The role of language in mathematical development: evidence from children with specific language impairments

Transcoding of French numbers for first- and second-language learners in third grade

Transcoding is the process of translating between spoken and written numbers, and it is correlated with other mathematical skills. In the present study, we investigated the link between French number writing of 49 students in the third grade (aged 7-9 years) and their language skills. Transcoding in French is of particular interest because the spoken number language system does not completely correspond to that of the written digits (e.g., quatre-vingt-dix [four-twenty-ten] and 90). We hypothesised that the complex linguistic structure of spoken numbers in French would be challenging for students who are learning to transcode. First and second French-language learners' accuracy and errors were recorded during a writing task of 3- to 7-digit numbers. Children also completed linguistic tests (e.g., receptive vocabulary, receptive syntax). Results showed that first- and second-language learners did not differ in their transcoding accuracy. Number size, decade complexity of stimulus number words in French (i.e., numbers containing a complex decade, operationalized as a number between soixante-dix, 70, and quatre-vingt-dix-neuf, 99), and receptive vocabulary predicted children's French transcoding skills. Students were more likely to produce errors (e.g., 68 or 6018 for 78) when they transcoded complex decade numbers compared with simple decade numbers. When an error was made on the complex decade portion of a number, it was likely a lexical error. In conclusion, third graders, both first- and second-language learners, found complex decade numbers challenging and their performance was related to their general vocabulary skills.

Recognition of small numbers in subset knowers Cardinal knowledge in early childhood

Previous research suggests that subset-knowers have an approximate understanding of small numbers. However, it is still unclear exactly what subset-knowers understand about small numbers. To investigate this further, we tested 133 participants, ages 2.6-4 years, on a newly developed eye-tracking task targeting cardinal recognition. Participants were presented with two sets differing in cardinality (1-4 items) and asked to find a specific cardinality. Our main finding showed that on a group level, subset-knowers could identify all presented targets at rates above chance, further supporting that subset-knowers understand several of the basic principles of small numbers. Exploratory analyses tentatively suggest that 1-knowers could identify the targets 1 and 2, but struggled when the target was 3 and 4, whereas 2-knowers and above could identify all targets at rates above chance. This might tentatively suggest that subset-knowers have an approximate understanding of numbers that is just (i.e. +1) above their current knower level. We discuss the implications of these results at length.

Talking About the Absent and the Abstract: Referential Communication in Language and Gesture

Human language permits us to call to mind objects, events, and ideas that we cannot witness directly, either because they are absent or because they have no physical form (e.g., people we have not met, concepts like justice). What enables language to transmit such knowledge? We propose that a referential link between words, referents, and mental representations of those referents is key. This link enables us to form, access, and modify mental representations even when the referents themselves are absent ("absent reference"). In this review we consider the developmental and evolutionary origins of absent reference, integrating previously disparate literatures on absent reference in language and gesture in very young humans and gesture in nonhuman primates. We first evaluate when and how infants acquire absent reference during the process of language acquisition. With this as a foundation, we consider the evidence for absent reference in gesture in infants and in nonhuman primates. Finally, having woven these literatures together, we highlight new lines of research that promise to sharpen our understanding of the development of reference and its role in learning about the absent and the abstract.

Phonological Processing, Visuospatial Skills, and Pattern Understanding in Chinese Developmental Dyscalculia

A number of previous studies have identified cognitive deficits in developmental dyscalculia (DD). Yet, most of these studies were in alphabetic languages, whereas few of them examined Chinese DD. Here, we conducted a study aiming to determine the cognitive factors associated with DD in Chinese children. Five candidate cognitive factors of DD-phonological retrieval, phonological awareness, visual-spatial attention, spatial thinking, and pattern understanding-were examined in the present study. A total of 904 Chinese children ages 8 to 11 years participated in this study. From the sample, 97 children were identified with DD through tests of arithmetic ability, and 93 age- and IQ-matched typically developing children were selected as controls. Logistic regression analysis revealed that phonological retrieval, pattern understanding, visual-spatial attention, and phonological awareness significantly predicted DD, whereas spatial thinking failed to do so. Results of logistic relative weights analysis showed that all five factors explained statistically significant amounts of variance in arithmetic scores. Phonological retrieval had the most influence on DD, followed by pattern understanding, visual-spatial attention, phonological awareness, and spatial thinking. These findings have important clinical implications for diagnosis and intervention of Chinese DD.

Gender-Based Performance in Mathematical Facts and Calculations in Two Elementary School Samples From Chile and Spain: An Exploratory Study

Gender differences in mathematical performance are not conclusive according to the scientific literature, although such differences are supported by international studies such as the Trends in International Mathematics and Science Study (TIMSS). According to TIMSS 2019, fourth-grade male students outperformed female students in Spanish-speaking countries, among others. This work approaches the study on gender difference by examining the basic calculation skills needed to handle more complex problems. Two international samples of second and third graders from Chile and Spain were selected for this exploratory study. Tests on basic mathematical knowledge (symbolic and non-symbolic magnitude comparisons, fluency, and calculation) were administered. The tests did not show significant difference or size effect between genders for mean performance, variance in the distribution of performance, or percentiles. As noted in the existing literature on this topic and reiterated by these findings, great care should be exercised when reporting on possible gender differences in mathematical performance, as these can contribute to low self-concept among female students.

Aided Hearing Moderates the Academic Outcomes of Children With Mild to Severe Hearing Loss

OBJECTIVES

There are very limited data regarding the spoken language and academic outcomes of children with mild to severe hearing loss (HL) during the elementary school years, and the findings of these studies are inconsistent. None of these studies have examined the possible role of aided hearing in these outcomes. This study used a large cohort of children to examine these outcomes and in particular to examine whether aided hearing moderates the effect of HL with regard to these outcomes.

DESIGN

The spoken language, reading, writing, and calculation abilities were measured after second and fourth grades in children with mild to severe HL (children who are hard of hearing; CHH, n = 183) and a group of children with normal hearing (CNH, n = 91) after the completion of second and fourth grades. Also, among the CHH who wore hearing aids, aided better-ear speech intelligibility index values at the age of school entry were obtained.

RESULTS

Oral language abilities of the CHH with mild and moderate HL were similar to the CNH at each grade. Children with moderately-severe HL (better-ear pure tone threshold >59 but <76 dB HL) had significantly poorer oral language and reading skills than the CNH at each grade. The children with mild and moderate HL did not differ from the CNH in oral language or reading. No differences were found between the CHH regardless of severity and CNH with regard to spelling, passage writing, or calculation. The degree to which hearing aids provided audible speech information played a moderating role in the oral language outcomes of CHH and this moderation of language mediated the relationship between the unaided hearing ability of the CHH and their academic outcomes.

CONCLUSIONS

As a group, children with mild and moderate HL have good outcomes with regard to language and academic performance. Children with moderately-severe losses were less skilled in language and reading than the CNH and CHH children with mild and moderate losses. Audibility provided by hearing aids was found to moderate the effects of HL with respect to these outcomes. These findings emphasize the importance of including the effects of clinical interventions such as aided hearing when examining outcomes of CHH.

Reconceptualizing Symbolic Magnitude Estimation Training Using Non-declarative Learning Techniques

It is well-documented that mathematics achievement is an important predictor of many positive life outcomes like college graduation, career opportunities, salary, and even citizenship. As such, it is important for researchers and educators to help students succeed in mathematics. Although there are undoubtedly many factors that contribute to students' success in mathematics, much of the research and intervention development has focused on variations in instructional techniques. Indeed, even a cursory glance at many educational journals and granting agencies reveals that there is a large amount of time, energy, and resources being spent on determining the best way to convey information through direct, declarative instruction. The proposed project is motivated by recent calls to expand the focus of research in mathematics education beyond direct, declarative instruction. The overarching goal of the presented experiment is to evaluate the efficacy of a novel mathematics intervention designed using principles taken from the literature on non-declarative learning. The intervention combines errorless learning and structured cue fading to help second grade students improve their understanding of symbolic magnitude. Results indicate that students who learned about symbolic magnitude using the novel intervention did better than students who were provided with extensive declarative support. These findings offer preliminary evidence in favor of using learning combination of errorless learning and cue fading techniques in the mathematics classroom.

Habilidades matemáticas tempranas en niños chilenos con Trastorno del Desarrollo del Lenguaje: Un estudio comparativo

En las últimas décadas se ha incrementado el interés de las investigaciones respecto a las dificultades académicas que presentan los niños con Trastorno del Desarrollo del Lenguaje (TDL). No obstante, su relación con las habilidades matemáticas es una de las menos estudiadas. El objetivo de este estudio consistió en determinar si existen diferencias relevantes entre las habilidades matemáticas tempranas de niños con TDL y con desarrollo típico (DT). Participaron 78 niños de 4 a 7 años 11 meses de edad, pertenecientes a colegios con programas de integración escolar de Santiago de Chile. Se conformó un grupo de 44 niños con TDL y un grupo de 34 con DT. Se establecieron comparaciones del rendimiento en tareas matemáticas pertenecientes a la versión en español del Test de Evaluación Matemática Temprana de Utrecht (TEMT-U): subtest relacionales (comparación, clasificación, correspondencia uno a uno y seriación), y subtest numérico (conteo verbal, conteo estructurado, conteo resultante y conocimiento general de los números); hallándose un rendimiento matemático significativamente menor en el grupo con TDL de educación infantil en ambos subtest. Los hallazgos sugieren que las dificultades propias de los niños con TDL impactan el aprendizaje matemático, especialmente en los niños más pequeños, por lo que resulta imperante disminuir las barreras que obstaculizan su proceso de aprendizaje.

Arithmetic in developmental cognitive disabilities

This paper reviews and discusses research on arithmetical strengths and weaknesses in children with specific developmental cognitive disabilities. It focusses on children with dyslexia, developmental language disorder, attention deficit hyperactivity disorder and autism. In general, studies show that arithmetical weaknesses are commoner in children with any of these disorders than in controls. Autism is sometimes associated with specific strengths in arithmetic; but even in autism, it is commoner for arithmetic to be a relative weakness than a relative strength. There may be some genetic reasons why there is an overlap between mathematical difficulties and other developmental learning difficulties; but much of the reason seems to be that specific aspects of arithmetic are often influenced by other factors, including language comprehension, phonological awareness, verbal and spatial working memory and long-term memory, and executive functions. The findings discussed here will be discussed in relation to Pennington's (2006) Multiple Deficit Model.

The Sensitivity and Specificity of Parental Report of Concern for Identifying Language Disorder in Children With Craniosynostosis

ABSTRACT

Many factors that may co-occur with craniosynostosis, such as oral structural anomalies, hearing impairment, visual impairment, cognitive difficulties and psychosocial factors, may predispose this population to communication difficulties. At the Oxford Craniofacial Unit, children's speech, language and communication are regularly monitored in accordance with a systematic developmental screening protocol developed by the Speech and Language Therapists in the 4 United Kingdom (UK) Highly Specialized Craniofacial Centers. In addition to routine assessments, when parents attend routine multidisciplinary clinic appointments, they are asked about their child's communication development, and whether they have any concerns.A retrospective review was undertaken of parental concerns about hearing, speech development, behavior, physical development, concentration, school and friendships as indicated by parents on the Oxford Craniofacial Unit Pre-Clinic Questionnaire. The areas of concern were then correlated with the results of a standardized, guided parent questionnaire about children's language development, (Children's Communication Checklist - 2 (CCC-2)), to determine whether parental concern alone is a reliable way of identifying whether patients require further assessment for Language Disorder associated with Craniosynostosis.Participants were parents of 89 monolingual English-speaking children with craniosynostosis (62 male; 27 female), age range four to 13 years (mean age = 8 years 7 months), receiving active care at the Oxford Craniofacial Unit (June 2017-July 2018). Results of the pre-clinic questionnaire indicated that 6% of parents had concerns about their child's communication development. Results of the CCC-2 indicated that 29/89 (32.6%) of children required further assessment for Language Disorder associated with Craniosynostosis. When language difficulties were identified on the CCC-2, only 14% (n = 4/29) parents indicated concern on the pre clinic questionnaire. Results indicated that parental concern about behavior was the most important factor in identifying language disorder (P = 0.023).Results reinforce that the pre-clinic questionnaire is useful for identifying areas of parental concern. Results also indicate that parental concern alone is not sufficient to identify language disorder, and that further, detailed assessment is warranted. The results are consistent with previously reported links between behavior and language in the general population.

The critical role of Arabic numeral knowledge as a longitudinal predictor of arithmetic development

Understanding the cognitive underpinnings of children's arithmetic development has great theoretical and educational importance. Recent research suggests symbolic and nonsymbolic representations of number influence arithmetic development before and after school entry. We assessed nonverbal ability and general language skills as well as nonsymbolic (numerosity) and symbolic (numeral) comparison skills, counting, and Arabic numeral knowledge (numeral reading, writing, and identification) in preschool children (4 years of age). At 6 years of age, we reassessed nonsymbolic (numerosity) and symbolic (numeral) comparison and arithmetic. A latent variable path model showed that Arabic numeral knowledge (defined by numeral reading, writing, and identification at 4 years of age) was the sole unique predictor of arithmetic at 6 years. We conclude that knowledge of the association between spoken and Arabic numerals is one critical foundation for the development of formal arithmetic.

Language-Related Longitudinal Predictors of Arithmetic Word Problem Solving: A Structural Equation Modeling Approach

We investigated the longitudinal relations between cognitive skills, specifically language-related skills, and word-problem solving in 340 children (6.10 to 9.02 years). We used structural equation modeling to examine whether word-problem solving, computation skill, working memory, nonverbal reasoning, oral language, and word reading fluency measured at second grade were associated with performance on measures of word-problem solving in fourth grade. Results indicated that prior word-problem solving, computation skill, nonverbal reasoning, and oral language were significantly associated with children's later word-problem solving. Multi-group modeling suggested that these relations were not significantly different for boys versus girls. Implications of these findings are discussed.

Consequential differences in perspectives and practices concerning children with developmental language disorders: an integrative review

BACKGROUND

Inter-professional collaboration (IPC) has been recommended for many years as a means by which the needs of children with developmental language disorders (DLD) can be met at school. However, effective IPC remains difficult to achieve and our knowledge of how to support it is limited. A shared understanding between those involved has been identified as critical to IPC.

AIMS

To examine the literature, as one source of data, for evidence of a shared understanding between the fields of speech and language therapy (SLT) and education about children with DLD and how such needs can best be met at school.

METHODS & PROCEDURES

An integrative review of the literature was undertaken. A systematic search of the published, peer-reviewed literature (between 2006 and 2016) was conducted for empirical and theoretical papers and a manual search was undertaken to obtain a representative sample of policy/professional guidelines. A total of 81 papers across SLT and education were included in the review. The papers were scrutinized using a qualitative content analysis.

MAIN CONTRIBUTION

Although some commonality between perspectives in the literature was identified, differences between the fields dominated. These differences related to how DLD is conceptualized; how children's needs are assessed; which outcomes are prioritized and how best these outcomes can be achieved. We also found differences about what constitutes useful knowledge to guide practice. We suggest that the nature of the differences we identified in the literature may have negative implications for practitioners wishing to collaborate to meet the needs of children with DLD in school. The perspectives of practising SLTs and teachers need to be sought to determine whether the findings from the literature reflect dilemmas in practice.

CONCLUSIONS

Effective IPC is essential to meet the needs of children with DLD in school; yet, it remains difficult to achieve. Our review of the literature across SLT and education indicates evidence of a lack of shared understanding about DLD. If these differences are also evident in practice, then a conceptual model to support IPC may be warranted.

Understanding comorbidity of learning disorders: task-dependent estimates of prevalence

BACKGROUND

Reading disorder (RD) and mathematics disorder (MD) frequently co-occur. However, the exact comorbidity rates differ largely between studies. Given that MD is characterised by high heterogeneity on the symptom level, differences in comorbidity rates may result from different mathematical subskills used to define MD. Comorbidity rates with RD are likely to be higher when MD is measured by mathematical subskills that do not only build on number processing, but also require language (i.e. arithmetic fluency), than when measured by magnitude processing skills.

METHODS

The association between literacy, arithmetic fluency and magnitude processing as well as the overlap between deficits in these domains were assessed in a representative sample of 1,454 third Graders.

RESULTS

Associations were significantly higher between literacy and arithmetic, than between literacy and magnitude processing. This was also reflected in comorbidity rates: comorbidity rates between literacy and arithmetic deficits were four times higher than expected by chance, whereas comorbidity rates between literacy and magnitude processing deficits did not exceed chance rate. Deficits in the two mathematical subskills showed some overlap, but also revealed dissociations, corroborating the high heterogeneity of MD. Results are interpreted within a multiple-deficit framework and implications for diagnosis and intervention are discussed.

CONCLUSIONS

The overlap between RD and MD depends on the subskills used to define MD. Due to shared domain-general factors mathematical subskills that draw on language skills are more strongly associated with literacy than those that do not require language. The findings further indicate that the same symptom, such as deficits in arithmetic, can be associated with different cognitive deficits, a deficit in language skills or a deficit in number processing.

Mathematical Abilities in Children With Developmental Language Disorder

Purpose

This review article provides a scoping review of the literature on mathematical abilities in developmental language disorder (DLD). Children with DLD typically struggle with learning in school; however, the mechanism by which DLD impacts academic success is unclear. Mathematics involves demands in the multiple domains and therefore holds potential for examining the relationship between language and academic performance on tasks mediated by verbal and nonverbal demands.

Method

A scoping review was performed via computerized database searching to examine literature on mathematics and DLD. The 21 review articles meeting inclusion criteria compared children with typical development or DLD on various tasks measuring numerical cognition.

Results

Children with DLD consistently performed below peers with typical development on number transcoding, counting, arithmetic, and story problem tasks. However, performance was similar to peers with typical development on most number line, magnitude comparison, and conceptual mathematics tasks.

Conclusions

The findings suggest a relationship between DLD and mathematics was characterized by more detrimental performance on tasks with higher verbal demands. Results are discussed with respect to typical academic curricula and demonstrate a need for early identification and intervention in DLD to optimize academic outcomes.

Mathematical thinking in children with developmental language disorder: The roles of pattern skills and verbal working memory

Previous research suggests that children with language disorders often have difficulties in mathematical tasks. In the current study, we investigated two relevant factors - working memory and pattern skills - that may underlie children's poor mathematics performance. Children with developmental language disorder (DLD, n = 18, ages 6-13) and age-matched typically-developing children (n = 18) completed three math tasks that tapped calculation skill and knowledge of concepts. Children also completed a visual pattern extension task and a verbal working memory task. There were four key findings: (1) children with DLD exhibited poorer mathematical knowledge than typically-developing children, both in calculation and on key math concepts, (2) children with DLD performed similarly to typically-developing children on the visual pattern extension task, (3) children with DLD had lower verbal working memory scores than typically-developing children, and these differences in working memory accounted in part for their poorer calculation performance, and (4) children's pattern extension scores predicted their arithmetic calculation scores, but not their concept scores.

The identification of speech and language problems in elementary school: Diagnosis and co-occurring needs

BACKGROUND

Oral language skills are the foundation for success at school and in employment. A significant minority of children experience difficulties in the acquisition of oral language resulting in speech and language needs (SLN). There are disjunctures between clinical studies using standardised assessment and educational studies. The current study examines teacher reported SLN alongside assessments of language and cognitive skills to explore children's profiles of needs, developmental trajectories and risk factors.

PROCEDURE

Data from the UK Millennium Cohort Study were used to examine teacher identification of SLN at seven (n = 8658) and 11 years (n = 7275).

RESULTS

There were high levels of co-occurrence between SLN and other special educational needs at seven and 11 years, with SLN being less common at 11. Vocabulary levels and parental concerns at three and five and educational attainment at seven were highly predictive of SLN at seven, slightly less so at 11. However, a significant proportion of parents of children who scored in the bottom 2nd centile on vocabulary measures did not report their child as experiencing a language problem. Gender and disadvantage were also predictive of SLN but were mediated by the cognitive and behavioural variables.

IMPLICATIONS

These results raise questions about whether children's language needs at age 11 are recognised in schools. The extent of co-occurrence challenges the way diagnostic categories should be used and supports the value of profiling of dimensions of need.

Quantifier comprehension is linked to linguistic rather than to numerical skills. Evidence from children with Down syndrome and Williams syndrome

Comprehending natural language quantifiers (like many, all, or some) involves linguistic and numerical abilities. However, the extent to which both factors play a role is controversial. In order to determine the specific contributions of linguistic and number skills in quantifier comprehension, we examined two groups of participants that differ in their language abilities while their number skills appear to be similar: Participants with Down syndrome (DS) and participants with Williams syndrome (WS). Compared to rather poor linguistic skills of individuals with DS, individuals with WS display relatively advanced language abilities. Participants with WS also outperformed participants with DS in a quantifier comprehension task while number knowledge did not differ between the two groups. When compared to typically developing (TD) children of the same mental age, participants with WS displayed similar levels regarding quantifier abilities, but participants with DS performed worse than the control group. Language abilities but not number skills also significantly predicted quantifier knowledge in a linear regression analysis, stressing the importance of linguistic abilities for quantifier comprehension. In addition to determining the skills that are relevant for comprehending quantifiers, our findings provide the first demonstration of how quantifiers are acquired by individuals with DS and WS, an issue not investigated so far.

Effectiveness of working memory training among children with dyscalculia: evidence for transfer effects on mathematical achievement-a pilot study

We examined whether the working memory (WM) capacity of developmentally dyscalculic children can be improved by a WM training program and whether outcomes relate to mathematical performance. The experimental design comprised two groups with developmental dyscalculia with grade 4 schooling: an experimental group (n = 14; mean age = 115.29 months) and a control group (n = 14; mean age = 116.07 months). All participants were assessed on measures of WM, mathematic attainment, and nonverbal mental ability (Raven test) before and after training. The WM training program focused on manipulating and maintaining arithmetic information. The results show that both WM and mathematical performances improved significantly after intervention, indicating a strong relationship between these two constructs. The control group improved slightly in Raven's progressive matrices and a reading number task. These findings are discussed in terms of near and far transfer toward trained and untrained skills and stress the positive impact of WM training on learning mathematics in children with dyscalculia.

When is working memory important for arithmetic? The impact of strategy and age

Our ability to perform arithmetic relies heavily on working memory, the manipulation and maintenance of information in mind. Previous research has found that in adults, procedural strategies, particularly counting, rely on working memory to a greater extent than retrieval strategies. During childhood there are changes in the types of strategies employed, as well as an increase in the accuracy and efficiency of strategy execution. As such it seems likely that the role of working memory in arithmetic may also change, however children and adults have never been directly compared. This study used traditional dual-task methodology, with the addition of a control load condition, to investigate the extent to which working memory requirements for different arithmetic strategies change with age between 9–11 years, 12–14 years and young adulthood. We showed that both children and adults employ working memory when solving arithmetic problems, no matter what strategy they choose. This study highlights the importance of considering working memory in understanding the difficulties that some children and adults have with mathematics, as well as the need to include working memory in theoretical models of mathematical cognition.

Contribution of spoken language and socio-economic background to adolescents' educational achievement at age 16 years

BACKGROUND

Well-documented associations exist between socio-economic background and language ability in early childhood, and between educational attainment and language ability in children with clinically referred language impairment. However, very little research has looked at the associations between language ability, educational attainment and socio-economic background during adolescence, particularly in populations without language impairment.

AIMS

To investigate: (1) whether adolescents with higher educational outcomes overall had higher language abilities; and (2) associations between adolescent language ability, socio-economic background and educational outcomes, specifically in relation to Mathematics, English Language and English Literature GCSE grade.

METHOD & PROCEDURES

A total of 151 participants completed five standardized language assessments measuring vocabulary, comprehension of sentences and spoken paragraphs, and narrative skills and one nonverbal assessment when between 13 and 14 years old. These data were compared with the participants' educational achievement obtained upon leaving secondary education (16 years old). Univariate logistic regressions were employed to identify those language assessments and demographic factors that were associated with achieving a targeted A^* -C grade in English Language, English Literature and Mathematics General Certificate of Secondary Education (GCSE) at 16 years. Further logistic regressions were then conducted to examine further the contribution of socio-economic background and spoken language skills in the multivariate models.

RESULTS & OUTCOMES

Vocabulary, comprehension of sentences and spoken paragraphs, and mean length utterance in a narrative task along with socio-economic background contributed to whether participants achieved an A^* -C grade in GCSE Mathematics and English Language and English Literature. Nonverbal ability contributed to English Language and Mathematics. The results of multivariate logistic regressions then found that vocabulary skills were particularly relevant to all three GCSE outcomes. Socio-economic background only remained important for English Language, once language assessment scores and demographic information were considered.

CONCLUSIONS & IMPLICATIONS

Language ability, and in particular vocabulary, plays an important role for educational achievement. Results confirm a need for ongoing support for spoken language ability throughout secondary education and a potential role for speech and language therapy provision in the continuing drive to reduce the gap in educational attainment between groups from differing socio-economic backgrounds.

An Extension of the Procedural Deficit Hypothesis from Developmental Language Disorders to Mathematical Disability

Mathematical disability (MD) is a neurodevelopmental disorder affecting math abilities. Here, we propose a new explanatory account of MD, the procedural deficit hypothesis (PDH), which may further our understanding of the disorder. According to the PDH of MD, abnormalities of brain structures subserving the procedural memory system can lead to difficulties with math skills learned in this system, as well as problems with other functions that depend on these brain structures. This brain-based account is motivated in part by the high comorbidity between MD and language disorders such as dyslexia that may be explained by the PDH, and in part by the likelihood that learning automatized math skills should depend on procedural memory. Here, we first lay out the PDH of MD, and present specific predictions. We then examine the existing literature for each prediction, while pointing out weaknesses and gaps to be addressed by future research. Although we do not claim that the PDH is likely to fully explain MD, we do suggest that the hypothesis could have substantial explanatory power, and that it provides a useful theoretical framework that may advance our understanding of the disorder.

Cognitive functions in preschool children with specific language impairment

OBJECTIVE

A growing body of research has focused on executive functions in children with specific language impairment (SLI). However, results show limited convergence, particularly in preschool age. The current neuropsychological study compared performance of cognitive functions focused on executive components and working memory in preschool children with SLI to typically developing controls.

METHOD

Performance on the measures cognitive flexibility, inhibition, processing speed and phonological short-term memory was assessed. The monolingual, Caucasian study sample consisted of 30 children with SLI (Mage = 63.3 months, SD = 4.3 months) and 30 healthy controls (Mage = 62.2 months, SD = 3.7 months). Groups were matched for age and nonverbal IQ. Socioeconomic status of the participating families was included.

RESULTS

Children with SLI had significantly poorer abilities of phonological short-term memory than matched controls. A tendency of poorer abilities in the SLI group was found for inhibition and processing speed.

CONCLUSIONS

We confirmed phonological short-term memory to be a reliable marker of SLI in preschoolers. Our results do not give definite support for impaired executive function in SLI, possibly owing to limited sensitivity of test instruments in this age group. We argue for a standardization of executive function tests for research use.

Visual Speech Perception in Children With Language Learning Impairments

PURPOSE

The purpose of the study was to assess the ability of children with developmental language learning impairments (LLIs) to use visual speech cues from the talking face.

METHOD

In this cross-sectional study, 41 typically developing children (mean age: 8 years 0 months, range: 4 years 5 months to 11 years 10 months) and 27 children with diagnosed LLI (mean age: 8 years 10 months, range: 5 years 2 months to 11 years 6 months) completed a silent speechreading task and a speech-in-noise task with and without visual support from the talking face. The speech-in-noise task involved the identification of a target word in a carrier sentence with a single competing speaker as a masker.

RESULTS

Children in the LLI group showed a deficit in speechreading when compared with their typically developing peers. Beyond the single-word level, this deficit became more apparent in older children. On the speech-in-noise task, a substantial benefit of visual cues was found regardless of age or group membership, although the LLI group showed an overall developmental delay in speech perception.

CONCLUSION

Although children with LLI were less accurate than their peers on the speechreading and speech-in noise-tasks, both groups were able to make equivalent use of visual cues to boost performance accuracy when listening in noise.

Designing Effective Speech-Language Interventions for Children in the Public Schools

In the U.S. public school system, more than 6 million children receive special education services, including many children with speech and language impairments. Speech-language pathologists (SLPs) design and implement effective interventions—including how much intervention children receive—to circumvent the negative effects of speech-language impairments on educational outcomes. Existing policy and position statements suggest that increasing the number of sessions (frequency) and amount of intervention (dose) would improve children’s outcomes, assuming that greater treatment intensity is associated with better treatment outcomes. However, current empirical evidence, coupled with cognitive theory, suggests that more treatment may not relate to improved outcomes. The present article draws on current empirical studies and established cognitive theories of spacing effects (learning distributed over time) to propose a systematic way for SLPs to plan and implement an effective intensity of intervention for children with speech and language impairments.

Reading Stories to Learn Math: Mathematics Vocabulary Instruction for Children with Early Numeracy Difficulties

The present study involved examining whether a storybook reading intervention targeting mathematics vocabulary, such as "equal," "more," and "less," and associated number concepts would increase at-risk children's vocabulary knowledge and number competencies. Children with early numeracy difficulties (N = 124) were recruited from kindergarten classes in four schools. Participants were randomly assigned to one of three groups: a storybook number competencies (SNC) intervention, a number sense intervention, or a business-as-usual control. Interventions were carried out in groups of four children over 8 weeks (24 thirty-minute sessions). Findings demonstrated that the SNC intervention group outperformed the other groups on measures of mathematics vocabulary, both in terms of words that were closely aligned to the intervention and those that were not. There was no effect of the SNC intervention, however, on general mathematics measures, suggesting a need to provide the mathematics vocabulary work along with more intensive instruction in number concepts.

Early language and executive skills predict variations in number and arithmetic skills in children at family-risk of dyslexia and typically developing controls

Two important foundations for learning are language and executive skills. Data from a longitudinal study tracking the development of 93 children at family-risk of dyslexia and 76 controls was used to investigate the influence of these skills on the development of arithmetic. A two-group longitudinal path model assessed the relationships between language and executive skills at 3-4 years, verbal number skills (counting and number knowledge) and phonological processing skills at 4-5 years, and written arithmetic in primary school. The same cognitive processes accounted for variability in arithmetic skills in both groups. Early language and executive skills predicted variations in preschool verbal number skills, which in turn, predicted arithmetic skills in school. In contrast, phonological awareness was not a predictor of later arithmetic skills. These results suggest that verbal and executive processes provide the foundation for verbal number skills, which in turn influence the development of formal arithmetic skills. Problems in early language development may explain the comorbidity between reading and mathematics disorder.

Lack of replication for the myosin-18B association with mathematical ability in independent cohorts

Twin studies indicate that dyscalculia (or mathematical disability) is caused partly by a genetic component, which is yet to be understood at the molecular level. Recently, a coding variant (rs133885) in the myosin-18B gene was shown to be associated with mathematical abilities with a specific effect among children with dyslexia. This association represents one of the most significant genetic associations reported to date for mathematical abilities and the only one reaching genome-wide statistical significance. We conducted a replication study in different cohorts to assess the effect of rs133885 maths-related measures. The study was conducted primarily using the Avon Longitudinal Study of Parents and Children (ALSPAC), (N = 3819). We tested additional cohorts including the York Cohort, the Specific Language Impairment Consortium (SLIC) cohort and the Raine Cohort, and stratified them for a definition of dyslexia whenever possible. We did not observe any associations between rs133885 in myosin-18B and mathematical abilities among individuals with dyslexia or in the general population. Our results suggest that the myosin-18B variant is unlikely to be a main factor contributing to mathematical abilities.

Mathematics and reading difficulty subtypes: minor phonological influences on mathematics for 5-7-years-old

Linguistic influences in mathematics have previously been explored through subtyping methodology and by taking advantage of the componential nature of mathematics and variations in language requirements that exist across tasks. The present longitudinal investigation aimed to examine the language requirements of mathematical tasks in young children aged 5–7 years. Initially, 256 children were screened for mathematics and reading difficulties (RDs) using standardized measures. Those scoring at or below the 35th percentile on either dimension were classified as having difficulty. From this screening, 115 children were allocated to each of the mathematical difficulty (MD; n = 26), MDRD (n = 32), RD (n = 22) and typically achieving (n = 35) subtypes. These children were tested at four time points, separated by 6 monthly intervals, on a battery of seven mathematical tasks. Growth curve analysis indicated that, in contrast to previous research on older children, young children with MD and MDRD had very similar patterns of development on all mathematical tasks. Overall, the subtype comparisons suggested that language played only a minor mediating role in most tasks, and this was secondary in importance to non-verbal skills. Correlational evidence suggested that children from the different subtypes could have been using different mixes of verbal and non-verbal strategies to solve the mathematical problems.

Core subjects at the end of primary school: identifying and explaining relative strengths of children with specific language impairment (SLI)

BACKGROUND

In general, children with specific language impairment (SLI) tend to fall behind their typically developing (TD) peers in educational attainment. Less is known about how children with SLI fare in particular areas of the curriculum and what predicts their levels of performance.

AIMS

To compare the distributions of performance of children with SLI in three core school subjects (English, Mathematics and Science); to test the possibility that performance would vary across the core subjects; and to examine the extent to which language impairment predicts performance.

METHODS & PROCEDURES

This study was conducted in England and reports historical data on educational attainments. Teacher assessment and test scores of 176 eleven-year-old children with SLI were examined in the three core subjects and compared with known national norms. Possible predictors of performance were measured, including language ability at ages 7 and 11, educational placement type, and performance IQ.

OUTCOMES & RESULTS

Children with SLI, compared with national norms, were found to be at a disadvantage in core school subjects. Nevertheless, some children attained the levels expected of TD peers. Performance was poorest in English; relative strengths were indicated in Science and, to a lesser extent, in Mathematics. Language skills were significant predictors of performance in all three core subjects. PIQ was the strongest predictor for Mathematics. For Science, both early language skills at 7 years and PIQ made significant contributions.

CONCLUSIONS & IMPLICATIONS

Language impacts on the school performance of children with SLI, but differentially across subjects. English for these children is the most challenging of the core subjects, reflecting the high levels of language demand it incurs. Science is an area of relative strength and mathematics appears to be intermediate, arguably because some tasks in these subjects can be performed with less reliance on verbal processing. Many children with SLI do have the potential to reach or exceed educational targets that are set at national levels for TD children.

Number processing and arithmetic skills in children with cochlear implants

Though previous findings report that hearing impaired children exhibit impaired language and arithmetic skills, our current understanding of how hearing and the associated language impairments may influence the development of arithmetic skills is still limited. In the current study numerical/arithmetic performance of 45 children with a cochlea implant were compared to that of controls matched for hearing age, intelligence and sex. Our main results were twofold disclosing that children with CI show general as well as specific numerical/arithmetic impairments. On the one hand, we found an increased percentage of children with CI with an indication of dyscalculia symptoms, a general slowing in multiplication and subtraction as well as less accurate number line estimations. On the other hand, however, children with CI exhibited very circumscribed difficulties associated with place-value processing. Performance declined specifically when subtraction required a borrow procedure and number line estimation required the integration of units, tens, and hundreds instead of only units and tens. Thus, it seems that despite initially atypical language development, children with CI are able to acquire arithmetic skills in a qualitatively similar fashion as their normal hearing peers. Nonetheless, when demands on place-value understanding, which has only recently been proposed to be language mediated, hearing impaired children experience specific difficulties.

Differences in the performance of children with specific language impairment and their typically developing peers on nonverbal cognitive tests: a meta-analysis

PURPOSE

This study used meta-analysis to investigate the difference in nonverbal cognitive test performance of children with specific language impairment (SLI) and their typically developing (TD) peers.

METHOD

The meta-analysis included studies (a) that were published between 1995 and 2012 of children with SLI who were age matched (and not nonverbal cognitive matched) to TD peers and given a norm-referenced nonverbal cognitive test and (b) that reported sufficient data for an effect size analysis. Multilevel modeling was used to examine the performance of children with SLI relative to their typically developing, age-matched peers on nonverbal IQ tests.

RESULTS

Across 138 samples from 131 studies, on average children with SLI scored 0.69 standard deviations below their TD peers on nonverbal cognitive tests after adjusting for the differences in the tests used, the low-boundary cutoff scores, the age of the participants, and whether studies matched the two groups on socioeconomic status.

DISCUSSION

The lower performance of children with SLI relative to TD children on nonverbal IQ tests has theoretical implications for the characterization of SLI and clinical and political implications regarding how nonverbal cognitive tests are used and interpreted for children with this disorder.

The Relationship Between Mathematics and Language: Academic Implications for Children With Specific Language Impairment and English Language Learners

Purpose

The present study examined the relationship between mathematics and language to better understand the nature of the deficit and the academic implications associated with specific language impairment (SLI) and academic implications for English language learners (ELLs).

Method

School-age children ( N = 61; 20 SLI, 20 ELL, 21 native monolingual English [NE]) were assessed using a norm-referenced mathematics instrument and 3 experimental computer-based mathematics games that varied in language demands. Group means were compared with analyses of variance.

Results

The ELL group was less accurate than the NE group only when tasks were language heavy. In contrast, the group with SLI was less accurate than the groups with NE and ELLs on language-heavy tasks and some language-light tasks. Specifically, the group with SLI was less accurate on tasks that involved comparing numerical symbols and using visual working memory for patterns. However, there were no group differences between children with SLI and peers without SLI on language-light mathematics tasks that involved visual working memory for numerical symbols.

Conclusion

Mathematical difficulties of children who are ELLs appear to be related to the language demands of mathematics tasks. In contrast, children with SLI appear to have difficulty with mathematics tasks because of linguistic as well as nonlinguistic processing constraints.

Supplemental Material

https://doi.org/10.23641/asha.6170279

Cognitive components of a mathematical processing network in 9-year-old children

We determined how various cognitive abilities, including several measures of a proposed domain-specific number sense, relate to mathematical competence in nearly 100 9-year-old children with normal reading skill. Results are consistent with an extended number processing network and suggest that important processing nodes of this network are phonological processing, verbal knowledge, visuo-spatial short-term and working memory, spatial ability and general executive functioning. The model was highly specific to predicting arithmetic performance. There were no strong relations between mathematical achievement and verbal short-term and working memory, sustained attention, response inhibition, finger knowledge and symbolic number comparison performance. Non-verbal intelligence measures were also non-significant predictors when added to our model. Number sense variables were non-significant predictors in the model and they were also non-significant predictors when entered into regression analysis with only a single visuo-spatial WM measure. Number sense variables were predicted by sustained attention. Results support a network theory of mathematical competence in primary school children and falsify the importance of a proposed modular 'number sense'. We suggest an 'executive memory function centric' model of mathematical processing. Mapping a complex processing network requires that studies consider the complex predictor space of mathematics rather than just focusing on a single or a few explanatory factors.

A pilot study of the effects of RightStart instruction on early numeracy skills of children with specific language impairment

This pilot study investigated the effects of an early numeracy program, RightStart Mathematics (RS), on Finnish kindergartners with specific language impairment (SLI). The study applied a pre-test-instruction-post-test design. The children with SLI (n=9, Mage=82.11 months) received RS instruction two to three times a week for 40 min over seven months, which replaced their business-as-usual mathematics instruction. Mathematical skill development among children with SLI was examined at the individual and group levels, and compared to the performance of normal language-achieving age peers (n=32, Mage=74.16 months) who received business-as-usual kindergarten mathematics instruction. The children with SLI began kindergarten with significantly weaker early numeracy skills compared to their peers. Immediately after the instruction phase, there was no significant difference between the groups in counting skills. In Grade 1, the children with SLI performed similarly to their peers in addition and subtraction skills (accuracy) and multi-digit number comparison, but showed weaker skills in arithmetical reasoning and in matching spoken and printed multi-digit numbers. Our pilot study showed encouraging signs that the early numeracy skills of children with SLI can be improved successfully in a kindergarten small-classroom setting with systematic instruction emphasizing visualization.

Predicting first-grade mathematics achievement: the contributions of domain-general cognitive abilities, nonverbal number sense, and early number competence

Early number competence, grounded in number-specific and domain-general cognitive abilities, is theorized to lay the foundation for later math achievement. Few longitudinal studies have tested a comprehensive model for early math development. Using structural equation modeling and mediation analyses, the present work examined the influence of kindergarteners' nonverbal number sense and domain-general abilities (i.e., working memory, fluid intelligence, and receptive vocabulary) and their early number competence (i.e., symbolic number skills) on first grade math achievement (i.e., arithmetic, shape and space skills, and number line estimation) assessed 1 year later. Latent regression models revealed that nonverbal number sense and working memory are central building blocks for developing early number competence in kindergarten and that early number competence is key for first grade math achievement. After controlling for early number competence, fluid intelligence significantly predicted arithmetic and number line estimation while receptive vocabulary significantly predicted shape and space skills. In sum we suggest that early math achievement draws on different constellations of number-specific and domain-general mechanisms.

Severity of specific language impairment predicts delayed development in number skills

The extent to which mathematical development is dependent upon language is controversial. This longitudinal study investigates the role of language ability in children's development of number skills. Participants were 229 children with specific language impairment (SLI) who were assessed initially at age 7 and again 1 year later. All participants completed measures of psycholinguistic development (expressive and receptive), performance IQ, and the Basic Number Skills subtest of the British Ability Scales. Number skills data for this sample were compared with normative population data. Consistent with predictions that language impairment would impact on numerical development, average standard scores were more than 1 SD below the population mean at both ages. Although the children showed improvements in raw scores at the second wave of the study, the discrepancy between their scores and the population data nonetheless increased over time. Regression analyses showed that, after controlling for the effect of PIQ, language skills explained an additional 19 and 17% of the variance in number skills for ages 7 and 8, respectively. Furthermore, logistic regression analyses revealed that less improvement in the child's language ability over the course of the year was associated with a greater odds of a drop in performance in basic number skills from 7 to 8 years. The results are discussed in relation to the interaction of linguistic and cognitive factors in numerical development and the implications for mathematical education.

Mathematics difficulties in children born very preterm: current research and future directions

Children born very preterm have poorer attainment in all school subjects, and a markedly greater reliance on special educational support than their term-born peers. In particular, difficulties with mathematics are especially common and account for the vast majority of learning difficulties in this population. In this paper, we review research relating to the causes of mathematics learning difficulties in typically developing children, and the impact of very preterm birth on attainment in mathematics. Research is needed to understand the specific nature and origins of mathematics difficulties in very preterm children to target the development of effective intervention strategies.

Impact of language abilities on exact and approximate number skills development: evidence from children with specific language impairment

PURPOSE

Counting and exact arithmetic rely on language-based representations, whereas number comparison and approximate arithmetic involve approximate quantity-based representations that are available early in life, before the first stages of language acquisition. The objective of this study was to examine the impact of language abilities on the later development of exact and approximate number skills.

METHOD

Twenty-eight 7- to 14-year-old children with specific language impairment (SLI) completed exact and approximate number tasks involving quantities presented symbolically and nonsymbolically. They were compared with age-matched (AM) and vocabulary-matched (VM) children.

RESULTS

In the exact arithmetic task, the accuracy of children with SLI was lower than that of AM and VM controls and related to phonological measures. In the symbolic approximate tasks, children with SLI were less accurate than AM controls, but the difference vanished when their cognitive skills were considered or when they were compared with younger VM controls. In the nonsymbolic approximate tasks, children with SLI did not differ significantly from controls. Further, accuracy in the approximate number tasks was unrelated to language measures.

CONCLUSIONS

Language impairment is related to reduced exact arithmetic skills, whereas it does not intrinsically affect the development of approximate number skills in children with SLI.