Intuitive Interference in Geometry: An Eye‐Tracking Study

Interference of irrelevant salient variables may cause difficulties for students. This study focused on eye tracking during the comparison of perimeters task, in which area is the interfering irrelevant salient variable. There were three trial types: congruent (larger area—larger perimeter), incongruent inverse (larger area—smaller perimeter), and incongruent equal (larger area—equal perimeter). Behavioral findings corroborated previous studies: congruent trials yielded higher accuracy and a shorter reaction time than did incongruent trials. Surprisingly, the area saliency could not be revealed in fixation location and duration measurements in incongruent inverse trials nor in the heat maps for incongruent inverse or incongruent equal trials, suggesting that such processing does not require overt attention; measures of attention shift from one geometrical shape to another were higher for incongruent equal trials, as was pupil dilation, suggesting that greater effort is associated with solving incongruent equal trials.     

The Influence of Number‐sense on Children's Ability to Estimate Measures

This study aimed at clarifying the relative developmental influences of age, number‐sense and context on primary school children's ability to estimate measures. Children (6‐11 years) were first assessed on three aspects of number‐sense (mental computation, understanding of relative number magnitude and understanding of relations between numbers) and were then assessed on their estimation of length and area within each of two task contexts (a ‘story’ frame and a ‘textbook’ frame). While number‐sense was found to improve with age, estimation did not. However, an ability to use and perceive number relations, together with an understanding of the relative magnitudes of larger numbers, were found to influence children's ability to estimate area. Children of all ages were also found to estimate more accurately in the ‘textbook’ context than in the ‘story’ context. These findings are discussed with reference to the notion of estimation as a situated activity     

手势图片的SNARC效应

采用Dehaene等人的实验范式,要求被试对呈现的数字或手势图片代表的数字快速分类.探讨了手势图片的SNARC效应及其与数字SNARC效应的差异.结果发现：（1）手势图片的加工中存在SNARC效应,进一步说明SNARC效应具有很大的稳定性和普遍性.（2）手势图片比阿拉伯数字的加工难度更大、过程更复杂,但在两种材料的加工中都出现SNARC效应,结果支持了Vergut等人数字加工的计算模型.     

The Stability of Individual Differences in Basic Mathematics‐Related Skills in Young Children at the Start of Formal Education

The current study investigated the development of children's performance on tasks that have been suggested to underlie early mathematics skills, including measures of cardinality, ordinality, and intelligence. Eighty‐seven children were tested in their first (T1) and second (T2) school year (at ages 5 and 6). Children's performance on all tasks demonstrated good reliability and significantly improved with age. Correlational analyses revealed that performance on some mathematics‐related tasks were nonsignificantly correlated between T1 and T2 (number line and number comparison), showing that these skills are relatively unstable. Detailed analyses also indicated that the way children solve these tasks show qualitative changes over time. By contrast, children's performance on measures of intelligence and nonnumerical ordering abilities were strongly correlated between T1 and T2. Additionally, ordering skills also showed moderate to strong correlations with counting procedures both cross‐sectionally and longitudinally. These results suggest that, initially, mathematics skills strongly rely on nonmathematical abilities.     

The difficulties of representing continuous extent in infancy: using number is just easier

This study investigates the ability of 6-month-old infants to attend to the continuous properties of a set of discrete entities. Infants were habituated to dot arrays that were constant in cumulative surface area yet varied in number for small (< 4) or large (> 3) sets. Results revealed that infants detected a 4-fold (but not 3-fold) change in area, regardless of set size. These results are in marked contrast to demonstrations that infants of the same age successfully discriminate a 2- or 3-fold change in number, providing strong counterevidence to the claim that infants use solely nonnumerical, continuous extent variables when discriminating sets. These findings also shed light on the processes involved in tracking continuous variables in infants.     

Children’s mental representation when comparing fractions with common numerators

Researchers debate whether one represents the magnitude of a fraction according to its real numerical value or just the discrete numerosity of its numerator or denominator. The present study examined three effects based on the notion that people possess a mental number line to explore how children represent fractions when they compare fractions with common numerators. Specifically, the effect of the spatial numerical association of response codes (SNARC), the distance effect and the size effect in representing fractions were examined in a sample of 72 sixth graders, who successfully solved the fraction comparison task with a real number (.2) or a fraction (1/5) as the reference. Results showed that in the fraction-reference group (1/5 as the reference), there was a significant reverse SNARC effect and a distance effect between the denominators of the target fractions and the reference fraction; in the real number-reference group, the three effects were also observed. These results revealed that both groups used the mental number line to represent fractions and did not represent their real numerical values but rather the discrete numerosities of denominators when comparing fractions with common numerators. It seems that the way people represent fractions may depend on their strategy choices.     

Complex fraction comparisons and the natural number bias: The role of benchmarks

People are often better at comparing fractions when the larger fraction has the larger rather than the smaller natural number components. However, there is conflicting evidence about whether this “natural number bias” occurs for complex fraction comparisons (e.g., 23/52 vs. 11/19). It is also unclear whether using benchmarks such as 1/2 or 1/4 enhances performance and reduces the bias (e.g., 11/19 > 1/2 and 23/52 < 1/2, hence 11/19 > 23/52). We asked 107 adults to solve complex fraction comparisons that did or did not afford using benchmarks, and we assessed response time and accuracy. We found a reverse bias (i.e., smaller components—larger fraction) that was greater among participants with lower mathematics experience. Fractions' proximity to 0 or 1 facilitated performance and decreased bias; effects of other benchmarks were nonsignificant. These results challenge the generality of the natural number bias in fraction comparison and highlight its variability.     

Does school‐based initial teacher training affect secondary school performance?

This article investigates the effects of trainee teachers on secondary school student outcomes. The additional resources which schools receive from being involved in teacher training offer them an opportunity to raise standards, but this has to be set against the possible losses due to school students being taught by inexperienced beginning teachers and the diversion of mentors' efforts away from the classroom. Inspection evidence is used to assess whether trainee teachers affect school students' test and examination results. The findings of this research are that the number of trainees has no significant effect on school results at A‐level or General Certificate of Secondary Education (GCSE), or on the overall value added between Key Stage 3 and GCSE level. However, at Key Stage 3 level at age 14, while there appears to be a very small depressing effect on achievement in schools with low numbers of trainees, there is a significant positive effect on achievement in schools with larger numbers of trainees.     

Preach what you teach! Teacher educators and congruent teaching

Teacher educators seem to agree that, to be able to support their student teachers' learning, they themselves should be good models of the kind of teaching they are trying to promote. However, it is clear from the literature that this congruent teaching is not self‐evident in teacher education. In the present article, we describe a small in‐depth study, in which we attempted to establish whether teacher educators begin to teach more congruently when supported, and the factors influencing the occurrence or non‐occurrence of such congruent teaching. To do so, we organised a workshop on the subject. Before and after the workshop, we interviewed the participating teacher educators, using videotapes of their lessons. To discover the possible contribution of the workshop to their congruent teaching, we later compared both interviews. We found that a particularly important aspect of congruent teaching, i.e. the teacher educators' ability to link their own teaching to theory, had improved. Our conclusion is that the acquisition of a language enabling them to talk about congruent teaching helps teacher educators to overcome problems with congruent teaching.     

Effects of Pointing Gestures on Memory for (In)Congruent Stimuli in Children and Young Adults

We investigated whether finger pointing toward picture locations can be used as an external cognitive control tool to guide attention and compensate for the immature cognitive control functions in children compared with young adults. Item and source memory performance was compared for picture‐location pairs that were either semantically congruent (e.g., a cloud presented at the upper half of the screen) or incongruent (e.g., a cloud presented at the lower part of the screen). Contrary to our expectations, pointing had an adverse effect on source memory compared to visual observation only, in both age groups. As expected, superior source memory performance was found for congruent compared to incongruent picture‐locations pairs in both age groups. These findings suggest that pointing toward pictures compared to only viewing may hamper memory, and that congruent picture locations are easier to remember than incongruent ones.     

HOMES AND SCHOOLS: SOCIAL DETERMINANTS OF EDUCABILITY

An investigation was carried out to ascertain how 700 children aged seven to 15 (half boys and half girls), acquired the ability to define certain moral concepts, how they decided on whether an action was right or wrong, and what influenced the acquisitional process. The results showed older age‐groups gaining significantly higher mean scores in defining concepts, with a sex difference favouring girls, but no significant social class differences. However, even older age‐groups encountered difficulties with some concepts, e.g. ‘doing right’ and ‘being good’. In deciding whether an action was right or wrong, more older children claimed they decided for themselves, and a significantly higher number of older girls stated that they did so. The sample claimed that their mothers had been a major influence in acquiring moral concepts, much more so than peer‐groups. The mass media was not thought by the sample to be accepted uncritically, and the church was believed to help them most. Evidence from this research would suggest that the teacher's contribution, to the acquisition of moral concepts during the early school years, seems highly relevant.     

Are class size differences related to pupils' educational progress and classroom processes? findings from the institute of education class size study of children aged 5–7 years

Abstract Despite evidence from the USA that children in small classes of less than 20 do better academically there is still a vociferous debate about the effects of class size differences in schools, and considerable gaps in our understanding of the effects of class size differences. This article summarises results from the most complete UK analysis to date of the educational consequences of class size differences. The study had two aims: first, to establish whether class size differences affect pupils’ academic achievement; and second, to study connections between class size and classroom processes, which might explain any differences found. The study had a number of features that were designed to be an improvement on previous research. It used an ‘observational’ approach, rather than an interventionist one, in order to capture the nature of the relationship between class size and achievement across the full range of observed classes, and it employed a longitudinal design with baseline assessment to adjust for possible non‐random selection of children into classes. The study followed a large sample of over 10,000 children from school entry through the infant stage, i.e. children aged 4–7 years. It used multilevel statistical procedures to model effects of class size differences while controlling for sources of variation that might affect the relationship with academic achievement, and a multimethod research approach, integrating teachers’ judgements and experiences with case studies, and also carefully designed time allocation estimates and systematic observation data. Results showed that there was a clear effect of class size differences on children's academic attainment over the (first) Reception year. In the case of literacy, the lowest attainers on entry to school benefited most from small classes, particularly below 25. Connections between class size and classroom processes were examined and a summary model of relationships presented. Effects were multiple, not singular; in large classes there are more large groups and this presented teachers with more difficulties, in smaller classes there was more individual teacher contact with pupils and more support for learning, and in larger classes there was more pupil inattentiveness and off‐task behaviour. Results support a contextual approach to classroom learning, within which class size differences have effects on both teachers and pupils. It is concluded that much will depend on how teachers adapt their teaching to different class sizes and that more could be done in teacher training and professional development to address contextual features like size of class.     

Naturally Acquired Mentoring Relationships and Young Adult Outcomes Among Adolescents with Learning Disabilities

We evaluated whether having a naturally acquired mentor during adolescence was associated with improved adult outcomes among youth with learning disabilities (YLD). Mentored youth were more likely to have graduated from high school, reported a higher level of self‐esteem, and reported a higher overall number of positive outcomes than nonmentored youth. Mentorship by teachers/guidance counselors was associated with larger differences in high school graduation rates and self‐esteem compared to nonmentored youth whereas mentorship by nonteachers was associated with smaller changes in self‐esteem and no differences in high school completion rates. Future research should include more in‐depth, objective assessments of youths’ learning disabilities, consideration of interactions with concurrent risk factors, and efforts to clarify optimal strategies for mentoring support of YLD.     

Procrastination—Not all it's put off to be

Although procrastination has devastating negative effects on performance, many of us employ common myth‐like justifications for it, thereby attempting to alleviate the guilt and stress that commonly accompany putting things off when we know we should not. Working better under pressure, being more creative at the last minute, and avoiding tasks because of perfectionism are three rationalizations that we often give for delay. The consequences of procrastination include missed deadlines, health and financial problems, guilt, stress, and work that isn't our best. To overcome a tendency to procrastinate, focusing on avoiding it is not the best response. Instead, adopting a task‐oriented, problem‐solving focus or set of strategies can work even for people with a long history of putting things off. These strategies include increasing the perceived value of a task, adjusting expectations for success, reducing impulsive temptations, and approaching larger projects or those with longer timelines in smaller segments with progress checks along the way. Procrastinators can learn how to change their approach to getting work done and thereby reduce their tendency to delay.     

Moving an Evidence‐Based Parenting Program Into the Community

Attachment and Biobehavioral Catch‐up (ABC) is a parenting program developed to enhance sensitivity among parents of infants who experience early adversity. In several randomized clinical trials, the intervention's efficacy has been demonstrated. Moving interventions into the community with adequate fidelity is challenging, though, and intervention effects are often much smaller than when tested in randomized clinical trials. To enhance the likelihood that ABC is delivered with high fidelity, a microanalytic fidelity assessment was developed. Using this fidelity tool as a central component of training, supervision, and certification, changes in parent sensitivity for 108 families with children ages 6 months to 2 years were as large as those seen in laboratory settings. These findings are discussed with regard to implications for moving other evidence‐based interventions into the community.     

Effectiveness of school‐based psychotherapy: A meta‐analysis of dissertation research

A meta‐analysis was conducted with 65 school‐based psychotherapy and counseling dissertations over the last 10 years (1998–2008) to assess if a file‐drawer problem (i.e., studies conducted but not published that, as a whole, have different results than studies in the same area published) exists in the school‐based outcome literature. An overall mean effect size of 0.44 was found for 73 treatment interventions. This effect size is comparable to Prout and DeMartino's 1986 meta‐analysis conducted with published school‐based studies and approximately half a standard deviation smaller than Prout and Prout's 1998 meta‐analysis of school‐based intervention studies. A bias does appear to exist but seems to be smaller than the bias found in the general child and adolescent psychotherapy outcome literature. Most of the dissertation studies evaluated group interventions and used a cognitive–behavioral or skills training intervention. Skills training and interventions with elementary‐school students yielded the largest effect sizes. Comparisons of the current study with previous school‐based intervention meta‐analyses are discussed as are suggestions for future research. © 2010 Wiley Periodicals, Inc.     

Improving the academic outcomes of undergraduate ESL students: the case for discipline‐based academic skills programs

This article examines the impact of an adjunct English language tutorial program on the academic performance of first‐year Architecture students. With increasing numbers of international students enrolling in Australian universities, language and academic skills programs have shifted from generic to more discipline‐specific models; however, there has been little research on the effects of these programs on ESL students' academic performance. This study uses a mixed‐method approach to evaluate the effectiveness of an English as a second language (ESL) intervention program. Findings indicate that students value a highly discipline‐specific approach to language and academic skills support and that regular participation in a content‐based ESL program can lead to positive learning outcomes for students. Preliminary findings also suggest that there are positive longer‐term benefits on students' academic outcomes. The authors suggest the need for longitudinal studies on the impact of discipline‐based programs for ESL students.     

Congruent numbers, elliptic curves, and the passage from the local to the global

The ancient unsolved problem of congruent numbers has been reduced to one of the major questions of contemporary arithmetic: the finiteness of the number of curves over Q which become isomorphic at every place to a given curve. We give an elementary introduction to congruent numbers and their conjectural characterisation, discuss local-to-global issues leading to the finiteness problem, and list a few results and conjectures in the arithmetic theory of elliptic curves.     

A classification of child abuse and its relation to treatment and prognosis

This paper is based on five years' clinical experience of assessing parents who injure their children. During this time it has become obvious that there is a complex variety, not only of parental and paediatric pathology, but also of response to treatment. “Abuse of children is not a disease entity but a pattern of behaviour and like all such patterns it has a multiplicity of paths by which it is reached” (Scott 1977).There is therefore a great need to evolve a way of breaking down the large psychiatrically heterogenous group into smaller groups, who not only share certain characteristics, but who have some predictive value in terms of treatment and prognosis. This has become particularly important as the number of referrals are rising and the spectrum is widening. We are not only seeing larger numbers of less severely injured children, but also many more less conspicuously abnormal parents. (N.S.P.C.C. Battered Child Research Department reports 1969–1977).     

Inference and Association in Children's Early Numerical Estimation

How do children map number words to the numerical magnitudes they represent? Recent work in adults has shown that two distinct mechanisms—structure mapping and associative mapping—connect number words to nonlinguistic numerical representations (Sullivan & Barner, 2012 ). This study investigated the development of number word mappings, and the roles of inference and association in children's estimation. Fifty‐eight 5‐ to 7‐year‐olds participated, and results showed that at both ages, children possess strong item‐based associative mappings for numbers up to around six, but rely primarily on structure mapping—an inferential process—for larger quantities. These findings suggest that children rely primarily on an inferential mechanism to construct and deploy mappings between number words and large approximate magnitudes.