Numerical competence in young children and in children with mathematics learning disabilities

A longitudinal study was conducted on 82 children to investigate, firstly the numerical competence of young children and the predictive value of (pre)-numerical tests in kindergarten, and, secondly, whether children's knowledge of the numerical system and representation of the number size is related to their computation and logical knowledge and to their counting skills. In an additional cross-sectional study on 30 children with a clinical diagnosis of mathematical learning disability (MLD) of 8,5 years, age- and ability-matched with 2 × 30 children the same parameters of numerical competence were assessed. The longitudinal data showed individual differences in numerosity, as well as the relationship between a delay in arithmetics in grade l and problems on numerosity in kindergarten. In the cross-sectional results some evidence was found for the independence of numerical abilities in MLD-children. About 13% of them had still severe pre-numerical processing deficits (in number sequence production, cardinality skills and logical knowledge) in grade 3. About 67% had severe difficulties in executing calculation procedures and a lack of conceptual knowledge. A feature of 87% of the MLD-children was severe translation deficits, with a significantly worse knowledge of number words compared with the knowledge of Arab numerals. Finally a severe deficit in subitizing was found to be present in 33% of the MLD children. On a group level the processing deficits were linked to understanding numerosity, since the ability-matched younger children and the MLD-children had the same pre-numerical and numerical profile. Implications for the assessment of mathematical disabilities and the value of TEDI-MATH® as an instrument in this process are discussed.     

Estimating the co-development of executive functions and math achievement throughout the elementary grades using a cross-lagged panel model with fixed effects

Executive functioning (EF) is associated with children’s math skill development, both concurrently and longitudinally. However, it is not known how components of EF might be related to mathematics skills and vice versa over the course of elementary school. The present study addresses this issue by investigating relations between math achievement and two key components of EF -- working memory (WM) and cognitive flexibility (CF) -- from kindergarten to 5th grade, using the large-scale nationally representative dataset (N = 18,174) from the Early Childhood Longitudinal Study-Kindergarten (ECLS-K: 2011). Results from cross-lagged panel models with fixed effects support a transactional theoretical model, demonstrating a long-term reciprocal relationship between WM and math achievement from kindergarten to 5th grade and between CF and math achievement from 2nd grade to 5th grade. However, we found that reciprocal relations decrease as children grow older, suggesting that their math achievement relies less on EF and more on prior math knowledge over time.     

The role of special schools for children with profound and multiple learning difficulties: is segregation always best?

The education of young people with profound and multiple learning difficulties continues to raise challenges and controversies. In this article, Ben Simmons, an ESRC funded PhD student and research assistant, and Phil Bayliss, programme director for the masters degree in special education and disability, both based in the School of Education and Lifelong Learning at the University of Exeter, describe their research into provision for pupils with profound and multiple learning difficulties in a special school in the south west of England. Their work, based in an interpretivist, qualitative approach, set out to illuminate issues relating to the inclusion of pupils with profound and multiple learning difficulties. The findings presented here suggest that the school, in spite of its strong reputation, struggled significantly to provide appropriate learning experiences for pupils with profound and multiple learning difficulties. Ben Simmons and Phil Bayliss discuss the need for improved staff development opportunities focused on enhancing current levels of knowledge and skills. They conclude by calling for a reappraisal of the established view that special schools necessarily provide the best learning environment for pupils with profound and multiple learning difficulties.     

Educational e-books: a support for vocabulary and early math for children at risk for learning disabilities

Mathematical learning difficulties can originate at an early age. However, research on young children’s math development, especially those who are at risk, is in its early stages. The current study is the first to examine the effects of an activity with an educational e-book on emergent math with 52 preschoolers at risk for learning disability (ALD). The effects on their emergent vocabulary of the e-book intervention was also tested. The findings revealed that following the intervention, children in the experimental e-book group improved both their vocabulary and early math skills as compared to the control group who engaged in their regular preschool activities. The implications of these results are discussed.     

Numerical magnitude processing in abacus-trained children with superior mathematical ability: an EEG study

Distance effect has been regarded as the best established marker of basic numerical magnitude processes and is related to individual mathematical abilities. A larger behavioral distance effect is suggested to be concomitant with lower mathematical achievement in children. However, the relationship between distance effect and superior mathematical abilities is unclear. One could get superior mathematical abilities by acquiring the skill of abacus-based mental calculation (AMC), which can be used to solve calculation problems with exceptional speed and high accuracy. In the current study, we explore the relationship between distance effect and superior mathematical abilities by examining whether and how the AMC training modifies numerical magnitude processing. Thus, mathematical competencies were tested in 18 abacus-trained children (who accepted the AMC training) and 18 non-trained children. Electroencephalography (EEG) waveforms were recorded when these children executed numerical comparison tasks in both Arabic digit and dot array forms. We found that: (a) the abacus-trained group had superior mathematical abilities than their peers; (b) distance effects were found both in behavioral results and on EEG waveforms; (c) the distance effect size of the average amplitude on the late negative-going component was different between groups in the digit task, with a larger effect size for abacus-trained children; (d) both the behavioral and EEG distance effects were modulated by the notation. These results revealed that the neural substrates of magnitude processing were modified by AMC training, and suggested that the mechanism of the representation of numerical magnitude for children with superior mathematical abilities was different from their peers. In addition, the results provide evidence for a view of non-abstract numerical representation.     

Collaborative learning with scientific approach and multiple intelligence: Its impact toward math learning achievement

Abstract

This study examined the effect of collaborative learning with a scientific approach (SA) on the learning achievement in mathematics viewed from the students’ multiple intelligences. This study compared two types of collaborative learning models, Three Steps Interview (TSI), and Think Pair Share (TPS). The participants of this study were grade 8 students of Secondary Schools in Sukoharjo, Central Java, Indonesia (N?=?262). This study was a quasi-experimental study with a 3?×?3 factorial design. The results of the study can be concluded as follows. (1) TSI with a scientific approach got better math learning achievement than TPS with a scientific approach and classical with a scientific approach. Besides, TPS with a scientific approach got better learning achievement than classical with a scientific approach. (2) Students with logical-mathematical intelligence got better math learning achievement than students with linguistic intelligence and students with interpersonal intelligence, students with linguistic intelligence got better math learning achievement than students with interpersonal intelligence.     

The timing of executive function development is associated with growth in math achievement from preschool through second grade

We examined whether the timing of executive function (EF) development was associated with growth in children's math achievement across eight measurement occasions from preschool through second grade. Using a prospective longitudinal sample of 351 children, we found that children who developed EF later, entered preschool with the lowest levels of math performance and did not catch-up to their intermediate or early EF developing counterparts despite exhibiting a similar math growth rate through second grade. This trend was also observed after controlling for children's biological sex, early language skills, and socioeconomic background. These findings suggest that developing EF late might place children at a unique risk for math difficulties independent of important child and family level characteristics and can provide insights for instructional strategies that take into account differences in children's EF development.     

The school-level standardized testing policy and math achievement in primary grades: The mediational role of math instructional approach

This study investigates how school-level standardized testing policy at Grade 1 is directly and indirectly linked to math achievement in primary grades. Using nationally representative Early Childhood Longitudinal Study-Kindergarten Cohort data drawn from the U.S., the sample consists of 6774 children nested in 925 elementary schools. Findings from a multilevel full structural mediation analysis indicate that despite children’s short-term gains at Grade 1, the positive effects of frequent testing policy at Grade 1 do not persist in Grade 3. In contrast, school-level standardized testing policies were negatively associated with math achievement at Grade 3 mediated by procedural instructional approaches (e.g., drills). The findings provide empirical evidence on the validity of standardized testing in primary-grade mathematics and offer implications for teachers, educational policymakers, and researchers.     

Stigma and stratification limiting the math course progression of adolescents labeled with a learning disability

Learning disability (LD) designations may produce stigma by masking the real causes of learning differences, altering perceptions, and legitimizing stratification. This study uses data on adolescents and their teachers from The Education Longitudinal Study of 2002 to show the negative effect of LD designations on adolescents' math course attainment is partially mediated by disparities in adolescents' earlier math course placements, and teachers' more negative attributions and expectations. Results indicate addressing low achievement through LD designations may reproduce disadvantage through stigma and stratification.     

Examining the dynamics of mathematics anxiety,perceived cost,and achievement: A control-value theory approach

Concerns about the influence of students’ perceived negative consequences of engagement in a task (i.e., cost) on their emotions, motivation, and cognition have increased in the last decade. The use of longitudinal models is needed to provide new insights into the role of perceived cost in mathematics learning. Grounded in the control-value theory, this study examined cross-lagged relations of mathematics anxiety, perceived cost, and mathematics achievement. The participants (N = 335) reported their mathematics anxiety and perceived cost four times during Grades 7 and 8, and their mathematics grades were attained from their school records. Cross-lagged panel model analysis revealed evidence of a long-term positive reciprocal relationship between mathematics anxiety and effort/emotional cost, a gradually diminished relationship between effort/emotional cost and mathematics performance, and a positive achievement to anxiety link during the transition between grade levels. Moreover, mathematics performance is a distal predictor of mathematics anxiety through effort/emotional cost rather than a proximal predictor or an outcome of anxiety. This study also clarified the distinction in the central role of effort/emotional versus opportunity cost in the interrelatedness of mathematics anxiety and performance, where the latter failed to demonstrate significant paths. Specific timing for interventions was discerned. Early cost prevention interventions along with considerations of academic achievement to alleviate both anxiety and perceived effort/emotional are highlighted as crucial for a positive high school mathematics experience.     

The effects of sustained classroom-embedded teacher professional learning on teacher efficacy and related student achievement

This paper reports on the impact of a classroom-embedded professional learning (PL) program for mathematics teaching in two contrasting districts in Canada, and investigates the relationship between teacher efficacy and student achievement. Before the PL, District A had lower teacher efficacy and student achievement than District B, but after the PL, this situation was reversed. Qualitative analysis revealed that the two districts reported learning very different things from the PL opportunity. The complexities of context, prior learning experiences, goal setting, and persistence of participants all factored into what and how teachers learned.     

The conundrum of low achievement and feedback for learning

Abstract

The literature on improving student engagement with assessment and feedback has a tendency to treat all students as if they are the same. Students with lower levels of attainment are generally under-represented within empirical studies and their feedback behaviours are less well understood. The recent drive to improve student assessment and feedback literacy and the move from ‘feedback’ being information about a task to being a process of understanding and using performance information is a larger conceptual leap for some students than others. In this paper, we consider issues surrounding the transition to new modes of feedback, focussing on what is needed for those who find study difficult and persistently are disappointed by their levels of attainment, to benefit from and take advantage of our feedback pedagogies. We examine literature advocating strategies such as increasing agency, using praise, developing feedback literacy and cultivating a growth mind-set. We argue that students who underachieve may benefit from strong relationships with educators and peers, exposure to feedback rich, low stakes environments, which permit repeated integrations of practice and feedback, and building feedback literacy through peer assessment activities.     

Performance in solving arithmetic problems: a comparison of children with different levels of achievement in mathematics and reading

The aim of the present study was to investigate the performance in arithmetic related to achievement levels in reading and mathematics. Basic arithmetical facts and multi‐step calculations were examined. The participants were 941 pupils aged 8 (N = 415), 10 (N = 274) and 13 (N = 252) years. The pupils were divided into four groups by standardized achievement tests. One group showed low achievement in both mathematics and reading (MLRL), a second group showed low achievement in mathematics only (ML‐only), a third group in reading only (RL‐only) and a fourth group showed normal achievement in both mathematics and reading (NA). The ML‐only and the MLRL groups did not differ significantly in basic arithmetical facts at any age level, but both groups performed below the RL‐only and NA groups. The two latter groups also performed similarly at all year levels. In multi‐step calculation all groups differed significantly at the lowest age level, with the NA as the group with the best achievement, followed by RL‐only, ML‐only and the MLRL group. At the two highest age levels the relations between the groups, in multi‐step calculation, were in accordance with the results regarding basic facts. The findings indicate, for both normal and low general mathematical ability, that low achievement in reading to a small extent interferes with the pupils’ development of arithmetic performance     

The social experience of early childhood for children with learning disabilities: inclusion,competence and agency

This paper tells of the social experiences of three four‐year‐old children with learning disabilities as they negotiate their daily lives in their homes and early education settings in England. We apply a social model of childhood disability to the relatively unexplored territory of young children and use vignettes drawn from video observation to explore the interactive spaces contained in settings with different cultures of inclusion. Using a multimodal approach to the data we show the nuanced ways in which the children enact their agency. We explore the relationships between agency, culture and structure, and argue that children with learning disabilities are active in making meaning within social and relational networks to which they contribute differently depending on the barriers to doing and being that each network presents. Thus, the paper provides an original use of the notion of distributed competence.     

The participation of children with multi-sensory impairment in person-centred planning

Consultation with pupils with learning disabilities through the use of person-centred planning methods is becoming increasingly common. However, little research has focused on pupils with multi-sensory impairment (MSI). Kim Taylor has taught children with special educational needs for over 25 years and holds a post-graduate diploma in multi-sensory impairment. In this article, she suggests that the characteristics of MSI affect the capacity of some pupils to participate in person-centred planning. Kim Taylor presents case studies in which she investigates the impact that the characteristics of MSI have upon adults'abilities to elicit the views of children with MSI about their experiences in the classroom. The article provides an analysis of the factors that maximised the children's involvement and participation and a commentary on the trustworthiness of the outcomes of the consultation processes described. At the end of her article, Kim Taylor commits herself to implementing improved approaches in the classroom and calls upon other practitioners to follow her example.     

The effects of cooperative learning on Turkish elementary students’ mathematics achievement and attitude towards mathematics using TAI and STAD methods

This study was designed to compare the effects of Team Assisted Individualization (TAI) and Student Teams-Achievement Divisions (STAD) on fourth grade students’ academic achievement in and attitudes towards mathematics. Seven classes of a school were randomly selected for this experimental study. Two of these were given instruction through TAI; two through STAD, and the remaining three were treated as a control group. For the purpose of the data analysis regarding academic achievement, the 3 X 1 covariance analysis was used to compare the groups. As a result of this comparison, both the TAI and STAD methods were found to have positive effects (d = 1.003 for TAI and d = 0.40 for STAD) on students’ academic achievement in mathematics. The pairwise comparisons showed that the TAI method had a more significant effect than the STAD method. The scores for the attitude towards mathematics were analyzed by using non-parametric statistics. As a result of this analysis, no significant difference was observed regarding students’ attitudes towards mathematics.     

Gendered pathways to educational aspirations: The role of academic self-concept,school burnout,achievement and interest in mathematics and reading

The aim of this study was to examine lower secondary school students' (N = 1152) pathways to educational aspirations. The study used multi-group structural equation modelling to investigate the predictions of academic self-concept, school burnout, achievement, and interest in mathematics and reading, in relation to educational aspirations for boys and girls. While certain factors were influential for students' academic aspirations irrespective of gender, some interesting differences also emerged. Academic self-concept and interest in reading predicted educational aspirations for both groups. However, gendered pathways emerged in how achievement and interest in mathematics predicted educational aspirations. Interest in mathematics predicted girls’ educational aspirations, whereas mathematics achievement was a significant predictor for boys. School burnout had negative indirect effects through interest in reading and mathematics in both groups, but for girls, there was also a direct positive effect on educational aspirations.     

The role of achievement goals in online test anxiety and help-seeking

The purpose of this study was to examine the role of achievement goals in online test anxiety and help-seeking while controlling for self-efficacy and potential demographic differences. A total of 150 online students participated in the survey. Separate hierarchical regression analysis results suggested the differential roles of achievement goals in online test anxiety and help-seeking. Avoidance goals were found to be predictive of online test anxiety, whereas only students with performance-avoidance goals unexpectedly reported more online help-seeking. Further, while self-efficacy predicted both test anxiety and help-seeking, undergraduate students reported more help-seeking than their graduate counterparts. Implications and future directions of the study are discussed.     

Implementing AAC with children with profound and multiple learning disabilities: a study in rationale underpinning intervention

There is a developing research base to support the rationale underpinning augmentative and alternative communication (AAC) for people with learning disabilities. However, there is a paucity of research examining the process involved in implementing AAC support for people who have profound disabilities. This paper seeks to explore the processes involved in planning and implementing AAC systems to support the communication of two 6 year olds with profound and multiple learning disabilities. Following assessment, a plan of intervention involving specific implementation of objects of reference, gestures and signs was implemented to enhance communication opportunities for both children. Both children improved their communication skills through use of specific AAC supports. Results suggest that important aspects to include when planning intervention are understanding the level of each child's cognition in relation to their receptive abilities and a consistent, collaborative approach where strategies are agreed between team members. Specific challenges are discussed.     

Developing mathematical understanding and students with emotional and behavioural disorders: a review of the literature

Recent shifts in focus on academic interventions for students diagnosed with emotional and behavioural disorders (EBD) create a need to evaluate existing interventional research in content areas such as mathematics. Literature reviews in the area of mathematics interventions for students with EBD have mostly focused on the outcomes and the rigour of existing studies with limited attention to the quality of the pedagogical methods used in those studies. The purpose of this conceptual review was to use a teaching-for-understanding lens to examine existing research interventions in mathematics for students with EBD. Teaching-mathematics-for-understanding requires pedagogical methods that aim to activate and capture students’ mathematical reasoning and thinking. An iterative electronic and hand search of the literature found 30 studies covering three decades (1985–2015) that met the criteria for inclusion in this review. Results of the analysis include: (1) mathematics assessments utilised ranged from very basic to comprehensive, with most studies applying basic assessments; (2) a majority of the studies focused on intervention strategies targeting procedural and rote knowledge; (3) most studies utilised quantitative inquiry methods; and (4) in more recent years, studies have increasingly examined conceptual mathematical understanding and incorporated qualitative inquiry methods.