Verbal Counting Research Articles

Individuality in the Early Number Skill Components Underlying Basic Arithmetic Skills.

Early number skills underlie success in basic arithmetic. However, very little is known about the skill profiles among children in preprimary education and how the potential profiles are related to arithmetic development. This longitudinal study of 440 Finnish children in preprimary education (mean age: 75 months) modeled latent performance-level profile groups for the early number skill components that are proposed to be key predictors of arithmetic (symbolic number comparison, mapping, and verbal counting skills). Based on three assessment time points (September, January, and May), four profile groups were found: the poorest-performing (6%), low-performing (16%), near-average-performing (33%), and high-average-performing children (45%). Although the differences between the groups were statistically significant in all three number skill components and in basic arithmetic, the poorest-performing children seemed to have serious difficulties in accessing the semantic meaning of symbolic numbers that was required in the number comparison and mapping tasks in this study. Interestingly, the tasks demanding processing between quantities and symbols also most differentiated the poorest-performing children from the low-performing children. Due to remarkable and stable individual differences in early number skill components, the findings suggest systematic support and progress monitoring practices in preeducational settings to diminish and avoid potential difficulties in arithmetic and mathematics in general.

Executive function in Chilean preschool children: Do short-term memory, working memory, and response inhibition contribute differentially to early academic skills?

A large body of literature demonstrates that different cognitive components related to executive function (EF), such as short-term memory, working memory, and response inhibition, are linked to early academic skills in preschool children. Nevertheless, few studies have focused on the unique contributions of these components to distinctive early numeracy and literacy skills in preschool children. Moreover, most studies have not considered the covariance between these early academic skills in preschool-aged children. The present study examined whether there are differential contributions of visual–spatial and verbal short-term memory, working memory, and response inhibition to specific early numeracy and literacy skills in preschool-aged children, taking into account the covariance among these outcomes. Several seemingly unrelated regression (SUR) analyses were conducted with 419 Chilean preschool-aged children (M = 53.9 months; SD = 4.22). The results show that both response inhibition and verbal short-term memory uniquely predicted all academic outcomes; working memory predicted all early academic skills (with the exception of verbal counting); and visual–spatial short-term memory predicted all numeracy skills and receptive vocabulary. When comparing the marginal effects of the EFs on the outcomes, response inhibition more strongly predicted applied problems than did working memory. Both visual–spatial short-term memory and response inhibition had a greater effect on explaining applied problems, compared to early decoding skills. Implications for teachers and interventions are discussed.

Preschoolers’ selective sustained attention and numeracy skills and knowledge

This brief report addresses preschoolers’ selective sustained attention (SSA) and early numeracy skills and knowledge. Past research indicates that children’s attention and early numeracy are positively associated, yet some concerns have emerged about the age appropriateness of tools used to measure preschoolers’ SSA. This study used a new measure—the Track-It Task—that demonstrates strong psychometric properties. In total, 31 at-risk preschoolers (Mage = 46.6 months) participated and were assessed on SSA, nonsymbolic quantity discrimination, and symbolic quantitative skills and knowledge. The ability to sustain attention in the face of distractions was positively correlated with preschoolers’ verbal counting and one-to-one correspondence, Arabic numeral recognition, and cardinal principle knowledge. SSA was not significantly associated with child age or performance on a memory task. This study provides preliminary evidence that SSA may facilitate the process whereby young children become reliable counters and learn that the symbol system of numbers represents specific quantities.

Steady state visual evoked potential (SSVEP) based brain-computer interface (BCI) performance under different perturbations.

Brain-computer interface (BCI) paradigms are usually tested when environmental and biological artifacts are intentionally avoided. In this study, we deliberately introduced different perturbations in order to test the robustness of a steady state visual evoked potential (SSVEP) based BCI. Specifically we investigated to what extent a drop in performance is related to the degraded quality of EEG signals or rather due to increased cognitive load. In the online tasks, subjects focused on one of the four circles and gave feedback on the correctness of the classification under four conditions randomized across subjects: Control (no perturbation), Speaking (counting loudly and repeatedly from one to ten), Thinking (mentally counting repeatedly from one to ten), and Listening (listening to verbal counting from one to ten). Decision tree, Naïve Bayes and K-Nearest Neighbor classifiers were used to evaluate the classification performance using features generated by canonical correlation analysis. During the online condition, Speaking and Thinking decreased moderately the mean classification accuracy compared to Control condition whereas there was no significant difference between Listening and Control conditions across subjects. The performances were sensitive to the classification method and to the perturbation conditions. We have not observed significant artifacts in EEG during perturbations in the frequency range of interest except in theta band. Therefore we concluded that the drop in the performance is likely to have a cognitive origin. During the Listening condition relative alpha power in a broad area including central and temporal regions primarily over the left hemisphere correlated negatively with the performance thus most likely indicating active suppression of the distracting presentation of the playback. This is the first study that systematically evaluates the effects of natural artifacts (i.e. mental, verbal and audio perturbations) on SSVEP-based BCIs. The results can be used to improve individual classification performance taking into account effects of perturbations.

Control of impact loading during distracted running before and after gait retraining in runners

ABSTRACTGait retraining using visual biofeedback has been reported to reduce impact loading in runners. However, most of the previous studies did not adequately examine the level of motor learning after training, as the modified gait pattern was not tested in a dual-task condition. Hence, this study sought to compare the landing peak positive acceleration (PPA) and vertical loading rates during distracted running before and after gait retraining. Sixteen recreational runners underwent a two-week visual biofeedback gait retraining program for impact loading reduction, with feedback on the PPA measured at heel. In the evaluation of PPA and vertical loading rates before and after the retraining, the participants performed a cognitive and verbal counting task while running. Repeated measures ANOVA indicated a significant interaction between feedback and training on PPA (F = 4.642; P = 0.048) but not vertical loading rates (F > 1.953; P > 0.067). Pairwise comparisons indicated a significantly lower PPA and vertical loading rates after gait retraining (P < 0.007; Cohen’s d > 0.68). Visual feedback after gait retraining reduced PPA and vertical loading rates during distracted running (P < 0.033; Cohen’s d > 0.36). Gait retraining is effective in lowering impact loading even when the runners are distracted. In dual-task situation, visual biofeedback provided beneficial influence on kinetics control after gait retraining.

Counting on fine motor skills: links between preschool finger dexterity and numerical skills.

Finger counting is widely considered an important step in children's early mathematical development. Presumably, children's ability to move their fingers during early counting experiences to aid number representation depends in part on their early fine motor skills (FMS). Specifically, FMS should link to children's procedural counting skills through consistent repetition of finger-counting procedures. Accordingly, we hypothesized that (a) FMS are linked to early counting skills, and (b) greater FMS relate to conceptual counting knowledge (e.g., cardinality, abstraction, order irrelevance) via procedural counting skills (i.e., one-one correspondence and correctness of verbal counting). Preschool children (N = 177) were administered measures of procedural counting skills, conceptual counting knowledge, FMS, and general cognitive skills along with parent questionnaires on home mathematics and fine motor environment. FMS correlated with procedural counting skills and conceptual counting knowledge after controlling for cognitive skills, chronological age, home mathematics and FMS environments. Moreover, the relationship between FMS and conceptual counting knowledge was mediated by procedural counting skills. Findings suggest that FMS play a role in early counting and therewith conceptual counting knowledge.

Conceptual correlates of counting: Children’s spontaneous matching and tracking of large sets reflects their knowledge of the cardinal principle

The acquisition of counting is a major milestone for children. A central question is how children’s non-verbal number concepts change as they learn to count. We assessed children’s verbal counting knowledge using the Give-N task and identified children who had acquired the cardinal principle (Cardinal Principle Knowers, or CP-knowers) and those who had not (Subset-Knowers, or SS-knowers). We compared their performance on two tests of nonverbal numerical cognition. We report comparable performance between SS- and CP-knowers for matching and tracking small sets of objects up to four, but disparate performance for sets between five and nine, with CP-knowers outperforming SS-knowers. These results indicate that the difference between CP- and SS-knowers extends beyond their knowledge of the verbal number system to their non-verbal quantitative reasoning. The findings provide support for the claim that children’s induction of cardinality represents a conceptual transition with concurrent, qualitative changes in numerical representation.

Evaluación de la matemática temprana mediante la primera validación italiana del Early Numeracy Test-Revised (ENT-R)

The purpose of this research was to adapt the Early Numeracy Test - Revised (ENT-R) to the Italian population. It is a tool for the evaluation of mathematical competence for children aged 4 to 7 years, designed and calibrated by Van Luit y Van de Rijt (2009). The test is designed to assess the competence of early mathematics and mathematical learn- ing and it is useful in identifying possible problems and in the specific areas of: concept of confrontation; classification (relative to the amount); one correspondence-ad-one; seriation; verbal count (use of cardinal numbers); structured count (count synchronously and in abbreviated form), resulting count; general knowledge of numbers and estimate on the line number. The test has been calibrated for a sample of 633 children (333 males and 300 females) from 14 schools in Rome and Trieste. The test analysis of validity and reliability (Cronbach’s alpha 0.93) allow to consider the ENT-R as an appropriate and useful tool for evaluating mathematical knowledge in Italian students at the end of kindergarten and the first years of primary school.

Primitive Concepts of Number and the Developing Human Brain

ABSTRACTCounting is an evolutionarily recent cultural invention of the human species. In order for humans to have conceived of counting in the first place, certain representational and logical abilities must have already been in place. The focus of this article is the origins and nature of those fundamental mechanisms that promoted the emergence of the human number concept. Five claims are presented that support an evolutionary view of numerical development: (1) number is an abstract concept with an innate basis in humans; (2) maturational processes constrain the development of humans’ numerical representations between infancy and adulthood; (3) there is evolutionary continuity in the neural processes of numerical cognition in primates; (4) primitive logical abilities support verbal counting development in humans; and (5) primitive neural processes provide the foundation for symbolic numerical development in the human brain. We support these claims by examining current evidence from animal cognition, child development, and human brain function. The data show that at the basis of human numerical concepts are primitive perceptual and logical mechanisms that have evolutionary homologs in other primates and form the basis of numerical development in the human brain. In the final section of this article, we discuss some hypotheses for what makes human numerical reasoning unique by drawing on evidence from human and non-human primate neuroimaging research.

IDENTIFICACIÓN Y ANÁLISIS DEL ÍNDICE DE COMPETENCIA MATEMÁTICA A TEMPRANA EDAD

Resumen.La teoría y la práctica sobre el desarrollo y enseñanza de los conceptos matemáticos en los niños/as pequeños ha estado fuertemente influida por este modelo de operaciones lógicas de Piaget y Szeminska (1941). La posición piagetiana apunta una fuerte relación entre las operaciones lógicas y los conceptos numéricos y también con las operaciones aritméticas. El modelo piagetiano ha recibido diversas críticas poniendo en duda el modelo lógico del número, puesto que proporcionaría una explicación incompleta de las competencias numéricas en el niño. Mayer et al., (2002) señalan la importancia del conteo en el desarrollo matemático. Por otro lado, Bryant y Nunes (2002) han sugerido que la base del desarrollo matemático es el pensamiento lógico, la enseñanza del sistema de numeración convencional y el aprendizaje significativo y contextualizado de los contenidos matemáticos. Otro punto de vista que denominamos interaccionista asume que las operaciones piagetianas y el conteo juntos contribuyen al desarrollo del número. Con este enfoque, el desarrollo del número es reformulado por el constructo denominado competencia matemática temprana (CMT). Un nivel suficiente de CMT es un requisito para ser capaz de seguir una educación matemática formal (Kroesbergen, et al., 2009), de ahí que resulte de alto interés poder lograr un procedimiento de evaluación de este tipo de competencia. En este sentido, el grupo de Van Luit ha desarrollado un procedimiento de evaluación exitoso a través del Early Numeracy Test-R (Van Luit et al., 2009). Esta prueba evalúa 9 componentes en niños de 4 a 7 años: Comparación, Clasificación, Correspondencia uno a uno, Seriación, Conteo verbal, Conteo estructurado, Conteo resultante o resultado del conteo (sin señalar), Conocimiento general de los números y Estimación. Para este trabajo se ha utilizado la versión española informatizada, con el objetivo de estandarizarla. Un total de 1391 alumnos participaron en este estudio (747 niños y 644 niñas). Los participantes evaluados tenían un rango de edad comprendido entre los 48 y los 95 meses. La prueba, (Alpha = 0.902) permite establecer un índice de la CMT en 6 niveles, teniendo en cuenta las características evolutivas de los participantes, concentrados en 10 grupos edad. Para cada uno de los niveles, la prueba sitúa al alumno en función del resultado en un valor cuantitativo y cualitativo respecto al grupo de edad de referencia. La ventaja de este índice de CMT es que tiene una considerable valor predictivo respecto al rendimiento matemático, permitiendo una detección temprana de las dificultades de aprendizaje.Palabras clave: Competencia Matemática Temprana, evaluación, Early Numeracy Test-r.

Oral counting sequences: a theoretical discussion and analysis through the lens of representational redescription

Empirical research has documented how children’s early counting develops into an increasingly abstract process, and initial counting procedures are reified as children develop and use more sophisticated counting. In this development, the learning of different oral counting sequences that allow children to count in steps bigger than one is seen as an essential skill that supports children’s mental calculation strategies. This paper proposes that the reification or refinement of the counting process that results to increased-in-sophistication use of counting is underlaid by the process of knowledge explicitation that the model of representational redescription postulates. The paper uses a case study to provide insight into the pathway that a 6-year-old child followed from learning how to verbally count in twos and tens to being able to use this knowledge for calculation purposes. The proposal is that knowledge of oral sequences is redescribed in more explicit and accessible formats before children are able to connect their knowledge of the verbal counting with the goal of using the sequence for calculation. The discussion presented here queries the notion of spontaneity as an inherent element of the theory and discusses the role that social interaction may play in supporting knowledge redescription. If it is the case that children’s knowledge of oral counting sequences is redescribed into increasingly explicit formats before it can be applied for calculation, then children need to be provided early in their education with structured activities that trigger knowledge redescription and support the necessary connections between counting, number structure and calculation.

Counting and rapid naming predict the fluency of arithmetic and reading skills

Understanding of the factors that underlie the development of fluency in reading and arithmetic is limited. This longitudinal study examined whether verbal counting and rapid automatized naming (RAN) were predictors of arithmetic and reading fluency in a population-based sample and to what extent related early emerging cognitive abilities and socioeconomic background accounted for the predictive power of counting and RAN. In addition, in order to examine the uniqueness of counting as a numerical predictor of reading fluency, the influence of another early number skill—number concept—was controlled. Three hundred and seventy-eight Finnish children were followed from kindergarten to Grade 3 (from 6 to 10 years). The results demonstrated that counting and RAN were powerful predictors of arithmetic and reading fluency. Controlling for phonological awareness, vocabulary, memory, and mother's education had little impact on the predictive relation of counting and RAN to fluency in arithmetic and reading. The number concept skill did not remove the predictive relation of counting with reading or arithmetic and had only a predictive relation to arithmetic fluency after controlling for cognitive skills. Findings suggest that the strong predictive relation counting had with reading and arithmetic fluency does not exist with all number skills. This finding supports the view that there is something specific in the verbal counting skill related to the development of fluency, which should be studied in the future.

What counts in estimation? The nature of the preverbal system.

It has been proposed that the development of verbal counting is supported by a more ancient preverbal system of estimation, the most widely canvassed candidates being the accumulator originally proposed by Gibbon and colleagues and the analogue magnitude system proposed by Dehaene and colleagues. The aim of this chapter is to assess the strengths and weaknesses of these models in terms of their capacity to emulate the statistical properties of verbal counting. The emphasis is put on the emergence of exact representations, autoscaling, and commensurability of noise characteristics. We also outline the modified architectures that may help improve models' power to meet these criteria. We propose that architectures considered in this chapter can be used to generate predictions for experimental testing and provide an example where we test the hypothesis whether the visual sense of number, ie, ability to discriminate numerosity without counting, entails enumeration of objects.

Preventive Support for Kindergarteners Most At-Risk for Mathematics Difficulties: Computer-Assisted Intervention

Weaknesses in early number skills have been found to be a risk factor for later difficulties in mathematical performance. Nevertheless, only a few intervention studies with young children have been published. In this study, the responsiveness to early support in kindergarteners with most severe difficulties was examined with two different computer programs. Two intervention groups were matched by age, visuo-spatial, and phonological working memory, as well as early number skills. After a short and intensive computerized intervention, the results indicated significant intervention effects for verbal counting Wilcoxon ES (r) = 0.46, and dot counting fluency, r = 0.52, when practiced with GraphoGame Math, as well as for basic arithmetic, r = 0.63, when practiced with Number Race. The findings suggest that a targeted computerized practice can produce specific training effects in kindergarteners most at-risk for mathematics difficulties. The results are discussed with regard to practical implications for educational game development.

Individual variance in responsiveness to early computerized mathematics intervention

We examined the effects of short, intensive computerized intervention in early number skills for kindergarteners with poor addition skills (below 1.5 SD). The mathematical content of the software was hierarchically organized, starting from one-to-one correspondence, comparing and ordering, and proceeding via number concept and counting to basic addition. The results showed positive within-group effects for basic addition (Wilcoxon ES (r)=.59), verbal counting (.56), and the Number Sets Test (.45; see Geary, Bailey, & Hoard, 2009). The effects remained stable over a 9-week follow-up period. However, there was no significant between-group difference in terms of gain scores as compared to a wait-list control group. Based on game-log data, individual variance in responsiveness to the intervention was analyzed. Even though the findings suggest that adaptive, hierarchically organized content could provide effective support for some children with poor early number skills, more specific instruction and feedback system are needed in individualizing interventions.

Development of a Protocol for Studying Premature Onset of Fear as a Feature of Pathological Fear: The Effects of Conditional Stimulus Duration and Counting Behavior

We propose that the premature onset of fear responding is a potentially important feature of pathological fear. A behavioral protocol to study the temporal regulation of fear in humans is, however, lacking. The present study aims at developing such a protocol for healthy individuals. To this end, we investigated the effect of conditional stimulus duration (50 seconds or 90 seconds) and the effect of verbal counting during presentation of the conditional stimulus (counting or no counting) in an aversive conditioning paradigm. Results favored training conditions in which participants were asked to count for the duration of the conditional stimulus, regardless of conditional stimulus duration. Under these training conditions, we observed optimal temporal control over the onset of fear. Furthermore, it was shown that intervals followed by an aversive stimulus were retrospectively estimated to have lasted longer than those that were not followed by an aversive stimulus. We argue that the developed protocol may serve as a powerful method to study premature onset of fear responding in future studies.

Preschool Children’s Spontaneous Focusing on Numerosity, Subitizing, and Counting Skills as Predictors of Their Mathematical Performance Seven Years Later at School

This seven-year longitudinal study examined how children’s spontaneous focusing on numerosity (SFON), subitizing based enumeration, and counting skills assessed at five or six years predict their school mathematics achievement at 12 years. The participants were 36 Finnish children without diagnosed neurological disorders. The results, based on partial least squares modeling, demonstrate that SFON and verbal counting skills before school age predict mathematical performance on a standardized test for typical school mathematics in Grade 5. After controlling for nonverbal IQ, only SFON predict school mathematics. Subitizing-based enumeration skills have an indirect effect via number sequence skills and SFON on mathematical performance at 12 years. Early mathematic skills do not predict reading skills at 12 years. Children’s early numerical skills, including SFON, before school age are important contributors to substantially later success in school mathematics.

Children’s mappings between number words and the approximate number system

Humans can represent number either exactly – using their knowledge of exact numbers as supported by language, or approximately – using their approximate number system (ANS). Adults can map between these two systems – they can both translate from an approximate sense of the number of items in a brief visual display to a discrete number word estimate (i.e., ANS-to-Word), and can generate an approximation, for example by rapidly tapping, when provided with an exact verbal number (i.e., Word-to-ANS). Here we ask how these mappings are initially formed and whether one mapping direction may become functional before the other during development. In two experiments, we gave 2–5year old children both an ANS-to-Word task, where they had to give a verbal number response to an approximate presentation (i.e., after seeing rapidly flashed dots, or watching rapid hand taps), and a Word-to-ANS task, where they had to generate an approximate response to a verbal number request (i.e., rapidly tapping after hearing a number word). Replicating previous results, children did not successfully generate numerically appropriate verbal responses in the ANS-to-Word task until after 4years of age – well after they had acquired the Cardinality Principle of verbal counting. In contrast, children successfully generated numerically appropriate tapping sequences in the Word-to-ANS task before 4years of age – well before many understood the Cardinality Principle. We further found that the accuracy of the mapping between the ANS and number words, as captured by error rates, continues to develop after this initial formation of the interface. These results suggest that the mapping between the ANS and verbal number representations is not functionally bidirectional in early development, and that the mapping direction from number representations to the ANS is established before the reverse.

Early Numeracy Assessment: The Development of the Preschool Early Numeracy Scales

Research Findings: The focus of this study was to construct and validate 12 brief early numeracy assessment tasks that measure the skills and concepts identified as key to early mathematics development by the National Council of Teachers of Mathematics (2006) and the National Mathematics Advisory Panel (2008)—as well as critical developmental precursors to later mathematics skills noted in the Common Core State Standards (2010). Participants were 393 preschool children ages 3 to 5 years old. Measure development and validation occurred through 3 analytic phases designed to ensure that the measures were brief, reliable, and valid. These measures were 1-to-1 counting, cardinality, counting subsets, subitizing, number comparison, set comparison, number order, numeral identification, set-to-numerals, story problems, number combinations, and verbal counting. Practice or Policy: Teachers have extensive demands on their time, yet they are tasked with ensuring that all students’ academic needs are met. To identify individual instructional needs and measure progress, they need to be able to efficiently assess children’s numeracy skills. The measures developed in this study not only are reliable and exhibit evidence of validity but also are easy to use and can be utilized for measuring the effects of targeted instruction on individual numeracy skills.

Verbal Counting Moderates Perceptual Biases Found in Children's Cardinality Judgments

A crucial component of numerical understanding is one's ability to abstract numerical properties regardless of varying perceptual attributes. Evidence from numerical match-to-sample tasks suggests that children find it difficult to match sets based on number in the face of varying perceptual attributes, yet it is unclear whether these findings are indicative of incomplete numerical abstraction abilities early in development or instead are driven by specific demands of the matching task. In this study, we explored whether perceptual biases would be found in data from a numerical task invoking verbal representations of number and whether these biases are moderated by verbal counting behavior. Three- to 6-year-old children classified as proficient counters (cardinal principle knowers) participated in a number cardinality task in which they were asked to identify which of 2 arrays—either perceptually homogeneous or heterogeneous in appearance—contained a specific number of animals (e.g., “12 animals”). Results revealed an overall performance bias for homogeneous trials in this cardinality task, such that children were better able to exactly identify the target cardinality when items within the sets were perceptually identical. Further analyses revealed that these biases were found only for those children who did not explicitly verbally count during the task. In contrast, performance was unaffected by the perceptual attributes of the array when the child spontaneously counted. Together, results reveal that cardinality judgments are negatively impacted by perceptual variation, but this relationship is muted in those children who engage in verbal counting.