Number sense in early and elementary mathematics education

no abstractNumber sense is crucial in daily life and therefore an important aspect of education. The development of number sense recently attracted the attention of an increasing number of researchers in the domains of cognitive and developmental (neuro)psychology, (psychology of) mathematics education, special education, and educational neuroscience. In this article, we integrate and discuss the major results of these numerous studies on children’s acquisition of number sense. We start with the definition of the concept of number sense. Afterwards, we summarize the major findings on children’s acquisition of number sense from infancy to the early school years. Next, we provide an overview of recent intervention studies aiming at stimulating the development of number sense in young children. We end with a summary of the major findings and future issues for studies in this domai

The acquisition of preschool mathematical abilities: theoretical, methodological and educational considerations

The acquisition of preschool mathematical abilities: theoretical, methodological and educational consideration

Desenvolvimento numérico de pré-escolares equatorianos: o papel do nível sócio econômico, da qualidade da educação matemática inicial e do tipo de escola

Este estudo teve como objetivo analisar o desenvolvimento de habilidades numéricas iniciais entre crianças equatorianas durante a pré-escola, em relação a seu status sócio econômico (SES), à qualidade da sua educação matemática inicial e ao tipo de escola frequentada. 179 pré-escolares equatorianos (18 classes, sendo 6 por tipo de escola) responderam um teste padronizado sobre numeramento inicial, tanto no começo quanto ao final do ano escolar. Em todas as salas de aula a qualidade da educação matemática inicial foi medida duas vezes por meio do instrumento COEMET. Em primeiro lugar, os resultados mostraram pontuações bastante baixas no teste de numeramento inicial, com apenas 50% (no início) e 70% (no final) dos itens resolvidos corretamente, ao lado de grandes diferenças interindividuais nesses escores. Em segundo lugar, a qualidade da educação matemática inicial nas salas de aula participantes também foi bastante baixa. Em terceiro lugar, as habilidades numéricas iniciais das crianças na entrada da pré-escola, o nível socio econômico (SES) e o tipo de escola foram preditores das habilidades numéricas das crianças no final do ano letivo. A qualidade da educação matemática inicial não contribuiu para o desenvolvimento das crianças em numeramento. Discutimos criticamente nossas descobertas com vistas a otimizar a qualidade da educação matemática inicial equatoriana, como um passo para melhorar o desenvolvimento das habilidades numéricas.This study aimed at analyzing the development of Ecuadorian children’s early numerical abilities during the Kindergarten year in relation to their SES, the quality of their early mathematics education, and the attended school type. 179 Ecuadorian Kindergartners (18 classrooms, 6 classrooms per school type) were offered a standards-based early numeracy test at both the start and the end of the Kindergarten year. In all classrooms, the quality of early mathematics education was assessed twice via the COEMET instrument. Results first showed rather low scores on the early numeracy test, with only 50% (at the start) up to 70% (at the end) of the items solved correctly, along with large inter-individual differences in these scores. Second, the quality of early mathematics education in the participating classrooms was also rather low. Third, children’s early numerical abilities at Kindergarten entry, SES, and school type predicted children’s early numerical abilities at the end of the school year. The quality of early mathematics education did not contribute to children’s numerical development. We critically discuss our findings in view of optimizing the quality of Ecuadorian early mathematics education as a stepping stone towards enhanced numerical development

Preschool teachers’ selection of picture books for mathematics instruction: an interview study

Various studies pointed to the potential of picture book reading (PBR) for supporting preschoolers’ mathematical development. The features of picture books vary greatly, and these features contribute to the effectiveness of PBR. It is therefore important to adequately select picture books for mathematics instruction. We analyzed the general and mathematical PB features preschool teachers take into account when selecting picture books for this aim. Interviews with 66 preschool teachers indicated that they rate general features and features related to basic mathematical skills as most important, and explain their importance based on instructional goals rather than preschooler characteristics. Our results point to the need for professional development initiatives on the selection of picture books for mathematics instruction

The potential of mathematical picture books: a systematic analysis of their domain-specific picture book features

Studies in the domain of early literacy and recently also mathematics point to the potential of picture book reading (PBR) activities for children’s early literacy resp. mathematical development. Contrasting the domain of early literacy, the contribution of picture book features to the effectiveness of PBR activities in the domain of mathematics is hardly studied. To increase our understanding of the topic, we systematically analysed the domain-specific features of 100 mathematical picture books. Our analyses pointed to the presence of features that previous studies assume to support and to hinder early mathematical development (Ward et al., 2017). These findings complement previous findings based on English mathematical picture books from the U.S. and offer important insights for future studies and educational practice

A stratégiahasználat rugalmassága az alsó tagozatos matematikában: elemzés és fejlesztés

A neveléslélektan kutatói és a matematikát tanítók régóta hangsúlyozzák annak pedagógiai jelentőségét, hogy felismerjük és serkentsük a gyerekek önmaguk alkotta stratégiáinak rugalmasságát, ami fontos pillére az alsó tagozatos matematikatanítás innovatív megközelítésének. Készítettek és kipróbáltak olyan tananyagokat és fejlesztő programokat, amelyekkel ezt a fajta rugalmasságot kívánták növelni (lásd például Brownell, 1945; Freudenthal, 1991; Thompson, 1999; Wittmann és Müller, 1990-92). A múlt század végének számos reform-tantervében megjelenik a stratégia-rugalmasság kifejlesztésének pedagógiai értékéről alkotott meggyőződés

Enfoque espontáneo en estructuras matemáticas: patrones y clasificación

The study aimed to examine whether preschool children spontaneously focus on mathematical structures - patterns and classification - and whether that spontaneous focus is associated with their patterning abilities. The methodology was quantitative, descriptive, and comparative. Participants included 60 preschoolers who were evaluated at the end of the school year. The results indicated that most of them spontaneously focus on creating a mathematical structure and that there is no association between their tendency to focus on mathematical structures and their patterning abilities. No differences were observed in the spontaneous focus related to gender or socioeconomic background. It is concluded that these results allow us to point to the universal nature of the spontaneous focus on mathematical structures.El propósito del estudio fue examinar si los niños preescolares se enfocan espontáneamente en estructuras matemáticas –patrones y clasificación– y si dicho enfoque se asocia con sus habilidades para trabajar patrones. La metodología fue cuantitativa de tipo descriptivo y comparativo. Participaron en el estudio 60 preescolares que fueron evaluados al finalizar el año escolar. Los resultados indicaron que la mayoría de ellos se enfoca espontáneamente en crear una estructura matemática y que no existe asociación entre su tendencia a enfocarse en estructuras matemáticas y su habilidad para trabajar patrones. No se observaron diferencias en el enfoque espontáneo relacionadas al género ni al nivel socioeconómico. Se concluye que estos resultados permiten apuntar a la naturaleza universal del enfoque espontáneo en estructuras matemáticas

Contemporary Research and Perspectives on Early Childhood Mathematics Education

Children's Spontaneous Focusing On Numerosity (SFON) predicts later mathematics performance. This association is assumed to rely on children's self-initiated practice in number recognition during everyday activities, which would enhance their further mathematical development. Consequently, SFON in experimental tasks should be associated with SFON during everyday activities. The present contribution aims to enhance our understanding of this association by critically discussing the major results of two recently conducted studies on the association between SFON in experimental tasks and SFON during picture book reading. Study 1 revealed no association between children's SFON in an Imitation task and their number-related utterances during numerical picture book reading. Study 2, in which we contrasted two different SFON tasks and their association to picture book reading, revealed a positive association between children's SFON in the Picture task (but not in the Imitation task) and their number-related utterances during picture book reading. Theoretical, methodological, and educational implications are discussed