A review of recent research in the area of initial fraction concepts

This paper reviews recent research in the area of initial fraction concepts. The common goal of the empirical studies which are represented in this analysis was to assist children develop a meaningful understanding of the rational number construct, founded on durable fraction concepts. Two interpretations of findings were derived from the research. One group of researchers identified initial fraction concepts emerging from the application of intuitive mechanisms, in particular partitioning in either continuous or discrete contexts, and leading to unit identification and iteration of the unit. The other group of researchers identified ideas of ratio and proportion present in young children's early thoughts about fractions.By generating links between studies, integrated research is created and consensus regarding critical problems and future directions is reached. Concluding remarks pose questions for further investigation.     

Examining and elaborating upon the nature of elementary prospective teachers’ conceptions of partitive division with fractions

The purpose of this study was to examine and elaborate upon elementary prospective teachers’ (PSTs) conceptions of partitive division with fractions. We examined the degree to which PSTs’ conceptions were connected (i.e., capable of translating between representations correctly; aware that partitive division generates a unit rate for its quotient) and flexible (i.e., capable of differentiating between opportunities to partition or iterate (or both) when solving a partitive division task; aware that partitioning or iterating (or both) could be associated with the operation of division, as appropriate). Seventeen PSTs participated in task-based interviews prior to instruction in a mathematics content course for teachers. These PSTs demonstrated disconnected conceptions of partitive division with fractions when they incorrectly translated between representations and either inconsistently or did not express awareness that the purpose of the task was to generate a unit rate. These PSTs demonstrated rigid conceptions of partitive division with fractions such that they did not express awareness that the process of iterating could be associated with the operation of division, even when they obtained a correct answer by iterating. Results extend prior research by looking beyond PSTs’ performance on tasks to elaborate upon PSTs’ conceptions of the operation of partitive division. This study contributes new insights into PSTs’ conceptions that can be used by mathematics teacher educators to inform the design of future instructional interventions.     

与"物"交往--幼儿独有的交往形式

以“物”为对象的交往形式是幼儿独有的。这种交往顺应了幼儿心理的泛灵论倾向，能够增强幼儿的识“物”能力和爱“物”品格，是幼儿成长的必经阶段。对幼儿这种独特的交往形式，成人应当给予特定的关注与支持。     

The development of children's strategies for the social control of emotion

It has been shown that young children can recognize emotional states in their peers, that they understand many of the antecedents of emotion, and they are motivated to change negative emotional states in others. The present study examined children's ability to nominate strategic social action that would alter the ongoing emotional state of a peer. Children of 3 ages--5, 8, and 12 years of age--viewed a picture of a young child actually experiencing happiness, sadness, anger, or in a neutral state. In a portion of instances, information was also provided about the social or nonsocial experience that led to the target child's state. The strategies children nominated fell into a small set of agonistic (nurturant) and antagonistic (aggressive) behaviors intended to change positive or negative states. With increasing age, children tended to nominate a greater proportion of verbal strategies, social strategies (with the exception of strategies nominated to change anger), and strategies that directly addressed the cause of another's emotional state.     

Individual Differences in Young Children's Pretend Play with Mother and Sibling: Links to Relationships and Understanding of Other People's Feelings and Beliefs

50 33-month-old children were observed at home with their siblings and mothers. Observational measures of pretend play, observer ratings of the child's, mother's, and sibling's behavior, and measures of family discourse about feelings were collected. At 40 months each child was assessed on Bartsch and Wellman's false beliefs task and Denham's affective perspective taking task. Results revealed individual differences in the amount and sophistication of young children's social pretend play and suggested that these individual differences are related to experiences in the relationships that young children have with their mothers and siblings. Results also indicated that early social pretend play was significantly related to the child's developing understanding of other people's feelings and beliefs. The data are interpreted as providing support for the notion that early experience in social pretense is associated with children's mastery of the relation between mental life and real life. The importance of considering the relationship context of social pretense is also discussed.     

中小学生业余钢琴学习问题的调查与思考

中小学生钢琴学习应是一种以人为本的学习活动,应让琴童在学习过程中形成用身心去感受音乐的能力与经验,以促进其个性的完善与发展;应把钢琴学习与琴童自身的爱好结合起来,并以此为切入点发展琴童对钢琴学习的兴趣;在中小学生钢琴学习过程中,教师家长应避免功利心,对中小学生钢琴学习效果的评价应以琴童自身水平为标准;应根据琴童自身的特点与学习水平制定学习计划,并以一颗平常心对待琴童,理解容忍琴童的缺点与错误;同时,教师家长应与琴童保持平等的关系,不断了解中小学生的心理特点,选择易于被琴童接受的方式,从长远发展的高度给予琴童切实的帮助。     

Object Properties and Knowledge in Early Lexical Learning

The ease with which young children learn object nouns suggests that they possess strategies to identify properties critical to lexical category membership. In previous work, young children used a same-shape criterion to extend new count nouns. The present research tested the generality of this shape bias. 2- and 3-year-olds were asked either to extend a novel count noun to new instances, or to choose unnamed objects to go together. The objects varied in shape, size, and texture. For half of the subjects, the objects had eyes--a property strongly associated with certain material kinds. If young children know this association, they should attend to texture as well as shape in classifying objects with eyes. With named objects only, both 2- and 3-year-old children classified eyeless objects by shape and objects with eyes by both shape and texture. The results suggest that very young children possess considerable knowledge about conditional relations between kinds of perceptual properties. Knowledge of such conditional relations may aid children in forming new categories and thus in discovering new word meanings.     

When young children are afraid

With panic clearly showing in his eyes, Josh dropped to the floor, locked his dad's leg between both arms, and screamed. It was Josh's first day at school. While young children's fears may not always appear to be rational in the eyes of adults, every child's fearful response deserves to be acknowledged as a genuine reaction to an actual or perceived threat. Because fear has the potential to interfere with the young child's quality of life, it would seem important to understand the nature and normal developmental course of early childhood fears.     

建构主义与我国学前教育课堂教学的现代革命

建构主义理论主张以儿童为中心的幼儿教学过程,强调儿童学习的主动参与和自主认知。它为当前我国学前课堂教学的现代变革方向,即强化教学呼应、注重儿童身心发展、提升师生创新意识、强调问题与过程的教学、关怀生命教育等方面提供理论依据和思想引领。     

Contexts of achievement: a study of American, Chinese, and Japanese children

The major purpose of this study was to attempt to understand some of the reasons for the high academic achievement of Chinese and Japanese children compared to American children. The study was conducted with first and fifth graders attending elementary schools in the Minneapolis metropolitan area, Taipei (Taiwan), and Sendai (Japan). 1,440 children (240 first graders and 240 fifth graders in each city) were selected as target subjects in the study. The children were selected from 20 classrooms at each grade in each city and constituted a representative sample of children from these classrooms. In a follow-up study, first graders were studied again when they were in the fifth grade. The children were tested with achievement tests in reading and mathematics constructed specifically for this study, the children and their mothers were interviewed, the children's teachers filled out a questionnaire, and interviews were held with the principals of the schools attended by the children. In the follow-up study, achievement tests were administered, and the children and their mothers were interviewed. Background information about the children's everyday lives revealed much greater attention to academic activities among Chinese and Japanese than among American children. Members of the three cultures differed significantly in terms of parents' interest in their child's academic achievement, involvement of the family in the child's education, standards and expectations of parents concerning their child's academic achievement, and parents' and children's beliefs about the relative influence of effort and ability on academic achievement. Whereas children's academic achievement did not appear to be a central concern of American mothers, Chinese and Japanese mothers viewed this as their child's most important pursuit. Once the child entered elementary school, Chinese and Japanese families mobilized themselves to assist the child and to provide an environment conducive to achievement. American mothers appeared to be less interested in their child's academic achievement than in the child's general cognitive development; they attempted to provide experiences that fostered cognitive growth rather than academic excellence. Chinese and Japanese mothers held higher standards for their children's achievement than American mothers and gave more realistic evaluations of their child's academic, cognitive, and personality characteristics. American mothers overestimated their child's abilities and expressed greater satisfaction with their child's accomplishments than the Chinese and Japanese mothers. In describing bases of children's academic achievement, Chinese and Japanese mothers stressed the importance of hard work to a greater degree than American mothers, and American mothers gave greater emphasis to innate ability than did Chinese and Japanese mothers.     

Mothers' and Child-Care Providers' Cognitive, Affective, and Behavioral Responses to Children's Misbehavior

This study compared mothers' and caregivers' attributions for children's misconduct and their corresponding affective and behavioral responses. Forty mothers of 4-year-olds and 40 caregivers employed in childcare settings responded to a series of hypothetical incidents in which a 4-year-old child engaged in a norm violation such as aggression or failed to be altruistic. ANCOVA analyses indicated that mothers and caregivers differed in their causal attributions for children's misbehavior. Mothers and caregivers also differed in their affective and behavioral responses to children's failures to be altruistic, but not in their responses to children's norm violations. Regression analyses performed on the combined scores of mothers and caregivers found that attributions to the stability of the behavior predicted use of induction and a greater emphasis on responding to the misbehavior. A power assertive response was particularly likely if a respondent believed that a behavior was caused by stable personality factors. The documentation of linkage between causal attributions and socialization behavior has implications for parent training and early childhood education. Increasing parents' awareness of developmental processes and external factors that affect a child's behavior may result in a less punitive approach to discipline. Early childhood curricula that encourages examination of adult biases in analyzing children's behavior may assist caregivers to become more reflective and self-aware in interactions with young children.     

Young children's understanding of perception, desire, and emotion

Very young children seem to know that people experience several mental states: desires, perceptions, emotions. In three studies, we investigated 2- and young 3-year-olds' judgments and communications about how these states connect together in people's lives and minds. Two experimental studies with 56 participants demonstrated young children's understanding of at least one set of connections: In appropriate circumstances, a person's perception of desirable or undesirable objects leads to related emotional experiences. A complementary investigation of four young children's everyday conversations demonstrated their awareness of and expression of several additional connections between people's desires, perceptions, and emotions.     

Parent Scaffolding in Children's Oral Reading

Parent coaching strategies during shared book reading were analysed according to the principles of scaffolding in a sample of 46 parent-child dyads during the latter half of grade one. The ways that parents responded to each of a child's oral reading errors or miscues were coded into levels of assistance that reflected increasing support at each successive level. In addition children's attempts at rereading miscued words were coded as successful or not. Parents often provided a string of feedback clues and analyses revealed that the level of support parents provided shifted up or increased when their child was unsuccessful in rereading a word after feedback. With increasing level of parental support children's success in rereading misread words increased. Moreover, children with weaker word recognition skill were offered feedback at higher levels of support by their parents. These results demonstrate how parents and children co-construct the feedback that parents provide when listening to their children read and the sensitivity on the part of parents to children's reading performance.     

Imagery, Action, and Young Children's Spatial Orientation: It's Not Being There That Counts, It's What One Has in Mind

Young children typically fail when asked to judge how objects would look if they moved or changed shape, and this has been taken to mean that they lack the competencies for dynamic imagery. We used a different approach to study young children's imagination and found evidence of much earlier competence. Across 6 experiments, people were asked to imagine familiar surroundings and anticipate their spatial orientation from different observation points there. In the first 2 experiments, children (2 1/2-9-year-olds) and their parents sat at home and were asked to call to mind knowledge of their (child's) classroom relative to the perspective at their (child's) seat at (pre)school. After this, subjects were asked to judge the perspective at the teacher's seat in each of 2 conditions. In the Locomotion Condition they were asked to imagine walking from their seat to the teacher's seat while physically walking a path that resembled the actual one in the remote classroom. In the Imagination-only Condition the instructions were the same but they were not accompanied with physical walking. Children 3 1/2 years of age and older, like the adults, were accurate and rapid in the Locomotion Condition. In the Imagination-only Condition the children almost never judged perspective correctly; the adults responded accurately but slowly. These findings were replicated and extended across 4 additional experiments designed to clarify the operating principles that link perceiving, imagining, and acting.     

The Concept of Tens and Hundreds in Students with Down Syndrome

ABSTRACT

We present an evaluation of the understanding that adolescents and adults with Down syndrome (DS) have of the decimal number system. The results of two studies are presented. The first was a case study with interviews of three adolescents and three adults with Down syndrome. Our results indicate that their conceptual understanding of the meaning of the tens and hundreds places is not as well developed as their ability to read, write and work with numbers of up to three digits. We also analyse the progress made by a 17- year-old student with Down syndrome after following a learning programme intended to improve her understanding of the tens place. To this end, we designed number tasks using four constructs: counting, grouping, partitioning and ordering. The student’s achievements in the counting construct were greater than in the others, exhibiting an understanding and use of the tens as a unit of counting to solve many of the number tasks proposed. Also evident was a progression in her understanding of the positional value. We observed differences in her success rate and variability in her responses depending on the method used in the tasks to represent the numbers.     

Developmental relations between notational counting and number conservation.

The 2 studies of this report sought to determine the developmental relationship between the child's use of counting as a notational symbol system to extract, compare, and reproduce numerical information and the development of number conservation. In study 1, children between 4 and 6 years of age were administered notational-counting and number-conservation tasks. Analysis of children's profiles across tasks indicated that children develop quantitative counting strategies (but do not necessarily count accurately) before they develop number-conservation concepts. In study 2, the generality of this sequence was tested. A population of 7- to 9-year-old "learning-disabled" children who reportedly were developing atypical counting skills were administered notational-counting and number-conservation tasks. All of these children who conserved number also used quantitative counting strategies, although some of these children frequently counted arrays inaccurately. The significance of these findings is discussed with respect to existing models of counting/number-conservation relations, and an alternative formulation is suggested based upon the new findings.     

Early Attachment Relationships as Predictors of Preschool Children's Emotion Regulation with a Distressed Sibling

The present study examined (1) the emotion regulation of preschool children by observing their emotional responses to a distressed younger sibling during a separation episode; (2) whether children's regulatory responses were related to sibling interaction observed during the separation episode, and (3) whether individual differences in these children's regulatory responses and the quality of sibling interaction could be predicted from early attachment relationships. Older siblings who ignored their younger siblings' distress were more likely to experience personal distress and use avoidant coping strategies. Emotion regulation strategies were related to the quality of sibling interaction such that older siblings who offered comfort to a distressed younger sibling were more likely to express positive affect in sibling interaction, whereas older siblings seeking adult assistance were less likely to engage in conflict and hostile behavior with a younger sibling. Preschool children who had an insecure-resistant infant-mother attachment at 1 year, were more likely to seek comfort from their younger siblings and engaged in more sibling conflict and hostility when they were 4 years old. The quality of infant-father attachment relationships was not significantly related to the child's emotion regulation at 4 years of age. Results are discussed with respect to the social origins of preschool children's emotional self-regulation and the consequences of emotional dysregulation in preschool settings.     

Correspondence between mothers' self-reported and observed child-rearing practices

The correspondence between self-reported child-rearing attitudes and practices and actual child management was examined among 68 mothers of young children. Data on mothers' verbal and physical control techniques along with children's responses (cooperation vs. resistance) were obtained during 90 min of spontaneous interaction in a naturalistic setting. Self-report data (the Block Q-Sort) were obtained 1-2 weeks later. The Block Q-Sort factors were combined to represent authoritarian and authoritative patterns of attitudes. The authoritarian pattern was positively associated with the use of direct commands, physical enforcements, reprimands, and prohibitive interventions, and negatively associated with the use of suggestions. The authoritative pattern was positively related to the use of suggestions and positive incentives, and negatively related to the use of physical enforcements, prohibitive interventions, and direct commands. Mothers' enjoyment of the parental role and their negative affect toward the child, as expressed in the Block Q-Sort, were more a result of the child's cooperation/resistance during the interaction than predictors of maternal control strategies.