Children's understanding of equity in the context of inequality

In the context of a pre‐existing resource inequality, the concerns for strict equality (allocating the same number of resources to all recipients) conflict with the concerns for equity (allocating resources to rectify the inequality). This study demonstrated age‐related changes in children's (3–8 years old, N = 133) ability to simultaneously weigh the concerns for equality and equity through the analysis of children's judgements, allocations, and reasoning in the context of a pre‐existing inequality. Three‐ to 4‐year‐olds took equity into account in their judgements of allocations, but allocated resources equally in a behavioural task. In contrast, 5‐ to 6‐year‐olds rectified the inequality in their allocations, but judged both equitable and equal allocations to be fair. It was not until 7–8 years old that children focused on rectifying the inequality in their allocations and judgements, as well as judged equal allocations less positively than equitable allocations, thereby demonstrating a more complete understanding of the necessity of rectifying inequalities. The novel findings revealed age‐related changes from 3 to 8 years old regarding how the concerns for equity and equality develop, and how children's judgements, allocations, and reasoning are coordinated when making allocation decisions.     

Feedback influences children's reasoning about math equivalence: A meta-analytic review

ABSTRACT

Decades of research have focused on children's reasoning about math equivalence problems for both practical and theoretical insights. Not only are math equivalence problems foundational in arithmetic and algebra, they also represent a class of problems on which children's thinking is resistant to change. Feedback is one instructional tool that can serve as a key trigger of cognitive change. In this paper, we review all experimental studies (N = 8) on the effects of feedback on children's (ages 6–11) understanding of math equivalence. Meta-analytic results indicate that feedback has positive effects for low-knowledge learners and negative effects for high-knowledge learners, and these effects are stronger for procedural outcomes than conceptual outcomes. Findings highlight the variable influences of feedback on math equivalence understanding and suggest that models of thinking and reasoning need to consider learner characteristics, learning outcomes, and learning materials, as well as the dynamic interactions among them.     

Parents' Estimations of Preschoolers' Number Skills Relate to at‐Home Number‐Related Activity Engagement

According to Hunt's match hypothesis, the accuracy of parents' beliefs about their children's abilities can influence the nature of the early learning experiences they provide. The present study examined the accuracy of parents' beliefs about their preschoolers' number development and relations to parent‐reported frequency of engaging children in number related experiences at home. Parents reported engaging their preschoolers more frequently in conventional numeracy activities, (i.e. counting and identifying numbers) than advanced number‐related activities (e.g. arithmetic) at home, though the frequency of advanced activities increased with the development of children's advanced number skills. Parents were most uncertain about their children's advanced number skills, though they demonstrated an overall tendency to overestimate their children's abilities across number tasks. Increased rates of overestimation and decreased rates of underestimation were associated with increased incidences of advanced activity engagement at home. Thus, results suggest guiding parents to understand their own children's numerical understanding in a wide range of number domains could promote more advanced at‐home number‐related activity engagement. Copyright © 2016 John Wiley & Sons, Ltd.     

Children's judgements and emotions about social exclusion based on weight

This study examined children's judgements and emotions associated with weight‐based social exclusion using an ethnically diverse sample of one hundred and seventeen 9‐ and 13‐year‐old children. Children were interviewed about three scenarios depicting weight‐based exclusion in athletic, academic, and social contexts. Children's judgements of exclusion, emotions attributed to the excluder and excluded targets, and justifications for judgements and emotions were examined. Overall, children judged weight‐based exclusion to be wrong for moral reasons. However, they viewed weight‐based exclusion in athletic contexts as less wrong compared with academic contexts, and they used more social‐conventional reasoning to justify judgements and emotions attributed to excluders in athletic contexts compared with academic and social contexts. Children also expected excluded targets to feel negative emotions, whereas a range of positive and negative emotions was attributed to excluders. In addition, older children were more accepting of weight‐based exclusion in athletic contexts than in academic and social contexts. We discuss the results in relation to the development of children's understanding of, and emotions associated with, exclusion based on weight.     

American and Chinese parental involvement in young children's mathematics learning

This study compared the involvement of American and Chinese mothers in their 5- and 7-year-old children's number learning in their everyday experience and during mother–child interaction on mathematics tasks pertaining to proportional reasoning. Results indicated that Chinese mothers of both the 5- and 7-year-old children were more likely to teach mathematics calculation in their everyday involvement with children's number learning than their American counterparts. No differences were found in maternal instruction between American and Chinese mothers during the mother–child interaction on mathematics tasks. However, maternal instruction was related to Chinese children's learning of proportional reasoning but negligibly related to American children's learning of proportional reasoning.     

The effects of source and type of feedback on child witnesses' metamemory accuracy

This study investigated the effect of feedback on the accuracy (realism) of 12‐year‐old children's metacognitive judgments of their answers to questions about a film clip. Two types of judgments were investigated: confidence judgments (on each question) and frequency judgments (i.e. estimates of overall accuracy). The source of feedback, whether it was presented as provided by a teacher or a peer child, did not influence metacognitive accuracy. Four types of feedback were given depending on whether the participant's answer was correct and depending on whether the feedback confirmed or disconfirmed the child's answer. The children showed large overconfidence when they received confirmatory feedback but much less so when they received disconfirmatory feedback. The children gave frequency judgments implying that they had more correct answers than they actually had. No main gender differences were found for any of the measures. The results indicate a high degree of malleability in children's metacognitive judgments. Copyright © 2004 John Wiley & Sons, Ltd.     

The Development of Proportional Reasoning: Effect of Continuous Versus Discrete Quantities

This study examines the development of children's ability to reason about proportions that involve either discrete entities or continuous amounts. Six-, 8- and 10-year olds were presented with a proportional reasoning task in the context of a game involving probability. Although all age groups failed when proportions involved discrete quantities, even the youngest age group showed some success when proportions involved continuous quantities. These findings indicate that quantity type strongly affects children's ability to make judgments of proportion. Children's greater success in judging proportions involving continuous quantities appears to be related to their use of different strategies in the presence of countable versus noncountable entities. In two discrete conditions, children—particularly 8- and 10-year-olds—adopted an erroneous counting strategy, considering the number of target elements but not the relation between target and nontarget elements, either in terms of number or amount. In contrast, in the continuous condition, when it was not possible to count, children may have relied on an early developing ability to code the relative amounts of target and nontarget regions.     

Croyances de contrôle et rendement scolaire chez des élèves francophones du primaire au Québec

Recent research in educational psychology, both in the United States and Europe, suggested that students' control beliefs must be considered to understand interindividual variations in students' personal engagement in learning and academic achievement. The present study was conducted with 780 French-speaking elementary school children from grade four to six. The objectives were to examine: (1) the relation between dimensions of control beliefs, (2) whether there were age-related changes in children's control beliefs, and (3) the relation between control beliefs and academic achievement across school grades. Results showed that the relations between dimensions of control beliefs and children's judgements about their importance in school achievement were stable across school grades. No relation was found between children's judgements about usefulness of specific means and academic achievement, but children's beliefs about their capacity to use these means was a powerful predictor of academic achievement. The discussion focuses on similarities and dissimilarities of these findings with those of studies conducted in the United States and Europe.     

Children's memory for the duration of a paediatric consultation

To learn about children's ability to estimate the duration of an event many days after it occurred, 6–12‐year‐old children were asked to judge the amount of time (range 5–45 minutes) they spent in the treatment room as part of a paediatric visit. Judgements were made 1 week or 1 month after the visit occurred. Children showed an average error of about 13 minutes. Retention interval did not significantly affect estimates. Other judgements of the length of the interview itself (mean length 8 minutes) provided what may be the first data on children's ability to make immediate retrospective duration estimates. The results also include information about children's capacity to judge how long ago they visited the clinic. Copyright © 2009 John Wiley & Sons, Ltd.     

Preschoolers trust novel members of accurate speakers' groups and judge them favourably

By age 3, children track a speaker's record of past accuracy and use it as a cue to current reliability. Two experiments (N?=?95 children) explored whether preschoolers' judgements about, and trust in, the accuracy of a previously reliable informant extend to other members of the informant's group. In Experiment 1, both 3- and 4-year-olds consistently judged an animated character who was associated with a previously accurate speaker more likely to be correct than a character associated with a previously inaccurate speaker, despite possessing no information about these characters' individual records of reliability. They continued to show this preference one week later. Experiment 2 presented 4- and 5-year-olds with a related task using videos of human actors. Both showed preferences for members of previously accurate speakers' groups on a common measure of epistemic trust. This result suggests that by at least age 4, children's trust in speaker testimony spreads to members of a previously accurate speaker's group.     

Assessing Knowledge Through Gesture: Using Children's Hands to Read Their Minds

Is the information that gesture provides about a child's understanding of a task accessible not only to experimenters who are trained in coding gesture but also to untrained observers? Twenty adults were asked to describe the reasoning of 12 different children, each videotaped responding to a Piagetian conservation task. Six of the children on the videotape produced gestures that conveyed the same information as their nonconserving spoken explanations, and 6 produced gestures that conveyed different information from their nonconserving spoken explanations. The adult observers displayed more uncertainty in their appraisals of children who produced different information in gesture and speech than in their appraisals of children who produced the same information in gesture and speech. Moreover, the adults were able to incorporate the information conveyed in the children's gestures into their own spoken appraisals of the children's reasoning. These data suggest that, even without training, adults form impressions of children's knowledge based not only on what children say with their mouths but also on what they say with their hands.     

Using cardinality to compare quantities: the role of social-cognitive conflict in early numeracy

A key question in early number development is how 4- and 5-year-olds learn the roles that counting and cardinal numbers play when comparing quantities. Children who wrongly used length to identify numerosity were assigned to five experimental groups and trained to judge whether a puppet--who sometimes miscounted--created equivalent sets. Over three training sessions, children who were asked to compare sets after they were counted learned to base their judgments on cardinal numbers when the puppet counted accurately by being given feedback. However, only the groups who were also asked to explain either their own or the experimenter's reasoning made progress in identifying the puppet's miscounts. This ability to recognize the importance of counting accuracy for quantitative comparisons predicted whether children would spontaneously count to compare sets on a post-test. The importance of asking children to identify miscounts is discussed alongside the social factors that influence children's recognition of the relationship between procedural counting, cardinality and relative number.     

Predictors of early numeracy: Is there a place for mistakes when learning about number?

It is one thing to be able to count and share items proficiently, but it is another thing to know how counting and sharing establish and identify quantity. The aim of the study was to identify which measures of numerical knowledge predict children's success on simple number problems, where counting and set equivalence are at issue. Seventy‐two 5‐year‐olds were given a battery of nine tasks on each of three sessions (at 3‐monthly intervals). Tasks measured procedural proficiency, conceptual understanding (using an error‐detection paradigm) and the ability to compare sets using number knowledge. Procedural skills remained fairly stable over the 6‐month period, and preceded children's ability to detect another's violations to those procedures. Regression analysis revealed that children who are sensitive to procedural errors in another's counting and sharing are more likely to recognize the significance of cardinal numbers for set comparisons. We suggest that although children's conceptual understanding of well‐rehearsed routines is often limited, conceptual insight might be achieved by setting tasks that require reflection rather than practice.     

A mental model analysis of young children's conditional reasoning with meaningful premises

Mental model theory has been used to explain many differing phenomena in adult reasoning, including the extensively studied case of conditional reasoning. However, the current theory makes predictions about the development of conditional reasoning that are not consistent with data. In this article, young children's performance on conditional reasoning problems and the justifications given are analysed. A mental model account of conditional reasoning is proposed that assumes that (1) young children can reason with two models and (2) the fleshing out of conditionals involves activation of information in semantic memory that uses the minor premise as a retrieval cue.     

The influence of familiarity on explicit eye gaze judgement in preschoolers

The current study explores the influence of familiarity on explicit eye gaze judgement in preschoolers. We introduce reaction times for touches as a new measure for children studies. Children aged four–six years saw either their caregiver's face or a stranger's face looking at an object or away from it. Children were asked to touch the face that was looking at the object and reaction times to correct touches were measured. Children reacted faster to strangers' faces than to their caregivers' faces. This may indicate that preschoolers used the face of a stranger more effectively as a source of information about the environment and for this reason detected the eye gaze-object relationship faster. In addition, children's reactions were faster in a nonsocial shape-matching task than in the social eye gaze-judgement task. The applied paradigm is appropriate to further investigate the development and influencing factors of explicit eye gaze judgements in preschoolers.     

Improved set‐size labeling mediates the effect of a counting intervention on children's understanding of cardinality

How does improving children's ability to label set sizes without counting affect the development of understanding of the cardinality principle? It may accelerate development by facilitating subsequent alignment and comparison of the cardinal label for a given set and the last word counted when counting that set (Mix et al., 2012). Alternatively, it may delay development by decreasing the need for a comprehensive abstract principle to understand and label exact numerosities (Piantadosi et al., 2012). In this study, preschoolers (N = 106, M_age = 4;8) were randomly assigned to one of three conditions: (a) count‐and‐label, wherein children spent 6 weeks both counting and labeling sets arranged in canonical patterns like pips on a die; (b) label‐first,wherein children spent the first 3 weeks learning to label the set sizes without counting before spending 3 weeks identical to the count‐and‐label condition; (c) print referencing control. Both counting conditions improved understanding of cardinality through increases in children's ability to label set sizes without counting. In addition to this indirect effect, there was a direct effect of the count‐and‐label condition on progress toward understanding of cardinality. Results highlight the roles of set labeling and equifinality in the development of children's understanding of number concepts.     

Drift in children's categories: when experienced distributions conflict with prior learning

Psychological intuitions about natural category structure do not always correspond to the true structure of the world. The current study explores young children's responses to conflict between intuitive structure and authoritative feedback using a semi‐supervised learning (Zhu et al., 2007) paradigm. In three experiments, 160 children between the ages of 4 and 8 learned a one‐dimensional decision criterion for distinguishing yummy and yucky ‘alien fruits’. They then categorized a large number of new fruits without corrective feedback. The distribution of the new fruits was manipulated such that the natural boundary in the stimuli did not always correspond to the learned boundary. Children changed their decision criteria to reflect the structure of the new stimuli, effectively unlearning the original boundary. Younger children were especially swayed by the distributional information, being relatively insensitive to feedback that the original non‐natural boundary was, in fact, still correct. Results are discussed in terms of children's ability to selectively attend to specific information (i.e. feedback vs. distribution), and their interests in forming generally useful representations of experience.     

The role of relational reasoning in children's addition concepts

The study addresses the relational reasoning of different‐aged children and how addition reasoning is related to problem‐solving skills within addition and to reasoning skills outside addition. Ninety‐two 5‐ to 8‐year‐olds were asked to solve a series of conceptually related and unrelated addition problems, and the speed and accuracy of all self‐reported strategies were used to monitor their addition performance. Children were also given a series of general relational reasoning tasks to assess their ability to solve problems based on thematic, causal and visual relations. The results revealed that, while children were able to reason about commutativity relations, recognition of relations based on additive composition was rare. Furthermore, children's ability to reason about addition concepts increased with age and problem‐solving proficiency. Reasoning about addition concepts was related to performance on the thematic, causal and visual reasoning tasks for older children but not for younger children. Overall, the findings suggest that while children's early knowledge of addition relations is domain specific, as children develop in their broader reasoning abilities these developments enhance their addition reasoning.