Adaptive number knowledge and its relation to arithmetic and pre-algebra knowledge

Traditionally measured skills with arithmetic are not related to later algebra success at levels that would be expected given the close conceptual relation between arithmetic and algebra. However, adaptivity with arithmetic may be one aspect of arithmetic competences that can account for additional variation in algebra attainment. With this in mind, the present study aims to present evidence for the existence and relevance of a newly acknowledged component of adaptivity with arithmetic, namely, adaptive number knowledge. In particular, we aim to examine whether there are substantial individual differences in adaptive number knowledge and to what extent these differences are related to arithmetic and pre-algebra skills and knowledge. Adaptive number knowledge is defined as the well-connected knowledge of numerical characteristics and relations. A large sample of 1065 Finnish late primary school students completed measures of adaptive number knowledge, arithmetic conceptual knowledge, and arithmetic fluency. Three months later they completed a measure of pre-algebra skills. Substantial individual differences in adaptive number knowledge were identified using latent profile analysis. The identified profiles were related to concurrent arithmetic skills and knowledge. As well, adaptive number knowledge was found to predict later pre-algebra skills, even after taking into account arithmetic conceptual knowledge and arithmetic fluency. These results suggest that adaptive number knowledge is a relevant component of mathematical development, and may help account for disparities in algebra development.     

PERFORMANCE IN MATHEMATICAL PROBLEM SOLVING AS A FUNCTION OF COMPREHENSION AND ARITHMETIC SKILLS

Many factors influence a student’s performance in word (or textbook) problem solving in class. Among them is the comprehension process the pupils construct during their attempt to solve the problem. The comprehension process may include some less formal representations, based on pupils’ real-world knowledge, which support the construction of a ‘situation model’. In this study, we examine some factors related to the pupil or to the word problem itself, which may influence the comprehension process, and we assess the effects of the situation model on pupils’ problem solving performance. The sample is composed of 750 pupils of grade 6 elementary school. They were selected from 35 classes in 17 Francophone schools located in the province of Quebec, Canada. For this study, 3 arithmetic problems were developed. Each problem was written in 4 different versions, to allow the manipulation of the type of information included in the problem statement. Each pupil was asked to solve 3 problems of the same version and to complete a task that allowed us to evaluate the construction of a situation model. Our results show that pupils with weaker arithmetic skills construct different representations, based on the information presented in the problem. Also, pupils who give greater importance to situational information in a problem have greater success in solving the problem. The situation model influences pupils’ problem solving performance, but this influence depends on the type of information included in the problem statement, as well as on the arithmetic skills of each individual pupil.     

Attitudes to Reading in English Primary Schools

This article reports on a two‐year research project investigating attitudes to reading held by teachers and pupils in a sample of English primary schools. The project draws on international and national surveys of reading engagement and the findings of previous research, but seeks to provide more detailed data relating to the attitudes of individual children and the strategies used by individual schools and teachers whose pupils demonstrate positive attitudes to reading. Results are related to previous research literature on reading motivation and attainment, and to motivational theory. In conclusion, it is argued that strategies which promote positive attitudes to reading need to be used alongside the teaching of reading skills in any effort to raise attainment.     

‘Over To You’: Group work to help pupils avoid school exclusion

This paper describes the support of secondary pupils at risk of school exclusion through a course of group work designed to promote individual responsibility for behaviour. Following self‐reflection the young people are encouraged to write their own behavioural targets and consider their progress in working towards them throughout the six‐session course. The results of a study involving a mixed group of five Year 8 pupils are reported. All the pupils increased their self‐rating scores on a social skills assessment form completed before and after the course, and were also rated more highly by their teachers. Seven months later the five pupils had maintained behavioural improvements and had not been excluded.     

Early cognitive profiles predicting reading and arithmetic skills in grades 1 and 7

The aim of this study was to investigate cognitive profiles composed of skills predicting the overlap between reading and arithmetic in kindergarten (phonological awareness, letter knowledge, rapid automatized naming, and counting sequence knowledge) and the relation of these profiles to reading and arithmetic skills at Grades 1 and 7. A total of four distinct cognitive profiles were identified in an unselected sample of 1,710 children aged 5–6 years: (1) high linguistic and high counting skills (39.2%), (2) low linguistic and low counting skills (25.4%), (3) high counting skills in relation to linguistic skills (15.3%), and (4) low counting skills in relation to linguistic skills (20.1%). Among most of the children (about 65%), the linguistic and counting skills varied together. Children characterized by high or low overall performance levels across linguistic and counting skills also showed, predictably, high or low overall performance levels in subsequent reading and arithmetic skills in Grades 1 and 7. Children characterized by a discrepancy between linguistic and counting skills (about 35% of the children) in turn showed somewhat discrepant subsequent levels of reading and arithmetic skills. The results point towards individual variation (i.e., heterogeneity) in cognitive profiles that predict both reading and arithmetic skills in Grades 1 and 7. Based on these findings, the linguistic and basic number skills predict differently the overlap between reading and arithmetic in Grades 1 and 7 depending on cognitive profile. The weaknesses across linguistic and counting skills are a greater risk for persistent overlapping difficulties in reading and arithmetic than weaknesses in only one of the learning domains. For difficulties in arithmetic skill development, however, weaknesses in only counting skills present an equal risk compared to weaknesses evident across linguistic and counting skills.     

Including pupils with autistic spectrum disorders in mainstream schools

The number of pupils with autistic spectrum disorders (ASD) being educated in mainstream schools is increasing. However, there is growing concern about their educational experiences. Research suggests that such pupils make easy targets for bullies, and are considered difficult to teach by teachers. Furthermore, pupils with ASD are more than 20 times more likely to be excluded from school than those without special educational needs. In light of such evidence, the aim of this article is to outline evidence‐based strategies to facilitate the presence, participation, acceptance and achievement of pupils with ASD in mainstream settings. The strategies are presented thematically, as follows: (i) challenge stereotypes and raise expectations, (ii) create order from chaos, (iii) promote peer understanding, (iv) develop social skills, (v) adapt academic subjects, and (vi) modify conversational language. These strategies are not intended to be completely comprehensive – rather, they are starting points on a journey towards inclusion for those with ASD.     

How can children with mild literacy difficulties be supported at the transition to secondary school? A small‐scale quasi‐experimental study

There is evidence that pupils with weak literacy skills struggle on transition to secondary school. Many experience a drop in attainment in the summer break between the two. A British government‐funded programme of rigorously designed research on boosting literacy at transition had (by 2015) found only four of 15 interventions evaluated had positive effects. This small‐scale quasi‐experimental study investigated the effectiveness of support for pupils with mild literacy difficulties on transition to secondary school. Thirty‐two pupils in three schools were involved; half received the programme. Pairs were matched on reading, spelling, age and gender. Intervention was designed around the individual needs of each pupil, focusing variously on language skills, writing, reading and spelling. The group receiving the programme made modest gains in spelling, reading efficiency and single word reading. The comparison group lost ground, relatively, in all three areas. The results suggest a promising line for more rigorous investigation.     

Speaking and listening in the primary curriculum: some themes and their impact

In a previous phase of a project based in a group of UK primary schools, speaking and listening was found to be an effective focus for improved learning across the curriculum and for teachers’ professional development. At the project's second stage and in the light of recently changed Department for Education guidelines, these findings have been extended to exploration of strategies in the development of pupils’ communicative skills and the potential value of these when transferred to other, cross-curricular contexts. Teachers’ perspectives have again been considered, in terms of their ability to manage the strategies but also of the impact on their views of themselves and their role. Data in the form of transcribed classroom recordings, observations and interviews, plus teachers’ diaries and pupils’ work, have been analysed for these purposes. They show that the skills in question can indeed be taught and will transfer across contexts when teaching is of a ‘dialogic’ character.     

Improving the effectiveness of collaborative group work in primary schools: effects on science attainment

This longitudinal research tests the effectiveness of the SPRinG programme, which was developed through a collaboration between researchers and teachers and designed to provide teachers with strategies for enhancing pupil group work in ‘authentic’ classroom settings. An evaluation study involved comparing pupils in SPRinG classrooms and trained in group work skills with those who were not in terms of science attainment. There were 560 and 1027 pupils (8–10 years) in the experimental and control groups respectively. ‘Macro’ attainment data were collected at the start of the year. ‘Micro’ attainment data were collected in the spring and summer before and after science lessons involving either group work (intervention) or the control teachers' usual approach. SPRinG pupils made greater academic progress than control pupils. Findings are discussed relative to enhancing the quantity and quality of group work in schools and a social pedagogic approach to classroom learning.     

Developing teaching assistants’ skills in positive behaviour management: an application of Video Interaction Guidance in a secondary school

This paper reports an action research project in a school in the UK designed to investigate the impact of a brief Video Interaction Guidance (VIG) intervention in promoting skills of non-teaching staff in positive behaviour management. A summary of the literature in relation to VIG is provided before describing the project and data collected. Ten teaching assistants (TAs) from a secondary school took part in an intervention using VIG. The impact on TA skills and confidence was assessed using participant ratings of the specific target outcomes of the intervention using the Target Monitoring and Evaluation (TME) system. Participants’ experiences of the intervention were explored during a focus group discussion after the intervention had taken place. TME data suggested a positive impact on TA skills and confidence to support individual pupils, while thematic analysis of focus group data showed a number of themes relevant to the application of VIG in this context, including promotion of effective staff development.     

Prenatal testosterone,visual-spatial memory,and numerical skills in young children

Lateralization of the brain is strongly influenced by prenatal androgens, with differential exposure thought to account for cognitive sex differences. This study investigated sex and individual differences and relationships between 2D:4D (the ratio of the 2nd to 4th digit [digit ratio] as a proxy indicator of prenatal testosterone exposure), visual-spatial memory, and numerical skills in 5-year-old children. No sex differences were found in any of the numerical or visual-spatial tasks. Visual-spatial memory was positively correlated with arithmetic score. Girls with a lower (more masculinised) 2D:4D had better number sense and visual-spatial skills, whilst boys with lower 2D:4D had better arithmetic skills. This suggests that prenatal testosterone exposure may have differential effects on the visual-spatial and numerical skills of girls and boys.     

Norwegian teachers’ safety strategies for Friluftsliv excursions: implications for inclusive education

The purpose of this study was to explore how teachers in friluftsliv (the Scandinavian equivalent of outdoor education and outdoor recreation) reflect upon their safety strategies in relation to pupils’ friluftsliv abilities in the upper secondary school ‘Sport and Physical Education programme’. This article is based on six focus group interviews of friluftsliv teachers. The analysis of the empirical material is inspired by John Evans’s understanding of the concept of abilities as dynamic sociocultural constructs and processes. In the findings, different challenges related to teachers’ experiences of a general decline in pupils’ winter friluftsliv abilities are identified. Furthermore, the article identifies and discusses challenges related to teachers’ safety strategies, which led to both inclusion and exclusion of pupils. The findings in this study reveal a tension between important winter outdoor skills and inclusive friluftsliv.     

Supporting Pupils with Dyspraxia in the Visual Arts Does Drawing from Observation Function as an Official and Discriminatory Discourse?

This article examines the demands that pupils with dyspraxia may face when engaging with the secondary art and design curriculum in a mainstream secondary school. It explores the possibility that there is an exclusive approach to art and design, prioritising a formalist approach to the teaching of specific skills and mastery of techniques, and considers the implications that this may have for such pupils. Specific attention is paid to the role of observational drawing and the demands that this may make for pupils with dyspraxia. The article will explore existing guidance offered for subject‐based practitioners and aims to contextualise this within the current debates on art and design education and the recollections of individual experiences of art and design. It will outline the hypothesis that pupils with dyspraxia may be one group of pupils amongst many for whom their art and design experience does not offer an inclusive experience, and it seeks to question the existence of a hierarchy of practice and its subsequent relevance.     

Transfer of strategy use by semantic recoding in arithmetic problem solving

Transfer of strategies between problems sharing the same formal structure is facilitated by a semantic recoding that makes evident the structural similarities between the problems. Two experiments were carried out among 4th and 5th grade pupils, with an experimental group trained to compare strategies in order to reinterpret an arithmetic word problem so that the calculations are consistent with the interpretation, and a control group. The experimental group in Experiment 1 improved significantly by choosing the alternative strategy in problems different from those used in training but no significant progress was observed in the control group. Experiment 2 showed that the improvement observed in the experimental group could not be attributed to the fact that children only learned to use a superficial rule. These results support the idea that the activity of problem re-representation may be a crucial step in mathematization.     

Growing Talent for Inclusion: using an appreciative inquiry approach into investigating classroom dynamics

This paper reports on an Appreciative Inquiry project called ‘Growing Talent for Inclusion’ which has been running since 2002. The project grew out the authors’ work in a Local Authority Support Service assisting schools to meet the needs of pupils with a range of additional educational needs. Faced with a large number of individual referrals, many relating to the emotional, social and behavioural needs of pupils, it was considered that an eco – systemic approach was required and that a priority was to support pupils and teachers in developing more effective and satisfying interpersonal relationships in the classroom. ‘Growing Talent for Inclusion’ uses Appreciative Inquiry to investigate a management change process which has been used within large organisations and communities but less commonly at classroom level. It is a type of action research which is solution not problem focused and therefore lends itself well to a research focus of improving classroom dynamics. The paper introduces a 4‐D Cycle of Appreciative Inquiry: discovery, dream, design and deliver, as advocated by Cooperrider and Srivastva, 1987, which guides the identification, acknowledgment and amplification of skills pertinent to improving social dynamics within the classroom and discusses the methodological issues which arise from this collaborative, participative form of inquiry. A combination of qualitative and quantitative methods has been used to identify and track the development of attributes for improving working relationships in four different primary and secondary classrooms in three schools. 76 pupils and four teachers have been involved in the project since its inception in 2002 with classes in a further three primary schools using the approach during the academic year 2005–2006. Findings from the project show an increase in the number of pupils with whom other pupils are happy to work, a reduction in the number of pupils identified as socially excluded at the beginning of the project and enhanced capacity of the group in terms of the talents identified for growth. Feedback from staff and students also suggests that the process of noticing and acknowledging strengths has contributed to improvements in working relationships.     

Research on Baseline Assessment in Mathematics at School Entry

This paper presents findings from research investigating the skills and knowledge in Mathematics of Cypriot pupils entering primary school (Average age=5.92 (decimal years)). A performance test, which was designed to assess skills and knowledge in Mathematics identified in the Curriculum of Primary Education in Cyprus, was administered to a representative sample of pupils in Year 1 (n=835). Teachers were also asked to complete a report for each pupil. The most important findings were as follows. Firstly, the skills included in the curriculum were differentiated into those which more than 75% of pupils entering primary schools had achieved and those which more than 30% of pupils entering primary school had not achieved. Secondly, significant differences among the skills and knowledge of the whole group of pupils entering primary school have been identified. Thirdly, cluster analysis revealed five relatively homogeneous groups of pupils according to their different knowledge and skills in Mathematics. Fourthly, a correlation was identified between findings gathered from the performance test and from teachers' assessment of pupils' skills in Mathematics. Implications for the development of a national policy on baseline assessment are drawn.     

How effective is role play in supporting speaking and listening for pupils with English as an additional language in the Foundation Stage?

This research investigated how role play supports the development of speaking and listening skills for pupils who have English as an additional language in the Foundation Stage. The literature highlighted sociocultural perspective on language development, importance of role play within Early Years pedagogy and key strategies for language learning which may be promoted through role play. Data was triangulated through questionnaires and interviews in relation to the key questions. The findings were positive with pupils demonstrating an improved use of English and a wider range of language learning strategies.     

Facilitating the social participation of pupils with special educational needs in mainstream schools: A review of school-based interventions

Inclusive education of pupils with special educational needs (SEN) has become a global trend. However, a considerable number of studies have shown that mere enrolment in mainstream classrooms is not enough to support the social participation of pupils with SEN. These children are at risk of experiencing difficulties in their involvement with peers at school. Thus, the question arises of how social participation can be fostered in mainstream classrooms. A systematic review of 35 studies was conducted to investigate which interventions are effective in inclusive mainstream preschool and elementary classrooms. Teaching interaction strategies to typically developing pupils, group activities in the academic context (cooperative learning and peer-tutoring), support groups for pupils with SEN, and training paraprofessionals to facilitate social interactions, were found to improve the social participation of pupils with SEN in general education classrooms. Nevertheless, there is need for more intervention studies implementing a variety of strategies and including different groups of pupils with SEN.     

儿童早期加法策略发展及其教育启示

计算策略是影响儿童计算能力发展的重要因素,反映了儿童的思维过程及问题解决水平。目前已有研究对儿童早期加法策略的类型、水平及发展特点进行了深入细致的探讨。幼儿园在开展计算教学活动时应积极利用这些研究成果,为儿童提供运用、表达与交流策略的机会,并积极促进儿童策略意识与水平的发展。     

Spontaneous focusing on numerosity and the arithmetic advantage

Children show individual differences in their tendency to focus on the numerical aspects of their environment. These individual differences in ‘Spontaneous Focusing on Numerosity’ (SFON) have been shown to predict both current numerical skills and later mathematics success. Here we investigated possible factors which may explain the positive relationship between SFON and symbolic number development. Children aged 4–5 years (N = 130) completed a battery of tasks designed to assess SFON and a range of mathematical skills. Results showed that SFON was positively associated with children's symbolic numerical processing skills and their performance on a standardised test of arithmetic. Hierarchical regression analyses demonstrated that the relationship between SFON and symbolic mathematics achievement can be explained, in part, by individual differences in children's nonsymbolic numerical processing skills and their ability to map between nonsymbolic and symbolic representations of number.