Verbal Counting Research Articles

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.

Spontaneous focusing on Arabic number symbols: A unique component of children’s early mathematical development?

ABSTRACT Children’s spontaneous focusing on Arabic number symbols (SFONS) has been identified as a relevant component of their early mathematical development. This study investigated whether SFONS is a separate construct from spontaneous focusing on numerosity (SFON) and examined whether it is uniquely related to numerical abilities and mathematics achievement. Participants were 159 kindergartners (4-5-year-olds) who completed measures of SFONS, SFON, numerical abilities, mathematics achievement, spatial ability, and language ability. Confirmatory factor analysis revealed that a two-factor model representing a separate SFONS and SFON factor best fitted the data, indicating that SFONS is separate from SFON. Correlation and regression analyses showed that SFONS was associated with numerical abilities and mathematics achievement. These associations – except for verbal counting – remained after controlling for age, parental education, spatial ability, language ability, and SFON. These findings suggest that SFONS is a unique component of early mathematical development that deserves attention in early mathematics education.

Spontaneous focusing on Arabic number symbols: A unique component of children’s early mathematical development?

ABSTRACT Children’s spontaneous focusing on Arabic number symbols (SFONS) has been identified as a relevant component of their early mathematical development. This study investigated whether SFONS is a separate construct from spontaneous focusing on numerosity (SFON) and examined whether it is uniquely related to numerical abilities and mathematics achievement. Participants were 159 kindergartners (4-5-year-olds) who completed measures of SFONS, SFON, numerical abilities, mathematics achievement, spatial ability, and language ability. Confirmatory factor analysis revealed that a two-factor model representing a separate SFONS and SFON factor best fitted the data, indicating that SFONS is separate from SFON. Correlation and regression analyses showed that SFONS was associated with numerical abilities and mathematics achievement. These associations – except for verbal counting – remained after controlling for age, parental education, spatial ability, language ability, and SFON. These findings suggest that SFONS is a unique component of early mathematical development that deserves attention in early mathematics education.

Counting to Infinity: Does Learning the Syntax of the Count List Predict Knowledge That Numbers Are Infinite?

By around the age of 5½, many children in the United States judge that numbers never end, and that it is always possible to add 1 to a set. These same children also generally perform well when asked to label the quantity of a set after one object is added (e.g., judging that a set labeled "five" should now be "six"). These findings suggest that children have implicit knowledge of the "successor function": Every natural number, n, has a successor, n+1. Here, we explored how children discover this recursive function, and whether it might be related to discovering productive morphological rules that govern language-specific counting routines (e.g., the rules in English that represent base-10 structure). We tested 4- and 5-year-old children's knowledge of counting with three tasks, which we then related to (a) children's belief that 1 can always be added to any number (the successor function) and (b) their belief that numbers never end (infinity). Children who exhibited knowledge of a productive counting rule were significantly more likely to believe that numbers are infinite (i.e., there is no largest number), though such counting knowledge was not directly linked to knowledge of the successor function, per se. Also, our findings suggest that children as young as 4years of age are able to implement rules defined over their verbal count list to generate number words beyond their spontaneous counting range, an insight which may support reasoning over their acquired verbal count sequence to infer that numbers never end.

Teachers’ knowledge of children’s mathematical development

This research was conducted due to the importance value of mathematics for early childhood and the fact some researches showed the early childhood education (ECE) teachers' low level of basic mathematical knowledge, especially the one related to childhood developmental stages. The participants of this research were 35 ECE teachers from one of the cities in West Java province with teaching experience approximately ten years. In this research, 30 minutes was given to the participants to solve 20 questions, which tested teachers' knowledge related to verbal counting sequence, counting, the ordinal number of words, addition/subtraction, divisions of sets, written number symbols, and words. Besides, the interview was conducted to get more in-depth information from the participants. The quantitative descriptive analysis was used to identify the frequency, percentage, mean value, and standard deviation. The result of the research showed that ECE teachers had limited knowledge of children's mathematical development. It was revealed by the result of the mean value of the teachers’ responses, which were only 33% correct answers and 16% no idea answers. This result can become input for the stakeholders to hold a professional development program which aims to increase the quality of ECE teachers related to mathematical development activity.

A Physically-Active Approach to Early Number Learning

This study evaluates the efficacy of a physically-active number learning game for young preschoolers. The intervention adapts Ramani and Siegler’s (Child Develop 79(2):375–394, 2008) successful The Great Race by modifying the mode of play from seated at a table to jumping with two feet on a large game mat. 75 children (mean age: 46 months) in the first year of a 2-year Title I preschool program were assessed in the fall on enumeration, verbal counting, cardinal principle knowledge (CPK), numeral recognition, and magnitude comparisons; children with a strong conceptual understanding of the cardinality principle were screened out (n = 11) of the intervention. 64 children were randomly assigned to the jumping game, the original seated game, or to a no-intervention control group. For the intervention, children met with an experimenter for four, 15–20-min sessions over a 3-week period and post-intervention assessments were completed 1 week later. All children completed a year-end assessment 5 months after the post-intervention assessment. Of the 64 children in the intervention group, 51 had complete data from all three time points. Repeated measures ANOVA and chi-square tests assessed the effectiveness of the intervention on children’s number knowledge and skills; models tested for the main effects of time and group and the interaction of time*group. Although all numeracy measures showed significant improvement over time, no differences between groups over time emerged. The absence of intervention effects is discussed in the context of intentionally aligning children’s number skills and knowledge with teacher practices and recent early numeracy interventions that target counting and set labelling.

Alignment Between Children’s Numeracy Performance, the Kindergarten Common Core State Standards for Mathematics, and State-Level Early Learning Standards

The current study examined preschoolers’ (N = 801) age-related performance on one measure of verbal counting and two measures of cardinality (“how many” and “give n”) aligned with the kindergarten Common Core State Standards for Mathematics (CCSSM) and included in the majority of states’ early learning guidelines for mathematics. Children were grouped into five age categories (3, 3.5, 4, 4.5, 5, 5.5), and within-age-group average rates of correct responses for each item within these three measures were calculated. Results demonstrated that the majority of children were already successfully meeting the CCSSM standards for both cardinal number knowledge tasks (86.5% and 53.3%, respectively) prior to kindergarten entry but that only 18.9% of the children were meeting the standard for verbal counting. Findings indicate potential misalignment between children’s existing capabilities and the CCSSM standards for cardinality and underscore the need to conduct large, nationally representative studies measuring children’s abilities on items that more closely assess the specific mathematics skills included in the CCSSM and early learning guidelines.

Using Number Games to Support Mathematical Learning in Preschool and Home Environments

ABSTRACT Research Findings: This study evaluated the effects of an early mathematics intervention designed to engage preschool children, their teachers, and their families in an interactive mathematics game. Previous research shows that playing this specific type of linear board game results in increased numerical skills and understanding in young children under controlled conditions. The current study explores the game’s effectiveness under more natural conditions – a classroom-based intervention with teachers and a related family engagement component. A pilot study informed a larger-scale experiment, comparing outcomes in multiple skill domains (verbal counting, counting on, number line estimation, numeral magnitude, and numeral recognition) with those of control group children who played memory matching games. The analysis sample included 256 children in classrooms that were randomly selected from volunteer teachers and randomly assigned within 10 centers to either the treatment group (mathematics games, 23 teachers) or the comparison condition (matching games, 22 teachers). The intervention resulted in positive impacts for numeral identification, but not the other domains. The number of math games played was positively associated with verbal counting. No impact of family game play was found; however, implementation challenges could have influenced this finding. Practice or Policy: Including simple, research-informed mathematics board games in the preschool classroom can support mathematical learning. Future work must include families and educators in the design of these supports.

ECT AMPLITUDE AND CLINICAL OUTCOMES

Introduction ECT is recognized for its efficacy in the treatment of depressive disorders, however neurocognitive impairment remains a major concern of treatment. Demographic factors, depression severity, and ECT treatment parameters influence neurocognitive outcomes. Studies examining ECT electrode placement and pulse width find that more focal stimulus delivery with right unilateral placement or ultrabrief pulse width can reduce cognitive side effects, however are associated with less efficacy than standard treatments. Pulse amplitude, which determines the induced electric field strength in the brain, is currently set at 800-900?mA on modern ECT devices without any clinical or scientific rationale. Lower pulse amplitudes also produce more focal electric fields and potentially reduce neurocognitive impairment. Recent small studies have demonstrated that low amplitude ECT can generate seizure induction, may improve depression severity, and result in fewer cognitive side effects. There are not yet prospective randomized studies examining the antidepressant and neurocognitive dose-response relationship relative of ECT pulse amplitude. The present study compares three different pulse amplitudes during an ECT series. We hypothesize that the lower amplitudes will maintain the antidepressant efficacy of the standard treatment and reduce the risk of neurocognitive impairment. Methods The present study (ClinicalTrials.gov identifier NCT0299929) prospectively randomized subjects to three treatment arms: 600mA, 700mA, and 800mA (active comparator). Clinical, neuropsychological, and imaging assessments were conducted pre-, mid- (after the sixth ECT treatment) and post-ECT (within one week of finishing the ECT series). Subjects had a diagnosis of major depressive disorder, met the clinical indication for ECT, were between 50 and 80?years of age, and right-handed. Depression severity was tracked using the Hamilton Depression Rating Scale 24-item (HDRS-24). The neuropsychological battery is focused on detecting longitudinal differences in hippocampal-dependent changes in cognitive performance. Our primary outcome measure was the Hopkins Verbal Learning Test-Revised (HVLT-R) raw retention score. All subjects were treated with right unilateral electrode placements with either ultrabrief pulse width (0.3 ms) or brief pulse widths (1.0ms, used for the last 14 subjects following interim data analysis). Treatments were individually titrated to supra-threshold, with subsequent treatments given at 6x seizure threshold. Results For this analysis, we focused on subjects that completed all three time points with RUL electrode placement. 62 patients were randomized to the three different pulse amplitude groups and completed at least the first and mid- visits. Demographics, including age, sex, duration of depressive episode, number of lifetime episodes, and baseline cognitive status were not significantly different between groups. Initial HDRS-24 scores were similar. The lowest amplitude group (600 mA) in our study showed significantly less antidepressant effect compared to the higher amplitudes (700mA and 800mA). The amplitude groups did not have significant differences in our primary cognitive outcome, the HVLT-R retention score. Several of the secondary cognitive outcomes were more sensitive to detecting cognitive impairment than the Hopkins Verbal Learning Test, revealing that subjects receiving 800?mA demonstrated greater impairment effects compared to the lower amplitude. This was most sensitive in the Delis Kaplan Executive Function System (DKEFS)-Verbal Fluency subset, DKEFS-Color Word Interference, and Dot Counting Test. Conclusions This study used a blinded randomized design to examine dose-dependent effects of pulse amplitude on depression response and neurocognitive measures. Despite seizure induction, treatment with the 600mA pulse amplitude did not achieve clinical efficacy in comparison to higher amplitudes. These findings support the concept that seizure is necessary but not sufficient for treatment response. The primary cognitive outcome, the Hopkins Verbal Learning Test-Revised (HVLT-R) raw retention score, did not show significant difference between amplitudes. However, neurocognitive battery outcomes of verbal fluency, color-word interference, and dot counting showed sensitivity in the secondary analyses. Focal electric field exposure through reduction of pulse amplitude may be beneficial in limiting the effects of some aspects of cognitive impairment. Limitations of our study include attrition and missing data from for some subjects who could not complete the full neurocognitive battery. Further work on understanding ECT treatment parameters can optimize and individualize care for patients undergoing ECT, maximizing benefit and reducing cognitive risk. This research was funded by: BRAIN Initiative U01 MH111826

Counting Enhances Kindergarteners' Mappings of Number Words Onto Numerosities.

We can make sense of how many a number represents by mapping the symbolic number word system onto the non-symbolic, approximate number system. This study adopted an intervention design to examine whether counting is essential in driving the formation of such symbolic-non-symbolic mappings. We compared kindergarteners’ mapping ability after reading stories (1) without cardinal labels, or (2) with cardinal labels, or (3) with cardinal labels and verbal counting. Results showed that children who had counted when reading the stories showed better mapping between number words and their approximate representations than their peers in the other two conditions – suggesting that counting plays a role in developing early symbolic-non-symbolic mappings. Such findings provides empirical support for parents and early educators to enhance young children’s mappings between numbers words and approximate representations through counting activities – such as counting the items in the story books while reading to children.

Do children use language structure to discover the recursive rules of counting?

We test the hypothesis that children acquire knowledge of the successor function — a foundational principle stating that every natural number n has a successor n + 1 — by learning the productive linguistic rules that govern verbal counting. Previous studies report that speakers of languages with less complex count list morphology have greater counting and mathematical knowledge at earlier ages in comparison to speakers of more complex languages (e.g., Miller & Stigler, 1987). Here, we tested whether differences in count list transparency affected children’s acquisition of the successor function in three languages with relatively transparent count lists (Cantonese, Slovenian, and English) and two languages with relatively opaque count lists (Hindi and Gujarati). We measured 3.5- to 6.5-year-old children’s mastery of their count list’s recursive structure with two tasks assessing productive counting, which we then related to a measure of successor function knowledge. While the more opaque languages were associated with lower counting proficiency and successor function task performance in comparison to the more transparent languages, a unique within-language analytic approach revealed a robust relationship between measures of productive counting and successor knowledge in almost every language. We conclude that learning productive rules of counting is a critical step in acquiring knowledge of recursive successor function across languages, and that the timeline for this learning varies as a function of count list transparency.

Differential contributions of cognitive precursors to symbolic versus non-symbolic numeracy in young Chinese children

Based on a longitudinal sample of young Hong Kong Chinese children (N = 104; age at the first wave of assessment: M ± SD = 59.69 ± 3.65 months), this study examined visual-spatial skills, working memory, phonological short-term memory, and phonological awareness in relation to symbolic and non-symbolic numerical skills. Children were tested first in their second year in kindergarten (K2; Time 1 [T1]) and then 12 months later in their third year (K3; Time 2 [T2]). Symbolic numerical skills were assessed using verbal counting, number recognition, number comparison, and written arithmetic tasks, while non-symbolic numerical skills were assessed using dot comparison and non-symbolic calculation tasks. Results from structural equation modeling showed that visual-spatial skills significantly predicted later non-symbolic numerical skills, while phonological short-term memory predicted later symbolic numerical skills. These associations remained even after controlling for the child's age and vocabulary. The findings highlight different constellations of cognitive skills that may be required in the development of young children's symbolic and non-symbolic numerical abilities.

Linguistic Effects on the Processing of Two-Digit Numbers

The syntactic structure of numbers in Arabic mainly differs from that of Hebrew in terms of the order of units and decades. In Arabic (inverted), two-digit numbers are written and read from right to left, i.e. the first digit is the units and the second is the decades (24 = four and twenty), while in Hebrew (non-inverted), the reverse. Therefore, studying transcoding in the two languages may enable us to tease out the relative effects of linguistic experience (first versus second language) and counting system transparency i.e. the syntactic representation of numbers (inverted versus non-inverted number system). For this purpose, the paradigm of reading and writing two-digit numbers from dictation, in both languages was used. Sixty university bilingual students were given two tasks in both Arabic-L1 (First language) and Hebrew-L2 (Second language): One task involved writing two-digit numbers to dictation, and the other involved reading two-digit numbers aloud. Reading times and the error rates were calculated in both languages according to type of error—total errors, substitution errors (replacement of two-digit number units with decades, and vice versa; for example, 23 ? 32), change errors (change of one digit 23 ? 28), and omission errors (omission of one digit; for example 23 ? 2). The participants made some errors in reading and especially in writing two-digit numbers. Their commonest errors were substitution errors compared to change and omission errors. Such errors were commoner for numbers which require processing the numerical syntactic structure than for decade numbers, or numbers from 11 to 19, which require less attention to numerical syntax. Speed and accuracy are greater in Arabic-L1 than Hebrew-L2, although the Arabic counting system has the inversion feature, and is thus less transparent than Hebrew. It is concluded that familiarity with the verbal counting system of the first language has a greater influence on transcoding than the transparency of the counting system. Theoretical and practical implications are discussed.

Verbal counting skill predicts later math performance and difficulties in middle school

This study examined the role of verbal counting skill as an early predictor of math performance and difficulties (at or below −1.5 standard deviation in basic math skills) in middle school. The role of fourth-grade level arithmetical skills (i.e., calculation fluency, multi-digit arithmetic i.e. procedural calculation, and word problem solving) as mediators was also investigated. The participants included 207 children in central Finland who were studied from kindergarten to the seventh grade. Path modeling showed that verbal counting in kindergarten is a strong predictor for basic math performance in seventh grade, explaining even 52% of the variance in these skills after controlling for the mothers’ education levels. This association between early verbal counting skill and basic math performance was partly mediated through fourth-grade procedural calculation and word problem solving skills. Furthermore, verbal counting had an unique predictive relation to middle school math performance above and beyond the basic arithmetical and problem solving skills in fourth grade. Poor kindergarten verbal counting skill was a significant indicator for later difficulties in mathematics.

Cognitive Correlates of the Covariance in Reading and Arithmetic Fluency: Importance of Serial Retrieval Fluency.

This study examines the core predictors of the covariance in reading and arithmetic fluency and the domain-general cognitive skills that explain the core predictors and covariance. Seven-year-old Finnish children (N=200) were assessed on rapid automatized naming (RAN), phonological awareness, letter knowledge, verbal counting, number writing, number comparison, memory skills, and processing and articulation speed in the spring of Grade 1 and on reading and arithmetic fluency in the fall of Grade 2. RAN and verbal counting were strongly associated, and a constructed latent factor, serial retrieval fluency (SRF), was the strongest unique predictor of the shared variance. Other unique predictors were phonological awareness, number comparison, and processing speed. Findings highlight the importance of SRF in clarifying the relation between reading and arithmetic fluency.

Numerical processing profiles in children with varying degrees of arithmetical achievement

Recent studies show basic cognitive abilities such as the rapid and precise apprehension of small numerosities in object sets (“subitizing”), verbal counting and numerical magnitude comparison significantly influence the acquisition of arithmetic and continues to modulate more advanced stages of mathematical cognition. Additionally, children with low arithmetic achievement (LAA) and Developmental Dyscalculia (DD) exhibit significant deficits in these cognitive processes. Nevertheless, the different cognitive profiles of children with varying degrees of numerical and arithmetic processing deficits have not been sufficiently characterized, despite its potential relevance to the stimulation of numerical cognition and the design of appropriate intervention strategies. Here, the cognitive profiles of groups of typically developing children, children with low arithmetical achievement and DD, exhibiting typical and atypical subitizing ability were contrasted. The results suggest that relatively independent neurocognitive mechanisms may produce distinct profiles at the behavioral level and suggest children with low arithmetic performance exhibiting atypical subitizing abilities are not only significantly slower, but rely on compensatory mechanisms and strategies compared to typical subitizers. The role of subitizing as a correlate of arithmetic fluency is revised in the light of the present findings.

Early childhood trauma alters neurological responses to mental stress in patients with coronary artery disease

BackgroundEarly childhood trauma is known to independently increase adverse outcome risk in coronary artery disease (CAD) patients, although the neurological correlates are not well understood. The purpose of this study was to examine whether early childhood trauma alters neural responses to acute mental stress in CAD patients. MethodsParticipants (n = 152) with CAD underwent brain imaging with High Resolution Positron Emission Tomography and radiolabeled water during control (verbal counting, neutral speaking) and mental stress (mental arithmetic, public speaking). Traumatic events in childhood were assessed with the Early Trauma Inventory (ETI-SR-SF) and participants were separated by presence (ETI+) or absence (ETI-) of early childhood trauma. Brain activity during mental stress was compared between ETI+ and ETI-. ResultsCompared to ETI-, ETI+ experienced greater (p < 0.005) activations during mental stress within the left anterior cingulate, bilateral frontal lobe and deactivations (p < 0.005) within the left insula, left parahippocampal gyrus, right dorsal anterior cingulate, bilateral cerebellum, bilateral fusiform gyrus, left inferior temporal gyrus, and right parietal lobe. Significant (p < 0.005) positive correlations between brain activation and ETI-SR-SF scores were observed within the left hippocampus, bilateral frontal lobe, left occipital cuneus, and bilateral temporal lobe. LimitationsResults in non-CAD samples may differ and ETI may be subject to recall bias. ConclusionEarly childhood trauma exacerbated activations in stress-responsive limbic and cognitive brain areas with direct and indirect connections to the heart, potentially contributing to adverse outcomes in CAD patients.

Spontaneous focusing on Arabic number symbols and its association with early mathematical competencies

Many studies have investigated the association between children’s spontaneous attention to number and their early mathematical abilities. This work has presented number in a non-symbolic format by exclusively using numerosities as their stimuli. Therefore, little is known about children’s spontaneous attention for Arabic number symbols. We aimed to address this gap by exploring, for the first time, whether we can observe individual differences in young children’s tendency to spontaneously focus their attention on Arabic number symbols (SFONS) using a newly developed Picture task. We investigated SFONS and its association with spontaneous focusing on numerosity (SFON), numerical abilities, and teacher ratings of mathematical competence in the three years of Flemish kindergarten. One hundred and eleven kindergartners (2 years 4 months – 6 years 2 months of age) completed a battery of tasks to measure their SFONS and SFON, as well as a range of numerical abilities (i.e., Arabic numeral identification, verbal counting, and counting objects). Kindergarten teachers were asked to rate their children’s mathematical competence on a 4-point Likert scale. Findings revealed that children in the three kindergarten years under study largely differed in their tendency to spontaneously attend to Arabic number symbols in the pictures they had to describe. We also observed differences in the levels of SFONS and SFON between the three kindergarten years. Although SFONS and SFON were not strongly associated in the three kindergarten years, significant associations were found between children’s SFONS and their numerical abilities in kindergarten year 1 and 2, and teacher ratings of their mathematical competence in kindergarten year 3. Together, these results suggest that SFONS is a relevant component of children’s early mathematical development.

Gender equality in 4- to 5-year-old preschoolers' early numerical competencies.

Numerical competencies acquired in preschool are foundational and predictive for children's later mathematical development. It remains to be determined whether there are gender differences in these early numerical competencies which could explain the often-reported gender differences in later mathematics and STEM-related abilities. Using a Bayesian approach, we quantified the evidence in favor of the alternative hypothesis of gender differences versus the null hypothesis of gender equality. Participants were 402 4- to 5-year-old children attending preschool in Flanders (Belgium). Children were selected via stratified cluster sampling to represent the full range of socioeconomic backgrounds. All children completed eight numerical tasks (verbal counting, object counting, numeral recognition, symbolic comparison, nonsymbolic comparison, nonverbal calculation, number order, dot enumeration). Results supported the gender equality hypothesis, and this evidence was substantial for seven of the eight numerical tasks. Preschoolers' early numerical competencies are characterized by gender equality. They probably do not explain later-reported gender differences.

Relations between preschoolers’ mathematical language understanding and specific numeracy skills

Understanding of mathematical language is critical for numeracy skill development. However, prior research has focused exclusively on relations between mathematical language and numeracy skills, broadly measured. Thus, the aim of the current study was to explore more targeted relations between preschoolers’ mathematical language and specific numeracy skills (e.g., cardinality, numeral comparison). The participants were 124 preschoolers aged 3.52 to 6.03 years (M = 4.78 years, SD = 0.53). Children were assessed on a battery of early numeracy skills and mathematical language as well as expressive vocabulary. Mixed-effects regression models were conducted, with school as a random effect and age, gender, and parental education as fixed effects covariates. Results indicated that mathematical language was significantly related to most numeracy skills, including verbal counting, one-to-one correspondence, numeral identification, cardinality, comparisons of sets and/or numerals, ordering numerals, and story problems. As hypothesized, mathematical language was not significantly related to either subitizing or formal addition because these skills are independent of general language ability. Importantly, mathematical language was generally more proximal to each of these numeracy skills than was general language. These results provide direction for future research, in particular for the development of more precise measures to identify children at risk for mathematics difficulties as well as the incorporation of focused mathematical language instruction within early mathematics interventions.