Early Numerical Competencies in 5- and 6-Year-Old Children With Autism Spectrum Disorder

Research Findings: To date, studies comparing the mathematical abilities of children with autism spectrum disorder (ASD) and typically developing children are scarce, and results remain inconclusive. In general, studies on this topic focus on mathematical abilities learned from elementary school onward, with little attention for possible precursors at younger ages. The current exploratory study focused on the important developmental period of preschool age, investigating 5 early numerical competencies in 30 high-functioning children with ASD and 30 age-matched control children: verbal subitizing, counting, magnitude comparison, estimation, and arithmetic operations. Children were examined at 5 or 6 years of age, attending the 3rd and final year of preschool. Overall, rather similar early number processing was found in children with and without ASD, although marginally significant results indicated a weaker performance of children with ASD on verbal subitizing and conceptual counting. Practice or Policy: Given the pervasiveness and impact of ASD on other domains of functioning, it is important to know that no general deficits in early numerical competencies were found in this study. However, some downward trends in mathematics performance were identified in children with ASD, which can serve as the basis for additional research in this field.     

Directionality in the interrelations between approximate number,verbal number,and mathematics in preschool-aged children

A fundamental question in numerical development concerns the directional relation between an early-emerging non-verbal approximate number system (ANS) and culturally acquired verbal number and mathematics knowledge. Using path models on longitudinal data collected in preschool children (M_age = 3.86 years; N = 216; 99 males; 80.8% White; 10.8% Multiracial, 3.8% Latino; 1.9% Black; collected 2013–2017) over 1 year, this study showed that earlier verbal number knowledge was associated with later ANS precision (average β = .32), even after controlling for baseline differences in numerical, general cognitive, and language abilities. In contrast, earlier ANS precision was not associated with later verbal number knowledge (β = −.07) or mathematics abilities (average β = .10). These results suggest that learning about verbal numbers is associated with a sharpening of pre-existing non-verbal numerical abilities.     

Improving the Numerical Knowledge of Children with Autism Spectrum Disorder: The Benefits of Linear Board Games

A lack of numerical knowledge early on can impede a child's academic development. In past research, playing linear board games improved children's understanding of numerical relations, which the authors theorised could extend to children with autism spectrum disorder. For this pilot study, 10 children played a board game where they moved tokens across coloured tiles displaying the numbers 1–10. During gameplay, students in the experimental group focused on the numbers on the tiles, while the control group focused on the colours. The assessment consisted of a number line estimation task, where students placed numbers ranging from 1 to 9 on a blank number line. Results showed children in the experimental group experienced statistically significant improvement in their understanding of numerical relationships of numbers on the number line estimation task. Findings indicate extended experiences with linear board games can support the numerical development of children with autism spectrum disorder.     

What really matters in the early literacy development of deaf children

With much earlier identification of hearing loss come expectations that increasing numbers of deaf children will develop literacy abilities comparable to their hearing age peers. To date, despite claims in the literature for parallel development between hearing and deaf learners with respect to early literacy learning, it remains the case that many deaf children do not go on to develop age-appropriate reading and writing abilities. Using written language examples from both deaf and hearing children and drawing on the developmental models of E. Ferreiro (1990) and D. Olson (1994), the discussion focuses on the ways in which deaf children draw apart from hearing children in the third stage of early literacy development, in the critical move from emergent to conventional literacy. Reasons for, and the significance of, this deviation are explored, with an eye to proposing implications for pedagogy and research, as we reconsider what really matters in the early literacy development of deaf children.     

Mathematical language and mathematical abilities in preschool: A systematic literature review

It is well established that early general language during preschool is critical for children's mathematical abilities. In an attempt to further characterize this association between language and mathematics, an increasing number of studies show that one specific type of language, namely mathematical language or the key linguistic concepts that are required for performing mathematical activities, is even more critical to children's mathematical abilities. The purpose of this systematic review is to summarize the evidence on mathematical language and mathematical abilities. We focus on preschool children as nearly all of the existing work has been done at this age. We first explain how mathematical language has been defined across studies, and report how it has been evaluated in studies in preschool. Next, we present the results of our systematic review. Following the PRISMA guidelines and after a critical appraisal, we ended with a set of 18 papers that were all of sufficient methodological quality. In these studies, mathematical language was defined as terms that are about numbers and operations on numbers (e.g., nine), but also included linguistic terms that do not directly refer to numbers, yet are important to understand mathematical concepts (i.e., quantitative and spatial terms such as fewest and middle, respectively). Some of these studies evaluated children's performance on mathematical language tasks, while others evaluated the mathematical language input provided to the child by their (educational) environment (teachers/parents/interventionists). Mathematical language correlated positively with children's mathematical abilities, concurrently and longitudinally. It also directly affected children's mathematical abilities, as was shown by intervention studies. We discuss potential directions for future research and highlight implications for education, arguing for more support for teachers and parents to improve the use of mathematical language in the classroom and in home settings.     

Young Children's Self‐Concepts Include Representations of Abstract Traits and the Global Self

There is debate about the abstractness of young children's self‐concepts—specifically, whether they include representations of (a) general traits and abilities and (b) the global self. Four studies (N = 176 children aged 4–7) suggested these representations are indeed part of early self‐concepts. Studies 1 and 2 reexamined prior evidence that young children cannot represent traits and abilities. The results suggested that children's seemingly immature judgments in previous studies were due to peculiarities of the task context not the inadequacy of children's self‐concepts. Similarly, Studies 3 and 4 revealed that, contrary to claims of immaturity in reasoning about the global self, young children update their global self‐evaluations in flexible, context‐sensitive ways. This evidence suggests continuity in the structure of self‐concepts across childhood.     

The Role of Intuitive Approximation Skills for School Math Abilities

Research has shown that educated children and adults have access to two ways of representing numerical information: an approximate number system (ANS) that is present from birth and allows for quick approximations of numbers of objects encountered in one's environment, and an exact number system (ENS) that is acquired through experience and instruction, that requires an understanding of language and symbols, and that is at the core of school math abilities. While these two systems are distinct, individual differences in the acuity of the ANS predict later math abilities and advancing the ENS leads to increases in the acuity of the ANS suggesting a reciprocal connection between the two systems. Recently, the focus of the field has turned toward elucidating the mechanisms that underlie this connection, but more work is also needed to understand the sources of individual differences in the ANS and ENS in the first place.     

Physical activity and music to support pre-school children’s mathematics learning

In order to give all children equal opportunities in school, methods to prevent early differences are needed. The overall aim of this study was to investigate the effectiveness of two structured teaching methods: Math in Action, characterised by physical activity and music, and common numerical activities. Children (28 girls, 25 boys) were assigned to 1 of the 2 conditions during a period of 3 weeks (2 times a week for a 30-minute session). The results show that children who learn mathematics in an environment characterised by physical activity and music develop their mathematical abilities significantly more than children who learn mathematics through common number activities. We have also shown that children with different motor skill abilities benefit from learning mathematics in an environment characterised by physical activity and music.     

提高幼小衔接阶段幼儿心理能力的对策

关注幼小衔接是当今幼儿教育研究的一个热门课题.提高幼儿心理能力成为了幼小衔接的关键.文章尝试根据幼儿教育心理学的有关知识及幼小衔接的相关要求,结合学龄前期幼儿的特点,探索如何提高幼儿心理能力,养成良好学习习惯,完成幼小衔接.     

What We Know about Integrating Early Childhood Education and Early Childhood Special Education Teacher Preparation Programs: A Review,a Reminder and a Request

In the last two decades, a myriad of political and social factors have converged and had a dramatic impact on Early Childhood Education (EC) and Early Childhood Special Education (ECSE). There have been sweeping changes in policy and shifts in society that have resulted in greater numbers of programs serving young children of all abilities and their families. Great strides in research related to early childhood development and early intervention have provided a growing knowledge of how children learn. The combination of these factors has created a call for increasingly higher quality services for young children. Professionals in both EC and ECSE have been responding to the demands and taken steps to prepare more and better-qualified teachers for children enrolled in early childhood programs. The most immediate avenue for effecting change in the profession is through the programs that prepare our teachers for the classrooms and the child care centers. This article reviews the research and the rationale regarding the implementation of integrated EC/ECSE programs.     

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.     

Development of SFON in Ecuadorian Kindergartners

This study explored the development of Ecuadorian Kindergartners’ spontaneous focusing on numerosity (SFON) during the kindergarten year, as well as the contribution of early numerical abilities to this development. One hundred Kindergartners coming from ten classrooms received two SFON tasks, one at the beginning and one at the end of the school year, and an early numerical abilities achievement test at the beginning of the school year. Results first demonstrated limited SFON development during the kindergarten year, with inter-individual differences and intra-individual stability of children’s SFON tendency. Second, both children’s SFON tendency and their early numerical abilities at the start of the kindergarten year were predictively related to their SFON tendency at the end of the year. Our results do not only add to our theoretical understanding of SFON in young children, but also inform educational policy and practices in the domain of early mathematics education in Ecuador, as they provide building blocks for optimizing the educational goals and curricula for kindergarten mathematics.     

Relating Math Words,Visual Images,and Math Symbols for Understanding and Competence

ABSTRACT

This paper briefly overviews my research in supporting children to learn number concepts by relating number words, research-based visual supports, and math symbols. I first outline my approach to helping children build relationships between the use of concrete materials and the building of abstract concepts. I then focus on two crucial early aspects of building meanings for numbers: (1) understanding break-apart partners such as 5=3+2 that support addition and subtraction with small numbers and children’s moving on to Level 2 counting on and algebraic problem representations, and (2) the use of visual five-groups in understanding numbers 1–1000 and in drawings to support multi-digit computations. The research-based learning path of visual-spatio supports is shown and discussed for each topic, including examples of children’s math drawings for representing word problems algebraically and for multi-digit computations. I have found math drawings to be a key visual support that helps children transition to working meaningfully with symbols and words alone. I close with a brief discussion of the difficulties children have with the number line. This overview can provide a framework within which future research on number learning by individuals with trisomy 21/Down syndrome can proceed.     

Accuracy of Area Model and Number Line Representations of Fractions for Students with Learning Disabilities

Assessment results are used to investigate relations between performance on a fraction number line estimation task and a circular area model estimation task for students with LD in Grades 6–8. Results indicate that students’ abilities to represent fractions on number lines and on circular area models are distinct skills. In addition, accurate fraction magnitude estimation using number lines was more strongly related to other fractions skills (e.g., fraction magnitude comparison) than accurate fraction magnitude estimation using circular area models. Our findings call for greater integration of the number line into early fractions instruction, and highlight the importance of explicitly teaching students to make connections between different visual representations of fractions. Implications for research and practice are presented.     

Everybody Counts,but Usually Just to 10! A Systematic Analysis of Number Representations in Children’s Books

Research Findings: Teachers and parents often use trade books to introduce or reinforce mathematics concepts. To date, an analysis of the early numeracy content of trade books has not been conducted. Consequently, this study evaluated the properties of numbers and counting within trade books. We coded 160 trade books targeted at establishing early numeracy skill in children to determine the numbers included; the representations of number presented; and how books used representations of number to inform children about numbers, including counting. The main findings included limited opportunity to learn the number 0 and numbers beyond 10 as well as limited exposure to multiple representations of number deemed necessary to build strong number understanding and counting skills. Practice or Policy: We discuss practical implications for the selection and use of trade books about number with young children.     

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.     

Domain‐General Learning and Memory Substrates of Reading Acquisition

Prior research has demonstrated that linguistic skills and knowledge contribute to successful reading acquisition. In contrast, little is known about the influence of domain‐general learning abilities on reading. To investigate associations between general memory functions and reading during the early stages of learning to read, performance measures of word‐level reading and of declarative and procedural learning were obtained in a cohort of 140 children, annually during their first 4 years of school. We hypothesized that differences in learning task performance would relate to reading ability in the early years, when children are first learning to read. We employed a series of linear mixed effects models to test the relationships between learning abilities and reading across time. Declarative learning performance predicted reading ability in first grade, while procedural learning performance predicted reading ability in second grade. Our findings suggest that reading acquisition may depend in part on general capacities for learning.     

The Emotionally Intelligent Early Childhood Educator: Self-Reflective Journaling

A current interest in education is the growing awareness that the development of social and emotional skills in children is critical for the foundation of academic knowledge in the classroom. The early childhood educator is in a position to be a powerful nurturer of the social emotional development in young children. It is important, therefore, to challenge early childhood teachers, particularly veteran teachers, to take a closer look at their own social and emotional skills and to systematically reassess these skills through an emotionally intelligent “lens”. The field of emotional intelligence is a new and exciting area of academic research that looks at emotional abilities within the following four domains: (1) perception skills; (2) accessing skills; (3) understanding skills; and (4) regulation skills. This article presents a userfriendly methodology to assess and enhance the emotional intelligence abilities of teachers, and thereby impact the abilities of the young children they teach.     

Wirksamkeit schulrelevanter Förderung in Kindertagesstätten

The present paper summarizes international and national research findings on the general and differential effectiveness of pedagogical work in early childhood education and care settings, evaluations of pilot projects on compensatory preschool education as well programs to support individual learning abilities. Based on these findings, the following conclusions are drawn: First, attending early childhood education and care settings at an early age (after the age of three) has a positive influence on the development of academic competences. Second, the effectiveness of these settings depends on the instructional quality, which could be considerably improved in Germany. Third, pilot projects on programs to support individual learning abilities could show that compensatory effects for disadvantaged groups of children exist, especially when they are interlinked with stimulating conditions in the family and at school. Fourth, effective training programs exist that can be implemented in early childhood education and care. However, a number of challenges need to be met before they can be successfully implemented.