Verbal Counting Research Articles

Finger Configurations and Kindergarteners’ Mathematical Abilities

ABSTRACT Previous research has demonstrated a link between children’s ability to name canonical finger configurations and their mathematical abilities. This study aimed to investigate the nature of this association, specifically exploring whether the relationship is skill and handshape specific and identifying the underlying mechanisms involved. Five-year-old children in Spain (N = 143) were assessed on their ability to name canonical finger configurations and analogous representations (buildings on a hill), alongside a range of mathematical skills (counting, knowledge of the verbal count sequence, single-digit arithmetic, and subitizing). Findings indicated that five-year-olds only recognize single-hand canonical finger configurations as summary symbols, processing them holistically. However, no direct association was found between the ability to recognize these configurations and the assessed mathematical skills. Notably, only the ability to name finger configurations corresponding to larger numbers (requiring enumeration) was associated with children’s arithmetic skills, suggesting that these configurations elicit combinatorial processes that are handshape specific. The implications of these findings for cognitive development and mathematical assessment are discussed, highlighting the potential for finger configurations as a tool for fostering mathematical understanding and the need for further exploration of their cognitive underpinnings.

Technology-Integrated Instructions and Basic Mathematics Skills Acquisition in Public Secondary Schools in Rwanda: A Case of Nyagatare District

This research investigated the effects of technology-integrated instructions on basic mathematics skills in Rwandan secondary education. The study aimed to assess the types of technology-integrated instructional methods used for acquiring basic math skills in Rwandan public secondary schools, assess the level of mathematics skills and performance in these schools, and determine the relationship between technology-integrated teaching and the acquisition of basic math skills. Schools were selected based on their location and type. Theory used in this research project was cognitive load theory and constructivism theory. The target population included 214 teachers, 422 students, and 80 head teachers, total of 716 respondents, with a sample size of 257 participants. Data was gathered using questionnaires, interviews, and observation, employing purposive, stratified, and simple random sampling methods. Both qualitative and quantitative data collection and analysis methods were used. Qualitative data were analysed through content analysis, while quantitative data were presented using descriptive statistics (frequency, percentage, mean, and standard deviation) and inferential statistics (correlational and regression analysis) with IBM SPSS Version 21.0. Findings for the first objective showed that 85.7% of respondents strongly agreed on the use of computer algebra systems, 93.5% strongly agreed on blended learning and online education, 87.0% strongly agreed on the use of mobile and handheld devices, and 63.6% strongly agreed on software applications for mathematics calculations as methods influencing the acquisition of basic math skills. Regarding the second objective, 87.0% of teachers strongly agreed that verbal counting ability indicates math skill levels, 93.5% agreed that identifying more and less of a quantity shows math skills, 85.7% agreed on problem-solving skills as an indicator, 66.2% on recognizing numerals, and 77.9% on understanding size, shape, and patterns as indicators of math skills and performance. The study revealed a strong positive relationship between skills such as identifying quantities, verbal counting, problem-solving, and blended learning or online education. Problem-solving skills were also positively linked with computer algebra systems and blended learning. The significance of verbal counting was confirmed, as indicated by a p-value of less than 0.05. The study recommends using digital tools like calculators and graphing software to improve understanding of mathematical concepts. Real-world examples and multimedia can foster problem-solving abilities, while group work can enhance teamwork and communication skills. Educational software and online platforms provide personalized learning, enabling students to learn at their own pace and receive specific support.

Interrelations Between Acuity of the Approximate Number System and Symbolic Skills in Preschool Children

ABSTRACT This study investigates how the approximate number system (ANS) and young children’s symbolic skills jointly develop and interact. Specifically, the study aims at disentangling the directionality of the association between ANS acuity and a wide range of symbolic skills that reflect 4- to 5-year-olds’ symbolic quantitative knowledge (enumeration skills, knowledge of the verbal count sequence, symbolic comparison skills, and single-digit arithmetic). After accounting for individual differences in several domain-general skills (visuospatial working memory, non-verbal reasoning, and phonological processing), path models on longitudinal data collected from 4-year-old childen in Spain (N = 62) over one year revealed that earlier single-digit arithmetic and symbolic magnitude comparison skills predicted changes in ANS acuity over time. No contribution from earlier ANS to improvements in symbolic skills was found. Notably, the strength of the effect of visuospatial working memory on improvements in ANS acuity over time was like that of the auto-regressor – the correlation between measures of ANS acuity across time points. Implications for extant theories on the nature of the associations between ANS and young children’s symbolic skills are drawn.

Remote assessment of the association between early executive function and mathematics skills

AbstractExecutive function (EF) skills are consistently associated with global mathematics assessments. However, less is known about which specific mathematics skills invoke EF in early childhood. We adapted batteries of EF, numerical, and patterning tasks to be conducted via synchronous video conferencing with typically developing 4‐year‐old children (N = 115, 56.6% female, 85.2% White, non‐Hispanic, 7.8% Multiracial, 0.9% Hispanic, 0.9% Black, 1.7% American Indian/Alaska Native, 2.6% Asian and 0.9% missing) from primarily upper middle class households (maternal education range: some college to graduate or professional degree, mode = graduate or professional degree) in the United States. We found feasibility of remote adaptation varied greatly by task. Just over half of enrolled children (57.02%) completed all tasks and there were higher rates of missingness compared to an in‐person sample with a similar age range collected in schools. Nonetheless, working memory predicted various mathematics skills, including patterning, verbal counting, and number comparison, controlling for age and maternal education. Relations between cognitive flexibility and patterning varied across model specifications. Overall, these findings provide insight into the costs and benefits of remotely administered direct assessments of EF and mathematics in early childhood and add to the growing body of literature suggesting working memory plays an important role in several foundational early mathematics skills. Suggestions are offered for remote assessment with preschoolers.Highlights Executive function and mathematics tasks were adapted for remote use and associations among skill sets were examined. Remotely administered data collection sessions had higher rates of missingness than comparable in‐person studies. Findings replicate and extend prior work on the associations between working memory and patterning, verbal counting, and number comparison in a remote setting.

Comorbid Word Reading and Mathematics Computation Difficulty at Start of First Grade.

The purpose of this analysis was to describe cognitive processes associated with comorbid difficulty between word reading (WR) and mathematics computation (MC) at the start of first grade among children selected for WR and MC delays. A sample of 234 children (mean age 6.50 years, SD = 0.31) was assessed on WR, MC, core cognitive processes (phonological processing, rapid automatized naming, verbal counting [VC]), and domain-general cognitive processes (working memory, oral language, nonverbal reasoning, attentive behavior). Structural equation modeling was used to predict a latent Comorbidity factor, which modeled shared variance between WR and MC, and to identify processes associated with that Comorbidity factor. Results identified each of the core cognitive processes, especially VC, and each of the domain-general cognitive processes, especially working memory, as explaining shared variance between WR and MC. Implications for understanding comorbid difficulty at the start of first grade and designing coordinated first-grade interventions are discussed.

КЕНЖЕ МЕКТЕП ОКУУЧУЛАРЫНЫН КОМПЕТЕНТТҮҮЛҮГҮН КАЛЫПТАНДЫРУУДА БАЛДАРДЫН ОЙ ЖҮГҮРТҮҮСҮН ӨНҮКТҮРҮҮ

In this article we will talk about mathematical and mathematical-functional financial literacy of younger schoolchildren. The development of memory and thinking of junior schoolchildren, the ability to apply the acquired knowledge in practice is considered as the basis for the formation of functional literacy, mathematical skills. The mathematics lesson discusses the development of logical thinking, verbal counting, conclusions and the depth of Webb's knowledge, problem setting, analysis, which is important for the formation of functional, mathematical-functional, financial literacy among students. In the math textbook for grades 1-4, the availability of financial literacy tasks is analyzed and it is proposed to reformulate them. Several examples and tasks for use in the classroom are analyzed, taking into account the system-activity approach to the development of competencies of younger schoolchildren.

Early symbolic numeracy and gross, fine, and perceptual-motor skills in Mexican preschool children

The relation between early numeracy and motor skills has previously been examined, however, different results have been obtained depending on whether gross, fine, or perceptual-motor skills were considered in the study and the numeracy outcomes that were analyzed. The goal of the present research was to examine the relation between preschool children’s performance on two assessments of symbolic numeracy and gross, fine, and perceptual-motor skills. A total of one-hundred-and-twenty-three Mexican preschool children were assessed on their gross, fine, and perceptual-motor skills, their numeracy skills (i.e., applied problem-solving and symbolic number comparison) their numeracy precursor skills (i.e., number identification, cardinality and verbal counting), inhibitory control and visual-spatial working memory. Results from hierarchical linear regressions showed that applied problem-solving was predicted only by children’s numeracy precursor skills while the ability to compare two symbolic numbers was significantly predicted only by perceptual-motor skills. The study highlights the importance of perceptual-motor skills to children’s early numeracy learning. Keywords: Early numeracy skills; motor skills; perceptual-motor skills; preschool children.

Winning or losing: Children’s proportional reasoning across motivational contexts

Children tend to prioritize whole number information over relational information in proportional reasoning tasks, such that they judge a spinner with 4/10 red pieces as more likely to land on red than a spinner with 2/3 red pieces, because 4 > 2 (e.g., Hurst & Cordes, 2018a; Jeong et al., 2007). This whole number bias is hypothesized to be a driven by fluency in verbal counting in early childhood, which is thought to promote attention to whole number information. In this study, we explored (1) the relation between verbal counting abilities and whole number biases and (2) whether distinct framing contexts – either encouraging children to maximize the number of stickers won, or minimizing the number of stickers lost - differentially impact children’s proportional reasoning. Three- to nine-year olds (N = 210, Mage = 5.7 years) chose which of two spinners they preferred to spin. Children in the Gain condition learned that if the spinner landed on red, they would win a sticker and if it landed on blue, nothing would happen; children in the Loss condition learned that if the spinner landed on red, nothing would happen, but if it landed on blue, they would lose a sticker. Counter to prior work, performance of both older (6–9 year olds) and younger (3–5 year olds) children revealed whole number biases. Notably, whole number biases were not related to counting abilities. Importantly, we find framing the task in a Loss scenario lessened whole number biases, suggesting that task framing can alter children’s attention to whole number information in a proportional reasoning context.

Verbal counting and the timing of number acquisition in an indigenous Amazonian group.

Children in industrialized cultures typically succeed on Give-N, a test of counting ability, by age 4. On the other hand, counting appears to be learned much later in the Tsimane’, an indigenous group in the Bolivian Amazon. This study tests three hypotheses for what may cause this difference in timing: (a) Tsimane’ children may be shy in providing behavioral responses to number tasks, (b) Tsimane’ children may not memorize the verbal list of number words early in acquisition, and/or (c) home environments may not support mathematical learning in the same way as in US samples, leading Tsimane’ children to primarily acquire mathematics through formalized schooling. Our results suggest that most of our subjects are not inhibited by shyness in responding to experimental tasks. We also find that Tsimane’ children (N = 100, ages 4-11) learn the verbal list later than US children, but even upon acquiring this list, still take time to pass Give-N tasks. We find that performance in counting varies across tasks and is related to formal schooling. These results highlight the importance of formal education, including instruction in the count list, in learning the meanings of the number words.

The effects of preschool and age on children’s early number skills

There are massive developments in children’s early number skills in the ages 4- to 6-year old during which they attend preschool education and before they transition to formal school. We investigated to which extent these developments can be explained by children’ schooling experiences during preschool or by chronological age related maturational changes. In a secondary data-analysis of an existing longitudinal dataset, we compared children who were similar in age but different in the amount of preschool education (Old Year 2, n = 104, Mage = 62 months SDage 0.9 months vs. Young Year 3, n = 71, Mage = 65 months, SDage = 1.5 months) as well as children who were similar in the amount of preschool experience but differed in age (Young Year 3, n = 71, Mage = 65 months, SDage = 1.5 months vs. Old Year 3, n = 104, Mage = 74 months, SDage = 1.1 months). All children completed measures of numbering (verbal counting, dot enumeration, object counting), relations (number order, numeral identification, symbolic comparison, nonsymbolic comparison) and arithmetic operations (nonverbal calculation). We observed effects of preschool on object counting, numeral recognition and number order. There were also effects of chronological age on verbal counting, number order, numeral recognition and nonverbal calculation. The current data highlight which early number skills may be particularly malleable through schooling. They provide a more careful characterization of the potential factors that contribute to children’s early numerical competencies.

Visual and sound gesture in dance communication

ABSTRACT The present study addresses the impact of multimodal complexity in the transmission of a dance exercise. This study examined what kind of temporal correspondence favors the clarity of a teaching instruction in the context of a dance class. From an autoethnographic perspective, we describe a real learning situation in which a teacher marks (bodily demonstration and verbal counting) a movement exercise for a dancer. We analyze (microanalysis) the components of this marking, considering the model of the visual spatial indicator and the zero velocity and the prosodic components of the voice. It was hypothesized that when the emphasis of the movement and the emphasis of the voice are synchronized in phase this favors the clarity of the instruction. Seventy-five participants – dancers; musicians; non-musicians-non-dancers – evaluated dance exercises (audiovisual clips) with different modes of synchronization between voice and movement following two testing strategies. We found that in-phase exercise markings are significantly easier to follow and understand than when they are not. The work aims to show that a neglect in the multimodal organization of the instruction can generate distortion (noise) between the conceptualization and the perception of the message, putting at risk the result of the communication.

Exact Number Concepts Are Limited to the Verbal Count Range

Previous findings suggest that mentally representing exact numbers larger than four depends on a verbal count routine (e.g., “one, two, three .”). However, these findings are controversial because they rely on comparisons across radically different languages and cultures. We tested the role of language in number concepts within a single population—the Tsimane’ of Bolivia—in which knowledge of number words varies across individual adults. We used a novel data-analysis model to quantify the point at which participants (N = 30) switched from exact to approximate number representations during a simple numerical matching task. The results show that these behavioral switch points were bounded by participants’ verbal count ranges; their representations of exact cardinalities were limited to the number words they knew. Beyond that range, they resorted to numerical approximation. These results resolve competing accounts of previous findings and provide unambiguous evidence that large exact number concepts are enabled by language.

Predicting Mathematical Learning Difficulties Status: The Role of Domain-Specific and Domain-General Skills

This study investigated which domain-specific and domain-general skills measured at grade 1 predict mathematical learning difficulties (MLD) status at grade 3. We used different cut-off criteria and measures of mathematics performance for defining the MLD status. Norwegian children’s (N = 206) numeracy, cognitive, and language skills were measured at grade 1 and arithmetic fluency and curriculum-based mathematics (CBM) at grade 3. Logistic regression analyses showed that symbolic numerical magnitude processing, verbal counting, and rapid automatized naming predicted MLD25 status (performance ≤ 25th percentile) based on arithmetic fluency, whereas verbal counting skills and nonverbal reasoning predicted the status based on CBM. The same predictors were found for MLD10 status (performance ≤ 10th percentile), and in addition, rapid automatized naming also predicted the status based on CBM. Only symbolic numerical magnitude processing and verbal counting predicted LOW status (performance between 11–25th percentile) based on arithmetic fluency, whereas nonverbal reasoning and working memory predicted LOW status based on CBM. Different cut-off scores and mathematics measures used for the definition of MLD status are important to acknowledge, as these seem to lead to relatively significant variation in which students are identified as having MLD and which factors contribute to the MLD status.

Characteristics of 3-Year-Old Preschool Children’s Evolving Number Knowledge: A One-Year Multiple-Case Study

There is a considerable body of research on children’s number knowledge development, and in particular on children ages 4 years and older and who have some counting experience. Children in early care preschool settings (ages 2 and 3) and who are not yet experienced counters are an understudied population. We conducted a multiple-case study on five 3-year-olds over the course of a year, investigated their challenges and successes as they moved through the developmental progressions for specific number knowledge domains, and determined their key shifts in learning as they related to early predictors of later mathematics achievement. We found interesting variations in their test scores and, with multiple data sources, determined key shifts in learning observed across cases including acquisition of verbal counting skill, one-to-one correspondence, cardinality, and connecting and coordinating their number skills. While the developmental progressions provide teachers with a framework for understanding typical mathematical development, every child’s learning path is different. This research provides an in-depth look at 3-year-old preschool children’s variability in number knowledge and their key shifts in learning as they relate to early predictors of later mathematics achievement. We share implications for how and when early preschool teachers can support learning.

Testing the role of symbols in preschool numeracy: An experimental computer-based intervention study.

Numeracy is of critical importance for scholastic success and modern-day living, but the precise mechanisms that drive its development are poorly understood. Here we used novel experimental training methods to begin to investigate the role of symbols in the development of numeracy in preschool-aged children. We assigned pre-school children in the U.S. and Italy (N = 215; Mean age = 49.15 months) to play one of five versions of a computer-based numerical comparison game for two weeks. The different versions of the game were equated on basic features of gameplay and demands but systematically varied in numerical content. Critically, some versions included non-symbolic numerical comparisons only, while others combined non-symbolic numerical comparison with symbolic aids of various types. Before and after training we assessed four components of early numeracy: counting proficiency, non-symbolic numerical comparison, one-to-one correspondence, and arithmetic set transformation. We found that overall children showed improvement in most of these components after completing these short trainings. However, children trained on numerical comparisons with symbolic aids made larger gains on assessments of one-to-one correspondence and arithmetic transformation compared to children whose training involved non-symbolic numerical comparison only. Further exploratory analyses suggested that, although there were no major differences between children trained with verbal symbols (e.g., verbal counting) and non-verbal visuo-spatial symbols (i.e., abacus counting), the gains in one-to-one correspondence may have been driven by abacus training, while the gains in non-verbal arithmetic transformations may have been driven by verbal training. These results provide initial evidence that the introduction of symbols may contribute to the emergence of numeracy by enhancing the capacity for thinking about exact equality and the numerical effects of set transformations. More broadly, this study provides an empirical basis to motivate further focused study of the processes by which children’s mastery of symbols influences children’s developing mastery of numeracy.

Links between early literacy and early numeracy during preschool education in France

ABSTRACT Children develop early literacy and numeracy skills from an early age. The primary aim of the current study is to examen links between early literacy skills and early numeracy skills during preschool education in France. This study involves 313 kindergarten students (152 girls and 161 boys), aged between 3.44 and 7.02 years (mean age = 5.07 years, standard deviation = 0.88). Regression analyses accounting for children’s characteristics and early literacy skills revealed that letter knowledge was a significant predictor of numeral identification and verbal counting in the three years of French école maternelle. Children’s characteristics (age and socioeconomic status) have an impact on early numeracy skills but only for the youngest students in school (petite section). These findings suggest that young children’s early numeracy skills are related to the acquisition of early literacy skills and to children’s characteristics. Implications for future research are discussed.

When one size does not fit all: A latent profile analysis of low-income preschoolers’ math skills

On average, preschoolers from lower-income households perform worse on symbolic numerical tasks than preschoolers from middle- and upper-income households. Although many recent studies have developed and tested mathematics interventions for low-income preschoolers, the variability within this population has received less attention. The goal of the current study was to describe the variability in low-income children’s math skills using a person-centered analysis. We conducted a latent profile analysis on six measures of preschoolers’ (N = 115, mean age = 4.6 years) numerical abilities (nonsymbolic magnitude comparison, verbal counting, object counting, cardinality, numeral identification, and symbolic magnitude comparison). The results showed different patterns of strengths and weaknesses and revealed four profiles of numerical skills: (a) poor math abilities on all numerical measures (n = 13), (b) strong math abilities on all numerical measures (n = 41), (c) moderate abilities on all numerical measures (n = 35), and (d) strong counting and numeral skills but poor magnitude skills (n = 26). Children’s age, working memory, and inhibitory control significantly predicted their profile membership. We found evidence of quantitative and qualitative differences between profiles, such that some profiles were higher performing across tasks than others, but the overall patterns of performance varied across the different numerical skills assessed.

Exploring adults' awareness of and suggestions for early childhood numerical activities.

This study focuses on adults who are neither preschool teachers nor professional caregivers and investigates their beliefs regarding the importance of engaging young children with numerical activities. It also examines the types of numerical activities adults report having observed children engaging with, as well as the types of activities they propose as a way for promoting counting, enumerating, recognizing number symbols, and number composition and decomposition. Findings showed that participants believed to a great extent that engaging young children with numerical activities is important. Most reported that they had observed children engaging with at least some numerical activity. In general, participants relayed more activities and more detailed activities when suggesting activities for each competency, than they did when reporting observed activities. Findings also suggested a need to enhance adults’ knowledge regarding the necessity to promote verbal counting, separate from object counting, as well as to increase adults’ awareness of number composition and decomposition. For mathematics educators wishing to plan workshops for adults, this study offers a method for investigating adults’ knowledge of early numerical activities, as well as a starting point with which to plan appropriate workshops.

Verbal count sequence knowledge underpins numeral order processing in children

Recent research has suggested that numeral order processing – the speed and accuracy with which individuals can determine whether a set of digits is in numerical order or not – is related to arithmetic and mathematics outcomes. It has therefore been proposed that ordinal relations are a fundamental property of symbolic numeral representations. However, order information is also inherent in the verbal count sequence, and thus verbal count sequence knowledge may instead explain the relationship between performance on numeral order tasks and arithmetic. We explored this question with 62 children aged 6- to 8-years-old. We found that performance on a verbal count sequence knowledge task explained the relationship between numeral order processing and arithmetic. Moreover many children appeared to explicitly base their judgments of numerical order on count sequence information. This suggests that insufficient attention may have been paid to verbal number knowledge in understanding the sources of information that give meaning to numbers.

Shared Book Reading Effects on Number Naming in Preschoolers at Risk for Numeracy Delays

Number naming, or knowledge of math numerals, has been described as a gatekeeper skill in preschool math development because it is necessary for later math tasks such as calculation. This article describes a small group intervention piloted with 10 preschoolers found to be at risk for delays in early numeracy development during universal screening. Target numerals were assigned randomly to one of three conditions (book, activity, and control). Using an adapted alternating treatment design, intervention conditions were delivered to small groups in 15-min sessions three times per week for 8 weeks. Each intervention session included a manualized counting book and activity, which were delivered in random order each session, but included the same numerals for number identification, verbal counting during one-to-one correspondence, and number naming. Across the 8 weeks of intervention, some preschoolers exhibited growth in number naming in intervention conditions as compared to control; participants varied in whether the book or activity intervention condition was more effective for their learning.