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.     

Linguistic and pedagogical factors affecting children's understanding of arithmetic word problems: A comparative study

2493 children aged from 5 to 15 years in 114 classes in 25 primary schools were asked to do a similar set of 22 arithmetic word problems. 1195 of the children were in Grades K through 6 in Victorian schools (Australia) and 1298 were in Grades 4 through 6 in Papua New Guinea (PNG) schools. For both samples the questions were posed in English. This was the first language for most children in the Victorian sample but, for the PNG sample, English was usually the second, third, or even fourth language (even though it is the language of instruction in PNG schools). While the test instrument was based on widely accepted information processing models of how children solve arithmetic word problems, the data obtained were not so much in accord with these models as with psycholinguistic theories on children's acquisition of polarised comparative pairs (like more and less). The data also indicate that children from the two samples used similar strategies and made similar errors, with the order of relative difficulty being the same for both samples, the main factor determining difficulty being the semantic structure of the questions. Differences in performance between corresponding grades from the two samples can be attributed to differences in the degree of English language competence rather than to numerical facility.     

Positivist and constructivist persuasions in instructional development

Constructivism has been an influential theoretical persuasion in recent years in the field of instructional design and development. Yet the theoretical tenets and applications of constructivism in instructional development (ID) have been often discussed outside the context of the long-standing paradigmatic pursuits from which constructivism stems. Efforts to continue an intellectual journey, exploring how different theoretical bases lead to different implications for ID, must be based on a clear understanding of different paradigms. Hence, constructivism is discussed here in the context of the underlying paradigm debate involving the old positivist paradigm and the new constructivist paradigm. This article explores how these different paradigms have shaped different theories and practices in ID. Specifically, three versions of constructivism and how they have influenced ID are critically examined. Finally, it is recommended that the two paradigms, positivism and constructivism, can be applied in a complementary way in ID.     

Developing children's conceptual understanding of area measurement: A curriculum and teaching experiment

The present study examined the effectiveness of three instructional treatments which had different combinations of mathematical elements regarding 2-dimensional (2-D) geometry and area measurement for developing 4th-grade children's understanding of the formulas for area measurement and their ability to solve area measurement problems. Participants were 120 fourth graders. The results showed that the enriched curriculum, involving the geometry motions and area measurement connections effectively facilitated children's mathematical judgments and explanations demanding high-level conceptual understanding. The instructional curricula accentuating only 2-D geometry or numerical calculations for area measurement did not exhibit such effectiveness. Interview data revealed that the geometric operations of superimposition, decomposition, re-composition as well as the concept of congruence were deemed essential by children for the conceptualization of the formulas for area measurement.     

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.     

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.     

Media and technology in education: A constructivist view

This paper is a version of the seventh ECTJ/ERIC-IR Young Scholar Paper, an annual award initiated to stimulate writing by young professionals in the field of instructional technology. Preparation of the paper was supported by the ERIC Clearinghouse on Information Resources at Syracuse, NY. - Ed.     

Enabling skills in early reading acquisition: A study of children in Latvian kindergartens

Preschool children in Latvia were tested in order to examine the relationships among various enabling skills and early reading performance. A principal component analysis indicated three factors: a phonemic awareness factor, a naming factor, and a short-term memory factor. Multiple regression analyses with word identification and sentence comprehension as dependent variables yielded further support to the powerful role played by phonemic awareness in explaining variance in both these aspects of reading. Unexpectedly, neither naming nor short-term memory contributed to explain unique variance in word and sentence reading. The Latvian orthography is very consistent, and our results provide further evidence to the importance of phonemic awareness in early reading acquisition especially in a transparent language. Therefore, the tasks used when assessing phonemic awareness can be very useful when screening children at risk for developing reading problems. Enhancing children's letter knowledge and phonemic awareness skills should be a priority goal in the kindergarten classroom.     

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.     

基于案例的幼儿园花卉资源开发与应用探索

幼儿园丰富的花卉资源可以开发为教育资源。在幼儿园的教育教学过程中,既可按照花卉主题来预设活动方案,也可由幼儿引发生成活动课程;既应以生活为契机,借助环境满足幼儿的探究欲望,也应加强幼儿园与家庭、社区的合作与有效互动以进一步丰富教学资源。     

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.     

A constructivist redesigning of the learning space: the development of a sense of class cohesion

Learning Environments Research - In recent years, the importance of the pedagogical and physical design of new learning environments has grown. Around the world, innovative pedagogy has been...     

Components of young children's trait understanding: behavior-to-trait inferences and trait-to-behavior predictions

Trait attribution is central to people's na?ve theories of people and their actions. Previous developmental research indicates that young children are poor at predicting behaviors from past trait-relevant behaviors. We propose that the cognitive process of behavior-to-behavior predictions consists of two component processes: (1) behavior-to-trait inferences and (2) trait-to-behavior predictions. Experiment 1 demonstrates that 4-, 5-, 7-, and 9-year-olds can infer trait labels from behaviors. Experiment 2 demonstrates that 4-, 5-, and 7-year-olds can predict behaviors from trait labels but not from past behaviors. Experiment 3 demonstrates that 4- and 5-year-olds understand traits as predictive and stable over time. Taken together, these three studies show that young children, in possessing component trait-reasoning processes, have a nascent understanding of traits.     

Career learning and development: a social constructivist model for the twenty-first century

In the UK there have been several calls for new models ‘fit for purpose’ for careers work in the twenty-first century and in response, this article presents a model for career learning and development. This brings together recent theory regarding the ways in which people make career decisions throughout their lives in rapidly changing, turbulent labour markets and globalised economies. The model is articulated through the metaphor of a suspension bridge, which is used to explore and explain the ongoing dilemmas experienced by career practitioners and their clients as they seek to balance the opposing tensions that enable the bridge to fulfil its vital functions.     

Remembering and understanding: the effects of changes in underlying knowledge on children's recollections

This study was designed to explore the influence of changes in children's knowledge on earlier constructed memories. Kindergartners' (N = 102) recall of a series of stories was examined as a function of their interpersonal knowledge about the main story character. Children's knowledge about the protagonist was manipulated prior to presentation of the stories, and the effects of their impressions on story recall were examined. A change in some of the children's impressions was then promoted, and the impact of this second knowledge manipulation on recall of previously heard stories was assessed. The results indicated that children's story recall was affected by their prior impressions. Moreover, following the second knowledge manipulation, children revised their story reports in ways that were consistent with their newly acquired impressions, which suggests that they had reconstructed their memories of previously heard stories. These findings provide evidence for both prospective and retrospective effects of knowledge on memory.     

Teacher views about constructivist instruction and personal epistemology: a national study in Taiwan

This study investigated the views about constructivist instruction and personal epistemology of the secondary earth science teachers in Taiwan. Participants were assessed through a paper‐and‐pencil survey and a Learning environment preference questionnaire (LEP) designed to explore personal epistemology. On a five‐point Likert scale, teachers, on average, showed a neutral agreement on constructivist instruction. The content analysis suggested that teachers held alternative views about the nature of the constructivist instruction. LEP scores were found to be statistically associated with gender, education, current teaching level and years of teaching; the score distribution indicated that most teachers had not developed a constructivist‐compatible epistemology. By one‐way ANOVA, it was suggested that views about the constructivist instruction were aligned with personal epistemology.     

Language development in deaf children's interactions with deaf and hearing adults: a Dutch longitudinal study

The language development of two deaf girls and four deaf boys in Sign Language of the Netherlands (SLN) and spoken Dutch was investigated longitudinally. At the start, the mean age of the children was 3;5. All data were collected in video-recorded semistructured conversations between individual children and deaf and hearing adults. We investigated the lexical richness and syntactic complexity of the children's utterances in SLN and spoken Dutch, as well as language dominance and interactional participation. Richness and complexity increase over time, as well as children's participation. An important outcome is that syntactic complexity is higher in utterances with both sign and speech. SLN does not have higher outcomes on richness or complexity, but is dominant in terms of frequency of use.     

A longitudinal study of pupils’ understanding of dynamics: Relationship between cognitive development and performance on dynamics items

In this article we describe a longitudinal study with secondary school pupils which focuses on the relationship between pupils’ cognitive development and understanding dynamics. Two classes of pupils the first between 12–14 and the second between 14 and 16, together with a sub-sample from each of these classes were followed for three years. The main sample completed two tests composed of standard dynamics items and a Piagetian cognitive task. The subsample were interviewed on some of the dynamics items tested and carried out additional cognitive tasks. The results showed that the majority of younger pupils, and the sub-sample reflect the tendency, make very little or no cognitive progress during the three years whereas the older pupils of the main sample and sub-sample make reasonable propgress mainly in the fourth year. The study showed that the relationship between cognitive scores and results on dynamics items is variable with both samples and sub-samples. Further different domains within dynamics related in different ways to cognitive development. An analysis of dynamics concepts suggested that some are more accessible to pupils than others. Three different types of relations are proposed between pupils’ understanding of dynamics concepts and the use of these in the real world.