RESUMO
We investigate number and arithmetic learning among a Bolivian indigenous people, the Tsimane', for whom formal schooling is comparatively recent in history and variable in both extent and consistency. We first present a large-scale meta-analysis on child number development involving over 800 Tsimane' children. The results emphasize the impact of formal schooling: Children are only found to be full counters when they have attended school, suggesting the importance of cultural support for early mathematics. We then test especially remote Tsimane' communities and document the development of specialized arithmetical knowledge in the absence of direct formal education. Specifically, we describe individuals who succeed on arithmetic problems involving the number five-which has a distinct role in the local economy-even though they do not succeed on some lower numbers. Some of these participants can perform multiplication with fives at greater accuracy than addition by one. These results highlight the importance of cultural factors in early mathematics and suggest that psychological theories of number where quantities are derived from lower numbers via repeated addition (e.g., a successor function) are unlikely to explain the diversity of human mathematical ability.
Assuntos
Desenvolvimento Infantil , Cognição , Criança , Humanos , Bolívia , Povos Indígenas , ConhecimentoRESUMO
Children's performance on number line tasks reflects their developing number system knowledge. Before 5 years of age, most children perform poorly on even the simplest number lines (i.e., 0-10). Our goal was to understand how number line skills develop before formal schooling. Chilean preschoolers attempted a 0-10 number line task three times over 2 years: at the beginning of pre-kindergarten (M = 4:7 [years;months]; Time 1), at the end of pre-kindergarten (M = 5:0; Time 2), and at the end of kindergarten (M = 5:10; Time 3). We used latent class analysis to group children according to their patterns of performance across number targets. At Time 1, 86% of children had error patterns indicating that they randomly placed estimates on the line. At Time 2, 56% of children continued to respond randomly. At Time 3, 56% of children showed competent performance across the number line, 23% were accurate only near the endpoints, and 21% were accurate only for low target numbers near the origin. Latent transition analyses showed that the transition from less to more proficient estimation classes was predicted by children's number identification skills. Thus, number line performance changed dramatically from 4 to 6 years of age as children began to develop the cognitive and numerical skills necessary to accurately estimate numbers on a number line.
Assuntos
Desenvolvimento Infantil , Instituições Acadêmicas , Criança , Pré-Escolar , Humanos , Matemática , Relações Pais-FilhoRESUMO
Es relativamente reciente el interés por parte del ámbito científico con respecto al estudio de la cognición numérica. En la actualidad, los hallazgos provenientes de la neurociencia cognitiva y la psicología cognitiva se consideran aportes muy significativos para comprender el desarrollo de la competencia numérica y sus dificultades y a partir de esta evidencia científica, reducir la incertidumbre teórica en el diseño de estrategias de intervención psicopedagógicas y pedagógicas.
The interest of the scientific field with respect to the study of the numerical cognition is relatively recent. Currently, evidence from cognitive neuroscience and cognitive psychology are considered very significant contributions to understand the development of numerical competence and its difficulties and, based on this scientific evidence, to reduce the theoretical uncertainty in the design of psychopedagogical and pedagogical strategies.
RESUMO
A presente revisão tem o objetivo de analisar as propostas apresentadas por estudos na área da cognição matemática sobre as habilidades quantitativas iniciais dos bebês e como estas habilidades iniciais podem levar à construção do conceito de número natural. A partir das evidências, o presente artigo discute se a ideia de número natural é inata, ideia defendida pela posição nativista original, ou se é derivada de um processo de desenvolvimento. Assim como também, apresenta dados de estudos recentes que sugerem ser o conhecimento de número natural um processo de desenvolvimento cognitivo gradual e de domínio genérico. Embora, mais estudos sejam necessários para se firmar esta última conjectura.(AU)
The present review aims to analyze the proposal put forward by researches on mathematical cognition about the initial quantitative abilities in human infants. Also, it analyses how the human infants may construct the concept of natural number upon these initial abilities. From the data presented, the paper discusses whether the idea of number has an innate basis, which is an original nativist's position, or a developmental process. Additionally, it presents data from new studies that point towards a cognitive process in the natural number concept that goes from general to specific domains. However, more studies are needed to support this proposal.(AU)
Assuntos
Formação de Conceito , Matemática , Aptidão , Cognição , Desenvolvimento Infantil , LactenteRESUMO
A presente revisão tem o objetivo de analisar as propostas apresentadas por estudos na área da cognição matemática sobre as habilidades quantitativas iniciais dos bebês e como estas habilidades iniciais podem levar à construção do conceito de número natural. A partir das evidências, o presente artigo discute se a ideia de número natural é inata, ideia defendida pela posição nativista original, ou se é derivada de um processo de desenvolvimento. Assim como também, apresenta dados de estudos recentes que sugerem ser o conhecimento de número natural um processo de desenvolvimento cognitivo gradual e de domínio genérico. Embora, mais estudos sejam necessários para se firmar esta última conjectura.
The present review aims to analyze the proposal put forward by researches on mathematical cognition about the initial quantitative abilities in human infants. Also, it analyses how the human infants may construct the concept of natural number upon these initial abilities. From the data presented, the paper discusses whether the idea of number has an innate basis, which is an original nativist's position, or a developmental process. Additionally, it presents data from new studies that point towards a cognitive process in the natural number concept that goes from general to specific domains. However, more studies are needed to support this proposal.