N = 61) religiously schooled preschoolers received theory-of-mind (ToM) tasks about the mental states of ordinary humans and agents with exceptional perceptual or mental capacities. Consistent with an anthropomorphism hypothesis, children beginning to appreciate limitations of human minds (e.g., ignorance) attributed those limits to God. Only 5-year-olds differentiated between humans' fallible minds and God's less fallible mind. Unlike secularly schooled children, religiously schooled 4-year-olds did appreciate another agent's less fallible mental abilities when instructed and reminded about those abilities. Among children who understood ordinary humans' mental fallibilities, knowledge of God predicted attributions of correct epistemic states to extraordinary agents. Results suggest that, at a certain point in ToM development, sociocultural input can facilitate an appreciation for extraordinary minds.     

The development of an intuitive understanding of entropy

Previous studies of the concept of entropy have indicated that before 7 to 9 years of age, children have difficulty understanding the effects of randomizing forces and often predict highly improbable events, such as a return to the original ordered state. In the present research, 306 children between 3 and 11 years of age were asked directly whether undifferentiated forces, such as the wind or objects being thrown into the air, could create order or disorder in a set of objects. The results showed that even 4-year-olds are sensitive to the asymmetrical effects of such events. Older children apply this principle more consistently and are able to use it in explaining their answers.