Cultural similarities and specificities of finger counting and montring: Evidence from Amazon Tsimane' people.

Numerical cognition might be embodied, that is, grounded in bodily actions. This claim is supported by the observation that, potentially due to our shared biology, finger counting is prevalent among a variety of cultures. Differences in finger counting are apparent even within Western cultures. Relatively few indigenous cultures have been systematically analyzed in terms of traditional finger counting and montring (i.e., communicating numbers with fingers) routines. Even fewer studies used the same protocols across cultures, allowing for a systematic comparison of indigenous and Western finger counting routines. We analyze the finger counting and montring routines of Tsimane' (N = 121), an indigenous people living in the Bolivian Amazon rainforest, depending on handedness, education level, and exposure to mainstream, industrialized Bolivian culture. Tsimane' routines are compared with those of German and British participants. Tsimane' reveal a greater variation in finger counting and montring routines, which seems to be modified by their education level. We outline a framework on how different factors such as handedness and reading direction might affect cross-cultural and within-cultural variation in finger counting.

Combining virtual reality and tactile stimulation to investigate embodied finger-based numerical representations.

Finger-based representation of numbers is a high-level cognitive strategy to assist numerical and arithmetic processing in children and adults. It is unclear whether this paradigm builds on simple perceptual features or comprises several attributes through embodiment. Here we describe the development and initial testing of an experimental setup to study embodiment during a finger-based numerical task using Virtual Reality (VR) and a low-cost tactile stimulator that is easy to build. Using VR allows us to create new ways to study finger-based numerical representation using a virtual hand that can be manipulated in ways our hand cannot, such as decoupling tactile and visual stimuli. The goal is to present a new methodology that can allow researchers to study embodiment through this new approach, maybe shedding new light on the cognitive strategy behind the finger-based representation of numbers. In this case, a critical methodological requirement is delivering precisely targeted sensory stimuli to specific effectors while simultaneously recording their behavior and engaging the participant in a simulated experience. We tested the device's capability by stimulating users in different experimental configurations. Results indicate that our device delivers reliable tactile stimulation to all fingers of a participant's hand without losing motion tracking quality during an ongoing task. This is reflected by an accuracy of over 95% in participants detecting stimulation of a single finger or multiple fingers in sequential stimulation as indicated by experiments with sixteen participants. We discuss possible application scenarios, explain how to apply our methodology to study the embodiment of finger-based numerical representations and other high-level cognitive functions, and discuss potential further developments of the device based on the data obtained in our testing.

Individual differences in numerical representations of risk in health decision making: A fuzzy-trace theory approach.

Fuzzy-trace theory predicts that decisionmakers process numerical information about risk at multiple levels in parallel: the simplest level, nominal (categorical some-none) gist, and at more fine-grained levels, involving relative comparison (ordinal less-more gist) and exact quantities (verbatim representations). However, little is known about how individual differences in these numerical representations relate to judgments and decisions, especially involving health tradeoffs and relative risks. To investigate these differences, we administered measures of categorical and ordinal gist representations of number, objective numeracy, and intelligence in two studies (Ns = 978 and 956). In both studies, categorical and ordinal gist representations of number predicted risk judgments and decisions beyond objective numeracy and intelligence. Participants with higher scores in categorical gist were more likely to choose options to avoid cancer recurrence risks; those who were higher in ordinal gist of numbers were more likely to discriminate relative risk of skin cancer; and those with higher scores in objective numeracy were more likely to choose options that were numerically superior overall in terms of relative risk of skin cancer and of genetic risks of breast cancer (e.g., lower numerical probability of cancer). Results support parallel-processing models that assume multiple representations of numerical information about risk, which vary in precision, and illustrate how individual differences in numerical representations are relevant to tradeoffs and risk comparisons in health decisions. These representations cannot be reduced to one another and explain psychological variations in risk processing that go beyond low versus high levels of objective numeracy.

Early numerical cognition in deaf and hearing children: Closer than expected? / Cognición numérica temprana en niños sordos y oyentes: ¿más cercana de lo esperado?

Abstract Deaf students show a significant delay in their understanding of numeracy and measurement concepts as well as verbal problem solving. There is still no consensus about the origin of this delay but several studies have shown that deaf people show differences in basic numerical skills and executive function (EF), which could underlie the differences in the way they learn and develop their cognitive abilities. Children have the innate ability to estimate and compare numerosities without using language or numerical symbols. The ability to discriminate large numerosities depends on the approximate number system (ANS), a cognitive system believed to be governed by a neural circuit within the intraparietal sulcus. Researchers hypothesize that the ANS underlies the development of arithmetic and there is data supporting the contribution of the ANS for math achievements. Little is known about the approximate number system of deaf children at early ages. Deaf and hearing preschool children were compared in terms of specific cognitive functions shown to be important for success in mathematics. Executive functions and symbolic and nonsymbolic magnitude comparison abilities of 7 deaf children and 14 hearing children aged 4-7 years (M = 69.90 months, SD = 11.42), were compared. To do so, neuropsychological assessments for school-aged children were adapted into Portuguese Sign Language. Significant group differences were found in abstract counting as well as in symbolic and nonsymbolic magnitude comparisons. These findings suggest that deaf children are less competent in these early numeracy skills than are their hearing peers.

Resumen La cognición de los sordos ha sido objeto de numerosos estudios que buscan comprender cómo los niños y adultos sordos procesan la información. Dichos estudios han demostrado que las personas sordas muestran diferencias en las habilidades numéricas y la función ejecutiva (FE), lo que podría ser la base de las diferencias conocidas en la forma en que las personas sordas aprenden y desarrollan sus habilidades cognitivas. Se han encontrado diferencias entre estudiantes sordos y oyentes en varias áreas de razonamiento numérico, en matemática y en la eficiencia en el procesamiento de representaciones numéricas como la comparación de magnitud. En las tareas de comparación de magnitud, los resultados dependían de si se estaban haciendo comparaciones simbólicas (números arábigos) o no simbólicas (puntos). En un estudio, los niños sordos fueron más lentos que sus compañeros oyentes en las tareas de comparación de magnitud simbólica, pero no en las tareas no simbólicas. Sin embargo, en un estudio más reciente, también se encontraron diferencias en las tareas no simbólicas. Se considera que la capacidad para comparar y discriminar grandes numerosidades depende del sistema numérico aproximado (ANS, Approximate Number System), un sistema cognitivo que se cree está gobernado por un circuito neuronal dentro del surco intraparietal. Los investigadores plantean la hipótesis de que el ANS subyace en cierta medida al desarrollo de la aritmética. Hay algunos datos que apoyan esta hipótesis: por ejemplo, las diferencias individuales en la agudeza del ANS se correlacionan positivamente con las habilidades numéricas y los logros futuros en matemática. Por otro lado, se ha encontrado un deterioro en la agudeza del ANS en niños con discapacidades de aprendizaje matemático. En consecuencia, los investigadores han propuesto que el ANS contribuye a la aparición de conceptos numéricos que los niños requieren para la competencia básica en el conteo y las comparaciones de magnitud simbólica. Otros han sugerido que la asociación entre la agudeza en la comparación de magnitud no simbólica y el rendimiento en matemática está moderada por factores de dominio general como las funciones ejecutivas (FE), en particular el control inhibitorio. En general, no está claro si existen diferencias en la agudeza de comparación de magnitud simbólica y no simbólica en niños sordos más pequeños y en qué medida se relacionan con las FE. El estudio actual examina la agudeza de las representaciones numéricas simbólicas y no simbólicas en niños sordos en edad preescolar e investiga la posible influencia del funcionamiento ejecutivo en estas habilidades matemáticas básicas. Se recolectaron datos de 21 niños portugueses del área de Lisboa, siete de los cuales eran sordos congénitamente y 14 tenían audición normal; los niños tenían entre 4 y 7 años de edad (M = 69.9 meses, DT = 11.42). Se seleccionaron tareas para medir lo siguiente: (a) FE, (b) memoria de trabajo, (c) lenguaje y (d) habilidades numéricas tempranas. Se empleó la tarea Shape School Task para evaluar FE. Se administró la versión portuguesa de la tarea de tapping de bloques de Corsi para evaluar la amplitud visuoespacial. Se desarrolló una tarea de comparación de puntos para examinar la capacidad de los niños de decidir instantáneamente cuál de las dos matrices de puntos es más grande utilizando el software Panamath. Se utilizaron dos tareas para evaluar la capacidad de los niños para producir palabras numéricas en un contexto cardinal y el Numeracy Screener para medir su capacidad para comprender la magnitud numérica simbólica. Los resultados indicaron que los niños sordos mostraron retrasos en las capacidades de comparación de magnitud simbólica y no simbólica. En las FE solo se encontraron diferencias en una tarea que implicaba una combinación de conmutación e inhibición; por lo demás, su función ejecutiva era comparable a la de los niños no sordos.

Running Online Behavioral Experiments Using R: Implementation of a Response-Time Decision Making Task as an R-Shiny App.

Online experiments allow for fast, massive, cost-efficient data collection. However, uncontrolled conditions in online experiments can be problematic, particularly when inferences hinge on response-times (RTs) in the millisecond range. To address this challenge, we developed a mobile-friendly open-source application using R-Shiny, a popular R package. In particular, we aimed to replicate the numerical distance effect, a well-established cognitive phenomenon. In the task, 169 participants (109 with a mobile device, 60 on a desktop computer) completed 116 trials displaying two-digit target numbers and decided whether they were larger or smaller than a fixed standard number. Sessions lasted ~7-minutes. Using generalized linear mixed models estimated with Bayesian inference methods, we observed a numerical distance effect: RTs decreased with the logarithm of the absolute difference between the target and the standard. Our results support the use of R-Shiny for RT-data collection. Furthermore, our method allowed us to measure systematic shifts in recorded RTs related to different OSs, web browsers, and devices, with mobile devices inducing longer shifts than desktop devices. Our work shows that precise RT measures can be reliably obtained online across mobile and desktop devices. It further paves the ground for the design of simple experimental tasks using R, a widely popular programming framework among cognitive scientists.

A Study on Congruency Effects and Numerical Distance in Fraction Comparison by Expert Undergraduate Students.

School mathematics comprises a diversity of concepts whose cognitive complexity is still poorly understood, a chief example being fractions. These are typically taught in middle school, but many students fail to master them, and misconceptions frequently persist into adulthood. In this study, we investigate fraction comparison, a task that taps into both conceptual and procedural knowledge of fractions, by looking at performance of highly mathematically skilled young adults. Fifty-seven Chilean engineering undergraduate students answered a computerized fraction comparison task, while their answers and response times were recorded. Task items were selected according to a number of mathematically and/or cognitively relevant characteristics: (a) whether the fractions to be compared shared a common component, (b) the numerical distance between fractions, and (c) the applicability of two strategies to answer successfully: a congruency strategy (a fraction is larger if it has larger natural number components than another) and gap thinking (a fraction is larger if it is missing fewer pieces than another to complete the whole). In line with previous research, our data indicated that the congruency strategy is inadequate to describe participants' performance, as congruent items turned out to be more difficult than incongruent ones when fractions had no common component. Although we hypothesized that this lower performance for congruent items would be explained by the use of gap thinking, this turned out not to be the case: evidence was insufficient to show that the applicability of the gap thinking strategy modulated either participants' accuracy rates or response times (although individual-level data suggest that there is an effect for response times). When fractions shared a common component, instead, our data display a more complex pattern that expected: an advantage for congruent items is present in the first experimental block but fades as the experiment progresses. Numerical distance had an effect in fraction comparison that was statistically significant for items without common components only. Altogether, our results from experts' reasoning reveal nuances in the fraction comparison task with respect to previous studies and contribute to future models of reasoning in this task.

Perfil de niños con déficits en la cognición numérica / Profile of Children with Deficits in Numerical Cognition

Resumen La presente investigación tuvo como objetivo caracterizar el perfil neurocognitivo de niños en relación con las habilidades cuantitativas, intelectuales, de memoria operativa y sus aspectos emocionales. La muestra fue de 42 niños de edad escolar de 8 a 10 años, divididos en dos grupos: con dificultades en aritmética (CDA = 21) y sin dificultades en aritmética (SDA = 21), que fueron evaluados a través de pruebas cognitivas y escalas de comportamiento, que analizaron variables como: rendimiento escolar, razonamiento abstracto, memoria operativa, cognición numérica, ansiedad y estrés. El perfil de los niños CDA se caracterizó por dificultades en el rendimiento escolar de forma general. Se encontraron síntomas de estrés compatibles con fases de alerta y resistencia, baja capacidad de memoria operativa y de cognición numérica, específicamente de procesamiento numérico y cálculo.

Abstract This study aimed to characterize the neurocognitive profile of children regarding quantitative, intellectual, and mnemonic skills; and their emotional state. The sample consisted of 42 school children 8-10 years old, divided into two groups: those with difficulties in arithmetic (CDA = 21) and without difficulties in arithmetic (SDA = 21). The children were evaluated through cognitive tests and behaviour scales, which analysed variables such as scholar achievement, abstract reasoning, working memory, numerical cognition, anxiety and stress. The profile of CDA children was characterized by global difficulties in schooling achievement. Also they had stress symptoms compatible with alert and resistance phases, low capacity in working memory and numerical cognition, specifically for numerical processing and calculation.

Enhancement of numeric cognition in children with low achievement in mathematic after a non-instrumental musical training.

Studies suggest that musical training enhances spatial-temporal reasoning and leads to greater learning of mathematical concepts. The aim of this prospective study was to verify the efficacy of a Non-Instrumental Musical Training (NIMT) on the Numerical Cognition systems in children with low achievement in math. For this purpose, we examined, with a cluster analysis, whether children with low scores on Numerical Cognition would be grouped in the same cluster at pre and post-NIMT. Participants were primary school children divided into two groups according to their scores on an Arithmetic test. Results with a specialized battery of Numerical Cognition revealed improvements for Cluster 2 (children with low achievement in math) especially for number production capacity compared to normative data. Besides, the number of children with low scores in Numerical Cognition decreased at post-NIMT. These findings suggest that NIMT enhances Numerical Cognition and seems to be a useful tool for rehabilitation of children with low achievement in math.

Cognição numérica em crianças com transtornos específicos de aprendizagem / . Numerical cognition in children with specific learning disabilities / Cognición numérica en niños con trastornos específicos de aprendizaje

O objetivo do presente estudo foi investigar o desenvolvimento de sistemas específicos da Cognição Numérica (Senso Numérico - SN, Compreensão Numérica - CN, Produção Numérica - PN e Cálculo - CA) em crianças brasileiras com Transtornos Específicos de Aprendizagem. Participaram do estudo 72 crianças (36 meninos), entre 9 e 10 anos, cursando os 4º ou 5º Anos do Ensino Fundamental em escolas públicas da região centro-oeste do Estado de São Paulo, Brasil; divididas em três grupos: controle (CT, N=42), com perfil de Dislexia do Desenvolvimento (DL, N = 11) e com perfil de Discalculia do Desenvolvimento combinada com dislexia (DDc, N = 19). Todas apresentavam nível intelectual médio para faixa etária. Os Transtornos Específicos de Aprendizagem foram aferidos pelo Teste de Desempenho Escolar (Stein, 1994), no qual as crianças com DDc obtiveram necessariamente classificação 'inferior' no Teste de Aritmética. Os três grupos foram similares em SN. As crianças DL e DDc apresentaram prejuízos leves em CN. Contudo, crianças com DDc apresentaram prejuízos moderados em PN e de leve a moderado em CA, o que indica um comprometimento mais generalizado em Cognição Numérica quando comparadas aos outros grupos. Em conclusão, crianças com DDc apresentaram maiores prejuízos e defasagem em relação às crianças DL e com desenvolvimento típico nos diferentes sistemas da Cognição Numérica.(AU).

The aim of this study was to investigate the development of specific domains of Numerical Cognition (Number Sense - NS, Number Comprehension - NC, Number Production - NP, and Calculation - CA) in Brazilian children with Specific Learning Disorders. The study included 72 children (36 boys), from 9-to 10-years-old, enrolled in 4th and 5th years of elementary school of public schools at countryside of Sao Paulo State, Brazil. They were divided into three groups: control (CT, N = 42), Developmental Dyslexia (DL, N = 11) and Developmental Dyscalculia combined with dyslexia (DDc, N = 19). All participants had intellectual level within the normal range, however, children from the last two groups had Learning Disorders classified by School Achievement Test - TDE (Stein, 1994) and DDc children received necessarily classification as 'inferior' in Arithmetic Test of TDE. The children did not differ in NS. DL and DDc children showed slight deficits in NC. However, DDc children had moderate in NP and mild to moderate deficits in CA, which indicates a more generalized impairment in Numerical Cognition. Furthermore, DDc children showed discrepancy in Numerical Cognition performance when compared to the other groups. Thus, children with Learning Disorders showed different performances in Numerical Cognition, although both groups had preserved SN, DDc children showed higher deficits and discrepancy in relation DL and typically developing children.(AU).

El objetivo de este estudio fue investigar el desarrollo de los sistemas específicos de la Cognición Numérica (el Sentido Numérico - SN, la comprensión numérica - CN, la producción numérica - PN y el Cálculo - CA) en niños brasileños con Trastornos Específicos de Aprendizaje. El estudio incluyó a 72 niños (36 chicos), con edad entre 9 y 10 años, estudiantes de los años 4to y 5to de primaria en escuelas públicas de un pueblo del Estado de São Paulo, Brasil; divididos en tres grupos: control (CT, N = 42), perfil de la Dislexia de Desarrollo (DL, N = 11) y el perfil de la Discalculia del Desarrollo combinado con dislexia (DDc, N = 19). Todos tenían el nivel intelectual dentro del rango medio. Los trastornos del aprendizajes e evaluaron a través de la Prueba de Rendimiento Académico (Stein, 1994), en el que los niños con DDc obtuvieron una clasificación necesariamente "inferior" en la prueba de aritmética. Los tres grupos fueron similares en SN. Los niños con DL y DDc mostraron ligeras pérdidas en CN. Sin embargo, los niños con DDc sufrieron daños moderados en PN y de leves a moderados en CA, por lo tanto, exhibieron un deterioro más generalizado en la cognición numérica en comparación a los otros grupos. En conclusión, los niños con DDc presentaron mayores perjuicios do que niños con DL o desarrollo típico de los diferentes sistemas de la Cognición Numérica.(AU).

Das representações numéricas inatas à matemática culturalmente construída / From innate numerical representations to culturally constructed mathematics / Desde las representaciones numéricas innatas hacia la matemática culturalmente construida

Dados oriundos de investigações recentes em psicologia cognitiva, neuropsicologia e neurociência cognitiva tem permitido um crescente consenso de que as representações numéricas nos adultos e o pensamento matemático culturalmente construído dependem da interação entre o chamado "senso numérico", observado em bebês humanos e em outras espécies animais, e a linguagem. Na pesquisa com bebês, a técnica do "olhar preferencial" tem permitido a descoberta de habilidades sofisticadas em idades precoces, entre elas as de soma e subtração. A neuropsicologia apresenta casos de lesões em áreas do cérebro que causam prejuízos a habilidades específicas, com preservação de outras. E a neurociência cognitiva, por meio de modernos recursos de neuroimagem, tem permitido a localização precisa de áreas cerebrais responsáveis pelo processamento numérico. Todas essas contribuições lançam luzes sobre a natureza da cognição numérica subjacente à matemática. São apresentados e discutidos dados produzidos por pesquisas nas referidas áreas, bem como suas implicações para as teorias clássicas do desenvolvimento cognitivo e do conceito de número, em particular. Discute-se também a visão decorrente sobre a relação entre biologia e cultura, que passam a ser vistas não mais de maneira dicotômica e sim como continuidade uma da outra, bem como implicações pedagógicas e sobre a formação de educadores.(AU).

Data from recent research in cognitive psychology, neuropsychology and cognitive neuroscience has allowed a growing consensus that the numerical representations in adults and the culturally constructed mathematical thinking depend on the interaction between the so-called "number sense", observed in human babies and in other animal species, and the language. In research with babies, the technique of "preferential looking" has allowed the discovery of sophisticated skills in early ages, among them those of addiction and subtraction. The neuropsychology presents cases of lesions in areas of the brain that cause damage to specific skills, with preservation of others. And cognitive neuroscience, by means of neuroimaging features modern, has allowed the precise location of brain areas responsible for numeric processing. All these contributions shed light on the nature of numerical cognition underlying mathematics. Data produced by those areas are presented and discussed research, as well as its implications for the classical theory of cognitive development and the concept of number in particular. It discusses also the vision arising on the relationship between biology and culture, which will be seen no more as dichotomous way but as a continuation of each other, as well as pedagogical implications and on the training of educators.(AU).

Datos de recientes investigaciones en psicología cognitiva, la neuropsicología y la neurociencia cognitiva han permitido un creciente consenso de que las representaciones numéricas en adultos y el pensamiento matemático culturalmente construido dependen de la interacción entre el llamado "sentido numérico", observados en bebés humanos y otras especies animales y la lengua. En la investigación con los bebés, la técnica de "mirada preferencial" ha permitido el descubrimiento de habilidades sofisticadas en edades tempranas, entre ellos los de suma y resta. La neuropsicología presenta casos de lesiones en áreas del cerebro que causan daño a las habilidades específicas, con la preservación de las demás. Y la neurociencia cognitiva, mediante modernos recursos de neuroimagen, ha permitido la ubicación precisa de las áreas del cerebro responsables por el procesamiento numérico. Todas estas contribuciones arrojan luz sobre la naturaleza de la cognición numérica subyacente a la matemática. Son presentados y discutidos datos de investigación producidos en esas áreas, así como sus implicaciones para la teoría clásica de desarrollo cognitivo y el concepto de número en particular. Se analiza también la visión que surge en la relación entre biología y cultura, que será vista no más como dicotómica sino como una continuación de ambas, así como implicaciones pedagógicas y respecto la formación de los educadores.(AU).

Das representações numéricas inatas à matemática culturalmente construída / From innate numerical representations to culturally constructed mathematics / Desde las representaciones numéricas innatas hacia la matemática culturalmente construida

Dados oriundos de investigações recentes em psicologia cognitiva, neuropsicologia e neurociência cognitiva tem permitido um crescente consenso de que as representações numéricas nos adultos e o pensamento matemático culturalmente construído dependem da interação entre o chamado "senso numérico", observado em bebês humanos e em outras espécies animais, e a linguagem. Na pesquisa com bebês, a técnica do "olhar preferencial" tem permitido a descoberta de habilidades sofisticadas em idades precoces, entre elas as de soma e subtração. A neuropsicologia apresenta casos de lesões em áreas do cérebro que causam prejuízos a habilidades específicas, com preservação de outras. E a neurociência cognitiva, por meio de modernos recursos de neuroimagem, tem permitido a localização precisa de áreas cerebrais responsáveis pelo processamento numérico. Todas essas contribuições lançam luzes sobre a natureza da cognição numérica subjacente à matemática. São apresentados e discutidos dados produzidos por pesquisas nas referidas áreas, bem como suas implicações para as teorias clássicas do desenvolvimento cognitivo e do conceito de número, em particular. Discute-se também a visão decorrente sobre a relação entre biologia e cultura, que passam a ser vistas não mais de maneira dicotômica e sim como continuidade uma da outra, bem como implicações pedagógicas e sobre a formação de educadores.

Data from recent research in cognitive psychology, neuropsychology and cognitive neuroscience has allowed a growing consensus that the numerical representations in adults and the culturally constructed mathematical thinking depend on the interaction between the so-called "number sense", observed in human babies and in other animal species, and the language. In research with babies, the technique of "preferential looking" has allowed the discovery of sophisticated skills in early ages, among them those of addiction and subtraction. The neuropsychology presents cases of lesions in areas of the brain that cause damage to specific skills, with preservation of others. And cognitive neuroscience, by means of neuroimaging features modern, has allowed the precise location of brain areas responsible for numeric processing. All these contributions shed light on the nature of numerical cognition underlying mathematics. Data produced by those areas are presented and discussed research, as well as its implications for the classical theory of cognitive development and the concept of number in particular. It discusses also the vision arising on the relationship between biology and culture, which will be seen no more as dichotomous way but as a continuation of each other, as well as pedagogical implications and on the training of educators.

Datos de recientes investigaciones en psicología cognitiva, la neuropsicología y la neurociencia cognitiva han permitido un creciente consenso de que las representaciones numéricas en adultos y el pensamiento matemático culturalmente construido dependen de la interacción entre el llamado "sentido numérico", observados en bebés humanos y otras especies animales y la lengua. En la investigación con los bebés, la técnica de "mirada preferencial" ha permitido el descubrimiento de habilidades sofisticadas en edades tempranas, entre ellos los de suma y resta. La neuropsicología presenta casos de lesiones en áreas del cerebro que causan daño a las habilidades específicas, con la preservación de las demás. Y la neurociencia cognitiva, mediante modernos recursos de neuroimagen, ha permitido la ubicación precisa de las áreas del cerebro responsables por el procesamiento numérico. Todas estas contribuciones arrojan luz sobre la naturaleza de la cognición numérica subyacente a la matemática. Son presentados y discutidos datos de investigación producidos en esas áreas, así como sus implicaciones para la teoría clásica de desarrollo cognitivo y el concepto de número en particular. Se analiza también la visión que surge en la relación entre biología y cultura, que será vista no más como dicotómica sino como una continuación de ambas, así como implicaciones pedagógicas y respecto la formación de los educadores.

Cognição numérica em crianças com transtornos específicos de aprendizagem / Numerical cognition in children with specific learning disabilities / Cognición numérica en niños con trastornos específicos de aprendizaje

O objetivo do presente estudo foi investigar o desenvolvimento de sistemas específicos da Cognição Numérica (Senso Numérico - SN, Compreensão Numérica - CN, Produção Numérica - PN e Cálculo - CA) em crianças brasileiras com Transtornos Específicos de Aprendizagem. Participaram do estudo 72 crianças (36 meninos), entre 9 e 10 anos, cursando os 4º ou 5º Anos do Ensino Fundamental em escolas públicas da região centro-oeste do Estado de São Paulo, Brasil; divididas em três grupos: controle (CT, N=42), com perfil de Dislexia do Desenvolvimento (DL, N = 11) e com perfil de Discalculia do Desenvolvimento combinada com dislexia (DDc, N = 19). Todas apresentavam nível intelectual médio para faixa etária. Os Transtornos Específicos de Aprendizagem foram aferidos pelo Teste de Desempenho Escolar (Stein, 1994), no qual as crianças com DDc obtiveram necessariamente classificação 'inferior' no Teste de Aritmética. Os três grupos foram similares em SN. As crianças DL e DDc apresentaram prejuízos leves em CN. Contudo, crianças com DDc apresentaram prejuízos moderados em PN e de leve a moderado em CA, o que indica um comprometimento mais generalizado em Cognição Numérica quando comparadas aos outros grupos. Em conclusão, crianças com DDc apresentaram maiores prejuízos e defasagem em relação às crianças DL e com desenvolvimento típico nos diferentes sistemas da Cognição Numérica.

The aim of this study was to investigate the development of specific domains of Numerical Cognition (Number Sense - NS, Number Comprehension - NC, Number Production - NP, and Calculation - CA) in Brazilian children with Specific Learning Disorders. The study included 72 children (36 boys), from 9-to 10-years-old, enrolled in 4th and 5th years of elementary school of public schools at countryside of Sao Paulo State, Brazil. They were divided into three groups: control (CT, N = 42), Developmental Dyslexia (DL, N = 11) and Developmental Dyscalculia combined with dyslexia (DDc, N = 19). All participants had intellectual level within the normal range, however, children from the last two groups had Learning Disorders classified by School Achievement Test - TDE (Stein, 1994) and DDc children received necessarily classification as 'inferior' in Arithmetic Test of TDE. The children did not differ in NS. DL and DDc children showed slight deficits in NC. However, DDc children had moderate in NP and mild to moderate deficits in CA, which indicates a more generalized impairment in Numerical Cognition. Furthermore, DDc children showed discrepancy in Numerical Cognition performance when compared to the other groups. Thus, children with Learning Disorders showed different performances in Numerical Cognition, although both groups had preserved SN, DDc children showed higher deficits and discrepancy in relation DL and typically developing children.

El objetivo de este estudio fue investigar el desarrollo de los sistemas específicos de la Cognición Numérica (el Sentido Numérico - SN, la comprensión numérica - CN, la producción numérica - PN y el Cálculo - CA) en niños brasileños con Trastornos Específicos de Aprendizaje. El estudio incluyó a 72 niños (36 chicos), con edad entre 9 y 10 años, estudiantes de los años 4to y 5to de primaria en escuelas públicas de un pueblo del Estado de São Paulo, Brasil; divididos en tres grupos: control (CT, N = 42), perfil de la Dislexia de Desarrollo (DL, N = 11) y el perfil de la Discalculia del Desarrollo combinado con dislexia (DDc, N = 19). Todos tenían el nivel intelectual dentro del rango medio. Los trastornos del aprendizajes e evaluaron a través de la Prueba de Rendimiento Académico (Stein, 1994), en el que los niños con DDc obtuvieron una clasificación necesariamente "inferior" en la prueba de aritmética. Los tres grupos fueron similares en SN. Los niños con DL y DDc mostraron ligeras pérdidas en CN. Sin embargo, los niños con DDc sufrieron daños moderados en PN y de leves a moderados en CA, por lo tanto, exhibieron un deterioro más generalizado en la cognición numérica en comparación a los otros grupos. En conclusión, los niños con DDc presentaron mayores perjuicios do que niños con DL o desarrollo típico de los diferentes sistemas de la Cognición Numérica.

Count on dopamine: influences of COMT polymorphisms on numerical cognition.

Catechol-O-methyltransferase (COMT) is an enzyme that is particularly important for the metabolism of dopamine. Functional polymorphisms of COMT have been implicated in working memory and numerical cognition. This is an exploratory study that aims at investigating associations between COMT polymorphisms, working memory, and numerical cognition. Elementary school children from 2th to 6th grades were divided into two groups according to their COMT val158met polymorphism [homozygous for valine allele (n = 61) vs. heterozygous plus methionine homozygous children or met+ group (n = 94)]. Both groups were matched for age and intelligence. Working memory was assessed through digit span and Corsi blocks. Symbolic numerical processing was assessed through transcoding and single-digit word problem tasks. Non-symbolic magnitude comparison and estimation tasks were used to assess number sense. Between-group differences were found in symbolic and non-symbolic numerical tasks, but not in working memory tasks. Children in the met+ group showed better performance in all numerical tasks while val homozygous children presented slower development of non-symbolic magnitude representations. These results suggest COMT-related dopaminergic modulation may be related not only to working memory, as found in previous studies, but also to the development of magnitude processing and magnitude representations.