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.     

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.     

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 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.     

Community cohesion and children's play: a new conceptual framework

This article poses the question: Can children's play help to create cohesive communities in segregated towns and cities? The growing body of literature on community cohesion provides a useful backdrop to this issue. The discussion contains data from an empirical investigation carried out between 2009 and 2010 in Blackburn – a cotton mill town in Lancashire in the north west of England. The research was both qualitative – including 21 observations of children's play in a range of social settings – and quantitative – a questionnaire survey of 303 parents living in the Blackburn with Darwen borough. The research yielded results that both support and refute the suggestion that children's play can be used as a cohesive strategy in segregated towns and cities. The analysis of the data lends itself to a new conceptual framework in which community cohesion is presented as an important social and political objective in an increasingly diverse society.     

Young children's perceptionsof scientists: a preliminary study

Background

Since the 1950s, there has been a growing body of research dealing with perceptions children have of scientists. Typically, research studies in this area have utilized children's drawings in an effort to discern what those perceptions are. Studies assessing perceptions children have of scientists have shown that children have stereotypical images of scientists. Although there is no direct evidence to demonstrate the link between children's images of science and scientists with their career choice, several researchers (including this researcher) have assumed that children's attitudes towards science are greatly influenced by their perceptions of science and scientists.

Purpose

This study aimed to find out if there was a difference in the way 5- to 8-year-old children drew scientists, taking account of age, gender and socio-economic status.

Sample

For this study a convenience sample of 30 young children was used. Participants included young children between the ages of 5 and 8 years from a public elementary school in Ankara, the capital city of Turkey. Although the sample of the study was obtained from one school in a metropolitan area, children involved in this preliminary study were from very different socio-economic backgrounds. As the sample size is very small for making comparisons, it was intended to have a similar number of children from different age groups and socio-economic backgrounds and both genders.

Design and methods

The researcher worked individually with each child who participated in this study in an interview setting. Although each child was asked a set of standard questions, and given a standard set of directions, each interview session was informal enough to allow the researcher to gain additional information about children's drawings and to clarify any of their responses. During the interview sessions, children's responses were noted by the researcher. Before the children were asked to draw their picture of a scientist, they were offered a set of coloured pencils or crayons and told to feel free to colour their drawing or any parts of it they would like to accentuate. At the end of the interview and drawing sessions, the researcher went through all the drawings and notes to get a ‘feel’ for and ascertain what was being said, identifying key themes in each drawing.

Results

The most common scientist type drawn in this study was the stereotypical scientist type: someone who conducts research, or someone who tries to invent a new material. But unlike previous studies, around 35% of the scientist figures drawn (n = 15) were of the social scientist type. Stereotypical images drawn by the current study participants included symbols of research, such as scientific instruments and laboratory equipment of all kinds, and symbols of knowledge, principally books and cabinets, technology and the products of science. An interesting finding of this study was that perceptions of young children differed due to their age. Children at the age of 8 years drew non-stereotypical scientist images, and they drew more detail than did their younger peers. When children were compared in terms of their gender, no significant differences were observed between girls and boys. But on the other hand, none of the boys drew female scientists, and five out of 30 children who were girls drew female scientists. While children of parents with lower socio-economic status drew more stereotypical scientist images, children of parents with higher economic status drew different images of scientists, a result which showed us that the scientist perceptions of young children differ with socio-economic status.

Conclusions

Emergent from this research has been a non-stereotypical perception of scientists, and some evidence exists that such a non-stereotypical perception differs due to age and socio-economic status. While these images may seem amusing, they also provide a reflection of the image that children have about what a scientist looks like. These images may have a powerful impact on present functioning and future plans of young children.     

Mental computation and conceptual understanding

The goal of this study was to assess the strategic flexibility of students in mental arithmetic up to the number 100. Sixty Dutch second-graders who took part in an experimental ‘realistic arithmetic’ program participated in the study. Results showed that students' preference for certain mathematical procedures depended on the number characteristics of the problems. This indicates that the students had a good conceptual understanding of numbers and procedures. Their actual use of these procedures, however, was somewhat limited. Most problems were solved within a sequential structure. A completely different procedure was used for solving subtraction problems that had a very small difference between the two numbers. Furthermore, it was found that a substantial increase in the students' use of a base-ten procedure occurred after the introduction of this procedure in the mathematics curriculum. Students' preference for this procedure also increased, although to a lesser extent. Another finding of the study was that students exhibited more flexible strategic behaviour with context problems than with numerical-expression problems.     

Young children's references to temporal attributes of allegedly experienced events in the course of forensic interviews

Developmental differences in references to temporal attributes of allegedly experienced events were examined in 250 forensic interviews of 4- to 10-year-old alleged victims of sexual abuse. Children's ages, the specific temporal attributes referenced, and the types of memory tapped by the interviewers' questions significantly affected the quantity and quality of temporal references produced. The findings documented age-related increases in 4- to 10-year-olds' references to temporal attributes, using the appropriate relational terminology, both spontaneously and in response to temporal requests. More references to temporal attributes were elicited from recall than from recognition memory, highlighting spontaneous reporting capabilities. Implications for theories concerning the developing understanding of temporal concepts and for the design of effective, age-appropriate, forensic interview techniques are discussed.     

Development in children's comprehension of linguistic register

For socially appropriate communication, speakers must command a variety of linguistic styles, or registers, that vary according to social context and social relationships. This study examined preschool children's ability to use a speaker's register choice to infer the identity of their addressee. Four-year-olds could draw correct inferences based on Spanish and formal speech, and had limited success with infant-directed and casual styles. Five-year-olds drew appropriate inferences with all 4 styles; moreover, these children demonstrated strong explicit understanding of register, as measured through response justifications. These results demonstrate that children can use language for social judgments that extend beyond evaluating the speaker, and can interpret social implications of language even when not directly engaged in the particular social interaction.     

A comparison of year 1 and year 6 students' conceptions of evaporation and condensation: dimensions of conceptual progression

A range of challenging activities centred on evaporation and condensation were explored with year 1 and year 6 children. Their explanations in group discussion, written responses and interview were analysed, using NUD*IST qualitative analysis software, to explore the nature and coherence of their conceptions. The data was used to critically evaluate previous claims in the literature concerning the characteristics of progression in understanding of evaporation, and to identify the main dimensions that characterize the differences in children's explanations. The older children displayed a surer sense of ontological categories, greater epistemological sophistication including their ability to link explanations and evidence, greater precision in the use of conceptual language, and a greater range of associations they could make.     

Young children's knowledge of fair sharing as an informal basis for understanding division: A latent profile analysis

This study examined patterns of individual differences in young children's early understanding of division. Two hundred and thirty-seven 5- and 6-year-old children completed division tasks that assessed their understanding of the direct and inverse relations in division in two different situations – partitive and quotitive. Two main results emerged from our latent profile analyses. First, all children who had good performance in the inverse-relation problems also performed well in the direct-relation problems, but the converse was not true. Second, all children who performed well in the inverse-relation problems in quotitive situations also performed well in the inverse-relation problems in partitive situations, but not vice versa. The findings highlight the importance of situations in determining children's success in recognizing the inverse relation in division. Several theoretical implications for the development of children's division concepts and educational implications for assessment and teaching are discussed.     

Three dimensions of reflective thinking in solving design problems: a conceptual model

Design tasks are omnipresent in our everyday lives. Previous research shows that reflective thinking is one of the critical factors in solving design problems. Related research has attempted to capture designers’ reflective thinking process. Yet a close inspection of designers’ reflective thinking taking place during their design process demands further effort. To understand designer’s reflective practice and to find better ways to promote novices’ reflective thinking in solving real-world design problems, a comprehensive model was developed. This model identified three dimensions to guide the understanding of designers’ reflective thinking during a design process: (1) the timing of reflection, indicating the points in the process where reflective thinking occurs, (2) the objects of reflection, showing the different types of objects that designers may reflect upon, and (3) the levels of reflection, referring to the different levels of designers’ reflection. This model provides for meaningful aspects of reflective thinking to be situated in a design process, which can guide educators and instructional designers in developing appropriate learning environments for facilitating novice and practicing designers’ reflective thinking. Moreover, the model can serve as a stepping stone for further research.     

Revealing conceptual understanding of international business

This study aims to identify an adequate approach for revealing conceptual understanding in higher professional education. Revealing students’ conceptual understanding is an important step towards developing effective curricula, assessment and aligned teaching strategies to enhance conceptual understanding in higher education. Essays and concept maps were used to determine how students’ conceptual understanding of international business can be revealed adequately. To this end, 132 international business students in higher professional education were randomly assigned to four conditions to write essays and to construct concept maps about an international business research topic. The conditions were: essay alone, essay after concept map, concept map alone, and concept map after essay. An assessment rubric was used to assess the breadth and depth of students’ conceptual understanding. Results show essays are the most adequate approach for revealing conceptual understanding of international business. In particular, concept maps revealed fewer facts and less reasoning than essays. Essays written after concept maps were less effective than essays, possibly since students perceived these essays as redundant. Further research is suggested on how educators can foster conceptual understanding.     

Prospective teacher learning: recognizing evidence of conceptual understanding

This study examined prospective teachers’ (PSTs) ability to recognize evidence of children’s conceptual understanding of mathematics in three content areas before and after an instructional intervention designed to support this ability. It also investigates the role PSTs’ content knowledge plays in their ability to recognize children’s mathematical understanding. Results of content knowledge assessments administered at the beginning of the study revealed that content knowledge did seem to support PSTs’ analyses of children’s understanding when the child’s response demonstrated understanding or demonstrated a misconception. Content knowledge did not seem to support PSTs’ analyses of children’s procedural responses, as many PSTs with good content knowledge initially characterized procedural solutions as evidence of conceptual understanding. Similarly, content knowledge did not seem to support PSTs’ analyses of children’s responses with features commonly associated with understanding but not evidence of understanding. After the instructional intervention consisting of three multifaceted lessons in which PSTs examined many examples of student thinking, they showed improved ability to analyze responses with conceptual features and no evidence of conceptual understanding and responses demonstrating procedural knowledge. Results suggest that content knowledge is not sufficient for supporting PSTs’ analysis of children’s thinking, and that building activities such as the intervention into content courses may help develop this ability. Implications for teacher education programs and future research are considered.     

Erratum: Student affect and conceptual understanding in learning chemistry

In this article (Journal of Research in Science Teaching 2007;44(7):908–937. DOI 10.1002/tea.20169 © 2007 Wiley Periodicals, Inc.), part of the author's affiliation had been inadvertently omitted. The corrected affiliation appears above. For the reader's information, the acronym “OISE/UT” stands for “Ontario Institute for Studies in Education of the University of Toronto.” The author regrets any inconvenience this may have caused.     

Creativity in events and practices: a lens for understanding children's multimodal texts

This article argues that it is possible to look at children's texts in relation to the lens of literacy events and practices from the New Literacy Studies, and apply this perspective to an understanding of creativity. Teachers can then use the possibilities within a text to ask children different kinds of questions. Drawing on a 2‐year ethnographic study of a partnership between a group of artists and teachers in an Infants School in England, and their impact on children's text‐making, the paper seeks to understand the ways in which such a text can be identified as creative. A detailed analysis of one child's text is offered as evidence of this argument. This account is set within a project to map children's play in a Foundation classroom.     

Young children's comprehension of montage

2 studies examined children's comprehension of brief stop-animation televised segments incorporating elements of cinematic montage such as pans, zooms, and cuts. Children reconstructed the action and dialogue in these segments using the same dolls and settings depicted. In Study 1, there was no effect of cinematic techniques on reconstruction performance of 3- and 5-year-olds as compared to control segments filmed without these techniques. The results challenged the assumption that the use of such techniques per se contributes to young children's poor comprehension of television shows. In Study 2, 12 new segments were produced in which comprehending the montage required inferences of character perspective, implied action sequences, spatial relationships, and simultaneity of different actions. Averaging across all segments, 62% of the 4-year-olds and 88% of the 7-year-olds demonstrated clear comprehension of the montage. Inferences concerning implied action sequences were easiest for both ages. Inferences of simultaneity were most difficult for 4-year-olds, whereas inferences of character perspective were most difficult for 7-year-olds. Preschool children are thus capable of understanding cinematic events conveyed through camera techniques and film editing, despite previous assertions to the contrary. This ability nevertheless substantially increases with age.     

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.     

Ordering and structuring ideas in text: From conceptual organization to linguistic formulation

The goal of this study was to analyze the development of the relationship between conceptual and linguistic processes as regards idea ordering and structuring (linearizing), when composing a text. Participants (from 7^th graders to University students) were required to compose a text using a list of eleven scrambled ideas. Conceptual rules allow to a priori determine an optimal ordering of these ideas. Results showed a significant increase, with grade level, in the establishment of the postulated conceptual order, and in the linguistic elaboration of the text structure. A large autonomy was observed between conceptual and linguistic processes. The discussion considers the following points: The relevance of the notion of text optimal order; the unequal development with grade level of the varied linguistic skills; the dissymmetry in conceptual-linguistic relationships; the usefulness of the experimental paradigm; some consequences for education.     

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.