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A divisão no 4º ano de escolaridade

Alcobia, Helena Isabel da Silva
Fonte: Instituto Politécnico de Lisboa Publicador: Instituto Politécnico de Lisboa
Tipo: Dissertação de Mestrado
Publicado em /12/2014 POR
Relevância na Pesquisa
45.85%
Dissertação apresentada para obtenção do grau de Mestre em Educação Matemática na Educação Pré-Escolar e nos 1.º e 2.º Ciclos do Ensino Básico; Este estudo tem como objetivos: (i) perceber qual a compreensão que os alunos do 4º ano de escolaridade têm do conceito de divisão e (ii) analisar o desempenho que os alunos evidenciam na resolução de problemas que têm implícito o conceito de divisão. Para tal, procurou responder-se a quatro questões: a) Como é que os alunos reconhecem a operação de divisão na resolução de problemas? (problemas que têm implícito o conceito de divisão); b) Que estratégias utilizam os alunos na resolução de problemas de divisão?; c) Que dificuldades manifestam os alunos quando resolvem tarefas de divisão?; d) Quais os aspetos do sentido do número revelados pelos alunos na resolução de tarefas de divisão? De acordo com a problemática em estudo, a abordagem metodológica adotada foi de natureza qualitativa com carácter interpretativo (Bogdan & Biklen, 1994), na modalidade de estudo de caso (Yin, 2009). O estudo consistiu na criação de uma sequência de aprendizagem, constituída por seis problemas de divisão, tendo sido a mesma aplicada numa turma do 4º ano do Ensino Básico...

Behavioral and Neural Basis of Number Sense in Infancy

Libertus, Melissa E.; Brannon, Elizabeth M.
Fonte: PubMed Publicador: PubMed
Tipo: Artigo de Revista Científica
Publicado em 01/12/2009 EN
Relevância na Pesquisa
46.03%
Approximate number discrimination in adult human and nonhuman animals is governed by Weber’s Law: The ratio between the values determines discriminability. Here, we review recent evidence from behavioral and neuroimaging studies that suggests that number sense in human infancy shares the same hallmark feature of Weber’s Law and may rely on the same neural substrates as previously found in adults, children, and nonhuman animals. These findings support the notion of ontogenetic and phylogenetic continuity in number sense. New methods described here may help uncover how infants’ early number sense supports the development of a mature number sense. Moreover, they may aid in understanding how children learn to map nonsymbolic number representations onto symbols for number by providing dependent measures that capture individual variability.

Changes in frontal-parietal activation and math skills performance following adaptive number sense training: Preliminary results from a pilot study

Kesler, Shelli R.; Sheau, Kristen; Koovakkattu, Della; Reiss, Allan L.
Fonte: PubMed Publicador: PubMed
Tipo: Artigo de Revista Científica
EN
Relevância na Pesquisa
46%
Number sense is believed to be critical for math development. It is putatively an implicitly learned skill and may therefore have limitations in terms of being explicitly trained, particularly in individuals with altered neurodevelopment. A case series study was conducted using an adaptive, computerized program that focused on number sense and general problem solving skills was designed to investigate training effects on performance as well as brain function in a group of children with Turner syndrome who are at risk for math difficulties and altered development of math-related brain networks. Standardized measurements of math and math-related cognitive skills as well as functional magnetic resonance imaging (fMRI) were used to assess behavioral and neurobiologic outcomes following training. Participants demonstrated significantly increased basic math skills, including number sense, and calculation as well as processing speed, cognitive flexibility and visual-spatial processing skills. With the exception of calculation, increased scores also were clinically significant (i.e. recovered) based on reliable change analysis. Participants additionally demonstrated significantly increased bilateral parietal lobe activation and decreased frontal-striatal and mesial temporal activation following the training program. These findings show proof of concept for an accessible training approach that may be potentially associated with improved number sense...

Impact of High Mathematics Education on the Number Sense

Castronovo, Julie; Göbel, Silke M.
Fonte: Public Library of Science Publicador: Public Library of Science
Tipo: Artigo de Revista Científica
Publicado em 25/04/2012 EN
Relevância na Pesquisa
45.87%
In adult number processing two mechanisms are commonly used: approximate estimation of quantity and exact calculation. While the former relies on the approximate number sense (ANS) which we share with animals and preverbal infants, the latter has been proposed to rely on an exact number system (ENS) which develops later in life following the acquisition of symbolic number knowledge. The current study investigated the influence of high level math education on the ANS and the ENS. Our results showed that the precision of non-symbolic quantity representation was not significantly altered by high level math education. However, performance in a symbolic number comparison task as well as the ability to map accurately between symbolic and non-symbolic quantities was significantly better the higher mathematics achievement. Our findings suggest that high level math education in adults shows little influence on their ANS, but it seems to be associated with a better anchored ENS and better mapping abilities between ENS and ANS.

Number sense across the lifespan as revealed by a massive Internet-based sample

Halberda, Justin; Ly, Ryan; Wilmer, Jeremy B.; Naiman, Daniel Q.; Germine, Laura
Fonte: National Academy of Sciences Publicador: National Academy of Sciences
Tipo: Artigo de Revista Científica
EN
Relevância na Pesquisa
46.06%
It has been difficult to determine how cognitive systems change over the grand time scale of an entire life, as few cognitive systems are well enough understood; observable in infants, adolescents, and adults; and simple enough to measure to empower comparisons across vastly different ages. Here we address this challenge with data from more than 10,000 participants ranging from 11 to 85 years of age and investigate the precision of basic numerical intuitions and their relation to students’ performance in school mathematics across the lifespan. We all share a foundational number sense that has been observed in adults, infants, and nonhuman animals, and that, in humans, is generated by neurons in the intraparietal sulcus. Individual differences in the precision of this evolutionarily ancient number sense may impact school mathematics performance in children; however, we know little of its role beyond childhood. Here we find that population trends suggest that the precision of one’s number sense improves throughout the school-age years, peaking quite late at ∼30 y. Despite this gradual developmental improvement, we find very large individual differences in number sense precision among people of the same age, and these differences relate to school mathematical performance throughout adolescence and the adult years. The large individual differences and prolonged development of number sense...

A Number Sense Intervention for Low-Income Kindergartners at Risk for Mathematics Difficulties

Dyson, Nancy I.; Jordan, Nancy C.; Glutting, Joseph
Fonte: PubMed Publicador: PubMed
Tipo: Artigo de Revista Científica
EN
Relevância na Pesquisa
46.04%
Early number sense is a strong predictor of later success in school mathematics. A disproportionate number of children from low-income families come to first grade with weak number competencies, leaving them at-risk for a cycle of failure. The present study examined the effects of an 8-week number sense intervention to develop number competencies of low-income kindergartners (n = 121). The intervention purposefully targeted whole number concepts related to counting, comparing, and manipulating sets. Children were randomly assigned either to a number sense intervention or a business as usual contrast group. The intervention was carried out in small group, 30-minute sessions, 3 days per week for a total of 24 sessions. Controlling for number sense at pretest, the intervention group made meaningful gains relative to the control group at immediate as well delayed posttest on a measure of early numeracy. Intervention children also performed better than controls on a standardized test of mathematics calculation at immediate posttest.

Number sense in infancy predicts mathematical abilities in childhood

Starr, Ariel; Libertus, Melissa E.; Brannon, Elizabeth M.
Fonte: National Academy of Sciences Publicador: National Academy of Sciences
Tipo: Artigo de Revista Científica
EN
Relevância na Pesquisa
46%
The uniquely human mathematical mind sets us apart from all other animals. How does this powerful capacity emerge over development? It is uncontroversial that education and environment shape mathematical ability, yet an untested assumption is that number sense in infants is a conceptual precursor that seeds human mathematical development. Our results provide the first support for this hypothesis. We found that preverbal number sense in 6-month-old infants predicted standardized math scores in the same children 3 years later. This discovery shows that number sense in infancy is a building block for later mathematical ability and invites educational interventions to improve number sense even before children learn to count.

Domain General Mediators of the Relation between Kindergarten Number Sense and First-Grade Mathematics Achievement

Hassinger-Das, Brenna; Jordan, Nancy C.; Glutting, Joseph; Irwin, Casey; Dyson, Nancy
Fonte: PubMed Publicador: PubMed
Tipo: Artigo de Revista Científica
EN
Relevância na Pesquisa
45.98%
Domain general skills that mediate the relation between kindergarten number sense and first-grade mathematics skills were investigated. Participants were 107 children who displayed low number sense in the fall of kindergarten. Controlling for background variables, multiple regression analyses showed that attention problems and executive functioning both were unique predictors of mathematics outcomes. Attention problems were more important for predicting first-grade calculation performance while executive functioning was more important for predicting first-grade performance on applied problems. Moreover, both executive functioning and attention problems were unique partial mediators of the relationship between kindergarten and first-grade mathematics skills. The results provide empirical support for developing interventions that target executive functioning and attention problems in addition to instruction in number skills for kindergartners with initial low number sense.

Why do we differ in number sense? Evidence from a genetically sensitive investigation☆

Tosto, M.G.; Petrill, S.A.; Halberda, J.; Trzaskowski, M.; Tikhomirova, T.N.; Bogdanova, O.Y.; Ly, R.; Wilmer, J.B.; Naiman, D.Q.; Germine, L.; Plomin, R.; Kovas, Y.
Fonte: Elsevier Publicador: Elsevier
Tipo: Artigo de Revista Científica
Publicado em /03/2014 EN
Relevância na Pesquisa
46.07%
Basic intellectual abilities of quantity and numerosity estimation have been detected across animal species. Such abilities are referred to as ‘number sense’. For human species, individual differences in number sense are detectable early in life, persist in later development, and relate to general intelligence. The origins of these individual differences are unknown. To address this question, we conducted the first large-scale genetically sensitive investigation of number sense, assessing numerosity discrimination abilities in 837 pairs of monozygotic and 1422 pairs of dizygotic 16-year-old twin pairs. Univariate genetic analysis of the twin data revealed that number sense is modestly heritable (32%), with individual differences being largely explained by non-shared environmental influences (68%) and no contribution from shared environmental factors. Sex-Limitation model fitting revealed no differences between males and females in the etiology of individual differences in number sense abilities. We also carried out Genome-wide Complex Trait Analysis (GCTA) that estimates the population variance explained by additive effects of DNA differences among unrelated individuals. For 1118 unrelated individuals in our sample with genotyping information on 1.7 million DNA markers...

Number sense or working memory? The effect of two computer-based trainings on mathematical skills in elementary school

Kuhn, Jörg-Tobias; Holling, Heinz
Fonte: University of Finance and Management in Warsaw Publicador: University of Finance and Management in Warsaw
Tipo: Artigo de Revista Científica
Publicado em 09/06/2014 EN
Relevância na Pesquisa
46.05%
Research on the improvement of elementary school mathematics has shown that computer-based training of number sense (e.g., processing magnitudes or locating numbers on the number line) can lead to substantial achievement gains in arithmetic skills. Recent studies, however, have highlighted that training domain-general cognitive abilities (e.g., working memory [WM]) may also improve mathematical achievement. This study addressed the question of whether a training of domain-specific number sense skills or domain-general WM abilities is more appropriate for improving mathematical abilities in elementary school. Fifty-nine children (Mage = 9 years, 32 girls and 27 boys) received either a computer-based, adaptive training of number sense (n = 20), WM skills (n = 19), or served as a control group (n = 20). The training duration was 20 min per day for 15 days. Before and after training, we measured mathematical ability using a curriculum-based math test, as well as spatial WM. For both training groups, we observed substantial increases in the math posttest compared to the control group (d = .54 for number sense skills training, d = .57 for WM training, respectively). Whereas the number sense group showed significant gains in arithmetical skills...

Building Kindergartners’ Number Sense: A Randomized Controlled Study

Jordan, Nancy C.; Glutting, Joseph; Dyson, Nancy; Hassinger-Das, Brenna; Irwin, Casey
Fonte: PubMed Publicador: PubMed
Tipo: Artigo de Revista Científica
EN
Relevância na Pesquisa
46.02%
Math achievement in elementary school is mediated by performance and growth in number sense during kindergarten. The aim of the present study was to test the effectiveness of a targeted small group number sense intervention for high-risk kindergartners from low-income communities. Children were randomly assigned to one of three groups (n = 44 in each group): a number sense intervention group, a language intervention group, or a business as usual control group. Accounting for initial skill level in mathematical knowledge, children who received the number sense intervention performed better than controls at immediate post test, with meaningful effects on measures of number competencies and general math achievement. Many of the effects held eight weeks after the intervention was completed, suggesting that children internalized what they had learned. There were no differences between the language and control groups on any math-related measures.

Sentido num??rico y gr??ficos estad??sticos en la formaci??n de profesores

Arteaga, Pedro; Batanero Bernab??u, Carmen; Ortiz de Haro, Juan J.; Contreras Garc??a, Jos?? Miguel
Fonte: Universidad de Granada Publicador: Universidad de Granada
Tipo: Artigo de Revista Científica
SPA
Relevância na Pesquisa
45.85%
En este trabajo analizamos la importancia de la adquisici??n de competencias de elaboraci??n de gr??ficos estad??sticos para los futuros profesores de Educaci??n Primaria. Resumimos los resultados de nuestra investigaci??n donde se muestran ejemplos de errores en gr??ficos producidos por futuros profesores y se sugiere que son originados por un insuficiente sentido num??rico. Como consecuencia, sugerimos la conveniencia de conectar en la formaci??n de profesores los temas de Tratamiento de la Informaci??n y Sentido Num??rico a los cuales se da atenci??n preferente en los Reales Decretos de Ense??anzas M??nimas para la Educaci??n Primaria.; In this paper we analyze the relevance of acquiring competence in building statistical graphs for pre-service primary school teachers. We summarize results from our own research that show examples of errors in graphs produced by pre-service teachers and suggest that these errors are consequence of scarce numerical sense in these teachers. Consequently, we suggest the interest of connecting the topics of Dealing with Data and Number Sense in the training of teachers, since these topics receive much attention in the curricular guidelines for Primary Education.

A aprendizagem da multiplicação; um estudo no 2º ano de escolaridade

Silva, Cátia Filipa Pagaime
Fonte: Repositório Comum de Portugal Publicador: Repositório Comum de Portugal
Tipo: Dissertação de Mestrado
Publicado em /07/2015 POR
Relevância na Pesquisa
45.96%
Este estudo tem como objetivo compreender como lidam os alunos com tarefas de multiplicação, tendo em vista a sua resolução. Mais concretamente, pretende identificar e analisar as estratégias e procedimentos de cálculo utilizados pelos alunos na resolução de tarefas de multiplicação e eventuais dificuldades que revelam na resolução dessas tarefas. A fundamentação teórica inclui quatro secções que discutem as seguintes temáticas: ensino e aprendizagem dos números e das operações, à luz das orientações curriculares; significado, componentes e desenvolvimento de sentido de número; significado e desenvolvimento de cálculo mental; e aprendizagem das operações aritméticas, nomeadamente da operação multiplicação. Este estudo insere-se num paradigma interpretativo e segue uma abordagem qualitativa, sendo também uma investigação sobre a própria prática. Nele participam 21 alunos pertencentes a uma turma do 2.º ano de escolaridade. Os dados foram recolhidos recorrendo à observação participante, à recolha documental, a conversas informais e à entrevista. A proposta pedagógica associada a este estudo incluiu a conceção/adaptação e exploração de quatro tarefas, todas elas visando a aprendizagem da multiplicação numa perspetiva de desenvolvimento de sentido de número...

Using Kindergarten Number Sense to Predict Calculation Fluency in Second Grade

Locuniak, Maria N.; Jordan, Nancy C.
Fonte: PubMed Publicador: PubMed
Tipo: Artigo de Revista Científica
Publicado em //2008 EN
Relevância na Pesquisa
46.04%
Children's number sense in kindergarten was used to predict their calculation fluency in second grade (N = 198). Using block entry regression, usual predictors of age, reading, memory, and verbal and spatial cognition were entered in the first block and number sense measures were added in the second block. Number sense measures contributed a significant amount of variance over and above the more general predictors (26%–42%). Uniquely predictive subareas were active memory for numbers, number knowledge, and number combinations, with number combinations standing out as the strongest single predictor. Number sense screening in kindergarten, using “at-risk” versus “not-at-risk” criteria, successfully ruled out 84% of the children who did not go on to have calculation fluency difficulties and positively identified 52% of the children who later showed fluency difficulties. The relation of early number skills to later calculation fluency has important implications for math screening and intervention.

Predicting first-grade mathematics achievement: the contributions of domain-general cognitive abilities, nonverbal number sense, and early number competence

Hornung, Caroline; Schiltz, Christine; Brunner, Martin; Martin, Romain
Fonte: Frontiers Media S.A. Publicador: Frontiers Media S.A.
Tipo: Artigo de Revista Científica
Publicado em 04/04/2014 EN
Relevância na Pesquisa
45.98%
Early number competence, grounded in number-specific and domain-general cognitive abilities, is theorized to lay the foundation for later math achievement. Few longitudinal studies have tested a comprehensive model for early math development. Using structural equation modeling and mediation analyses, the present work examined the influence of kindergarteners' nonverbal number sense and domain-general abilities (i.e., working memory, fluid intelligence, and receptive vocabulary) and their early number competence (i.e., symbolic number skills) on first grade math achievement (i.e., arithmetic, shape and space skills, and number line estimation) assessed 1 year later. Latent regression models revealed that nonverbal number sense and working memory are central building blocks for developing early number competence in kindergarten and that early number competence is key for first grade math achievement. After controlling for early number competence, fluid intelligence significantly predicted arithmetic and number line estimation while receptive vocabulary significantly predicted shape and space skills. In sum we suggest that early math achievement draws on different constellations of number-specific and domain-general mechanisms.

The Importance of Number Sense to Mathematics Achievement in First and Third Grades

Jordan, Nancy C.; Glutting, Joseph; Ramineni, Chaitanya
Fonte: PubMed Publicador: PubMed
Tipo: Artigo de Revista Científica
Publicado em 01/04/2010 EN
Relevância na Pesquisa
46.02%
Children's symbolic number sense was examined at the beginning of first grade with a short screen of competencies related to counting, number knowledge, and arithmetic operations. Conventional mathematics achievement was then assessed at the end of both first and third grades. Controlling for age and cognitive abilities (i.e., language, spatial, and memory), number sense made a unique and meaningful contribution to the variance in mathematics achievement at both first and third grades. Furthermore, the strength of the predictions did not weaken over time. Number sense was most strongly related to the ability to solve applied mathematics problems presented in various contexts. The number sense screen taps important intermediate skills that should be considered in the development of early mathematics assessments and interventions.

Estrategias de sentido numérico en estudiantes del Grado en Matemáticas

Almeida, Rut; Bruno, Alicia; Perdomo Díaz, Josefa
Fonte: Universidade Autônoma de Barcelona Publicador: Universidade Autônoma de Barcelona
Tipo: Artigo de Revista Científica Formato: application/pdf
Publicado em //2014 SPA
Relevância na Pesquisa
45.89%
Se presentan resultados de una investigación sobre el sentido numérico de un grupo de estudiantes universitarios del Grado en Matemáticas en España. El objetivo de la investigación es estudiar el uso de estrategias asociadas al sentido numérico que manifiestan estos estudiantes. Los resultados muestran que, a pesar de la alta formación matemática de estos alumnos, manifiestan bajo éxito en las respuestas a determinadas cuestiones numéricas, cuando se les pide resolverlas siguiendo métodos no tradicionales de cálculo.; This paper presents results of an investigation about the number sense of a student group from the Mathematics Degree from Spain. The objective of this research is to study the use of strategies associated to number sense shown by these students. Results show that, despite the high mathematical knowledge of these students, they show a low success when answering to certain numerical questions, if they are asked to solve them without using traditional calculation methods.

Sentido de número na infância: uma interconexão dinâmica entre conceitos e procedimentos; El sentido del número en la infancia: una interconexión dinámica de conceptos y procedimientos; Sense of numbers in early childhood: a dynamic interconnection between concepts and procedures

Barbosa, Heloiza Helena de Jesus
Fonte: Universidade de São Paulo. Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto Publicador: Universidade de São Paulo. Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto
Tipo: info:eu-repo/semantics/article; info:eu-repo/semantics/publishedVersion; Formato: application/pdf
Publicado em 01/08/2007 POR
Relevância na Pesquisa
55.93%
La revisión presentada se ocupa de analizar qué nos revelan los estudios académicos y experimentales sobre procesos cognitivos de desarrollo implicados en la conceptuación de número hecha por los niños. Presentemente, dos grupos de orientaciones teóricas opuestas han argumentado sobre la naturaleza de la habilidad numérica de los niños. Aunque el debate esté todavía abierto, investigaciones revistas en este artículo parecen apuntar para la existencia de una interconexión entre conceptos y procedimientos en el proceso de construcción de sentido de número. Veremos, también, como la calidad del sentido de número construido por niños puede estar relacionada con su desempeño académico en matemática.; The present review describes what academic and experimental studies in mathematics have revealed about cognitive processes in young children's numerical abilities. Currently, two groups with opposite theoretical approaches are discussing the nature of children's numerical abilities. Although the debate is far from being conclusive, the studies revised in this article seem to indicate that there is a dynamic interconnection between concepts and procedures in the process of constructing the sense of number. In addition, it is discussed how the quality of the number sense constructed by the child might be connected with his/her school math achievement.; A presente revisão tem o objetivo de analisar o que estudos acadêmicos e experimentais têm revelado sobre os processos cognitivos de desenvolvimento envolvidos na conceituação de número pela criança. Presentemente...

The Neural Basis of the Number Sense

DeWind, Nicholas Kurshan
Fonte: Universidade Duke Publicador: Universidade Duke
Tipo: Dissertação
Publicado em //2014
Relevância na Pesquisa
46.14%

The ability to enumerate approximately without counting is an evolutionarily ancient and developmentally early core cognitive ability known as the "number sense". We use the number sense when we estimate a number without counting individual items, as when we guess the number of people in a crowded room. The number sense is theorized to form an instinctual building block upon which we create the conceptual structures of mathematics. This dissertation addresses three research questions regarding the number sense.

The first is the question of whether the number sense is malleable, and if so, what are the neural correlates of malleability. In Chapter 2 we gave adults number sense training, which we found improved the accuracy of numerical estimation. In Chapter 4 we recorded from single neurons in monkeys while they viewed arrays of items on a computer screen. Similar recordings have been made previously, but usually using monkeys that were trained to discriminate sets based on number. Recordings in trained animals demonstrated that individual neurons in the monkey's brain track the number of items in a set. We reasoned that if the neural correlates of the number sense were altered by the training experience, then we would get different results in untrained monkeys. We did find neurons encoding numerical information in untrained monkeys...

Place value without number sense: Exploring the need for mental mathematical skills assessment within the Annual National Assessments

Graven,Mellony; Venkat,Hamsa; Westaway,Lise; Tshesane,Herman
Fonte: South African Journal of Childhood Education Publicador: South African Journal of Childhood Education
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/01/2013 EN
Relevância na Pesquisa
66.04%
In this paper we examine the extent of the focus on number sense, enabled and accompanied by the development of efficient strategies for mental maths, in the foundation and intermediate phase. We do this through documentary analysis of the Curriculum and Assessment Policy Statements (CAPS) for these phases and the Annual National Assessments (ANAs). We argue that number sense and mental agility are critical for the development and understanding of algorithms and algebraic thinking introduced in the intermediate phase. However, we note from our work with learners, and broader evidence in the South African landscape, that counting-based strategies in the foundation phase are replaced in the intermediate phase with traditional algorithms. We share experiences in the form of vignettes to illuminate this problem. Whilst literature and the CAPS curriculum emphasise the important role of mental computation within number sense, we note that the ANAs do not include a "mental mathematics" component. This absence in assessment, where assessment often drives teaching, is problematic. We conclude with the suggestion that research be conducted into the viability/appropriateness of an orally administered mental mathematics assessment component in the ANAs as a way to establish a focus on number sense across the foundation and intermediate phases.