Spatial structuring and the development of number sense: A case study of young children working with blocks

Nes, Fenna van; Eerde, Dolly van

doi:10.1016/j.jmathb.2010.08.001

Cited by 22 publications

(17 citation statements)

References 28 publications

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“…Thus, poorly developed number sense may lead to later mathematical failures Gersten et al 2005;Malofeeva et al 2004). Moreover, without appropriate intervention, which can be effective (Van Luit and Schopman 2000;Van Nes and Van Eerde 2010), children who start school with poor number sense are likely to remain low achievers throughout school (Aubrey et al 2006;Geary 2013). This is important in light of research that number sense acquisition may be linked to a child's family's socio-economic status in general (Melhuish et al 2008;Starkey et al 2004) and parental education levels in particular (Ivrendi 2011;Penner and Paret 2008).…”

Section: Introductionmentioning

confidence: 99%

Identifying Opportunities for Grade One Children to Acquire Foundational Number Sense: Developing a Framework for Cross Cultural Classroom Analyses

Andrews

Sayers

2014

Early Childhood Educ J

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It is known that an appropriately developed foundational number sense (FONS), or the ability to operate flexibly with number and quantity, is a powerful predictor of young children's later mathematical achievement. However, until now not only has FONS been definitionally elusive but instruments for identifying opportunities for children to acquire its various components have been missing from the classroom observation tools available. In this paper, drawing on a constant comparison analysis of appropriate literature, we outline the development of an eight dimensional FONS framework. We then show, by applying this framework to three culturally diverse European grade one lessons, one English, one Hungarian and one Swedish, that it is both straightforwardly operationalised and amenable to cross cultural analyses of classroom practice. Some implications are discussed.

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Section: Introductionmentioning

confidence: 99%

Identifying Opportunities for Grade One Children to Acquire Foundational Number Sense: Developing a Framework for Cross Cultural Classroom Analyses

Andrews

Sayers

2014

Early Childhood Educ J

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“…In this case, the ability to recognise and manipulate numbers spatially, through the use of, for example, dice, dominoes and ten-frames, plays a significant role in the development of children's understanding of both number and arithmetic (Hunting, 2003;Mulligan & Mitchelmore, 2009;Van Nes & De Lange, 2007;Van Nes & Van Eerde, 2010). Indeed, research has shown that conceptual subitising can be taught through mathematical tasks that provide structured images of numbers (Clements, 2007;Mulligan et al, 2006), including fingers to represent small numbers (Penner-Wilger et al, 2007).…”

Section: Conceptual Subitisingmentioning

confidence: 99%

“…Significantly, the use of finger strategies increases as socio-economic status increases, justifying targeted interventions Levine et al, 1992) The use of manipulatives, particularly linking blocks, facilitates counting and the identification of errors (Van Nes and Van Eerde, 2010). Thus, the better the connections between different representations the more likely a child is to become arithmetically competent (Mundy and Gilmore, 2009;Richardson, 2004;De Lange, 2007, Van Nes andVan Eerde, 2010). …”

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confidence: 99%

The Role of Conceptual Subitising in the Development of Foundational Number Sense

Sayers

Andrews

Boistrup

2016

Mathematics Education in the Early Years

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INTRODUCTIONOver the last fifteen years since the publication of Clements' (1999) well-known paper, various scholars, particularly in the United states, have been encouraging teachers to attend to the development of young learners' conceptual subitising (See, for example, Clements & Sarama, 2009;Conderman et al., 2014); where conceptual subitising is the ability to recognise quickly and without counting relatively large numerosities by partitioning these large groups into smaller groups that can be individually subitised (Clements & Sarama, 2007;Geary, 2011). Various claims, which we discuss below, have been made with respect to the efficacy of conceptual subitising-focused instruction. In a related vein, our own recent work has focused on a conceptualisation of foundational number sense (FoNS), which we describe as those number-related competences expected of a typical first grade student that require instruction (Back et al., 2014;Andrews & Sayers, 2014a). FoNS is characterised by eight components, which we describe below. The purpose of this paper, drawing on excerpts from grade one lessons taught by a case study teacher in each of Hungary and Sweden, is to examine the extent to which conceptual subitising-focused activities have the propensity to facilitate students' acquisition of the various FoNS components and, in so doing, examine the warrant for their claimed efficacy. WHAT IS SUBITISING?Subitising refers to being instantly and automatically able to recognise small numerosities without having to count (Clements, 1999;Jung et al., 2013;Moeller et al., 2009;Clements & Sarama, 2009). Children as young as three are typically able to subitise numerosities up to three (Fuson, 1988, Moeller et al., 2009), while most adults are able instantly to recognise without counting the numerosity represented by the dots on the face of a die (Jung et al. 2013). This process, innate to all humans, is typically known as perceptual subitising (Gelman & Tucker, 1975) and forms an element of the preverbal number sense we describe below. In short, perceptual subitising is recognizing a numerosity without using other mathematical processes (Clement, 1999). Conceptual subitisingHowever, a second form of subitising, conceptual subitising (Clements, 1999), which is not unrelated to FoNS, has been shown to have considerable implications for teaching and learning. Conceptual subitising relates to how an individual identifies "a whole quantity as the result of recognizing smaller quantities... that make up the whole" (Conderman et al., 2014, p.29). More generally, it can be summarised as the systematic management of perceptually subitised numerosities to facilitate the management of larger numerosities (Obersteiner et al., 2013). For example, when a child is confronted by two dice, one showing three and another showing four, each is perceptually subitised before any sense of seven can emerge.Subitising can be construed as having a synonymity with the spatial structuring of numbers (Battista et al., 1998). In this case, the ability to ...

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“…Before conducted the learning activity, researcher discuss the activity with teacher to help her in preparing the lesson. The role of researcher in the learning activity are to stand by, ask the students some additional questions, to observe the learning activity, to coordinate the activity, and to make last-minute change to the activity that is necessary for providing relevant information for research (Van Nes & Van Eerde, 2010),.…”

Section: Data Collection and Data Analysismentioning

confidence: 99%

“…The video is segmented into clips based on sequences of observed interactions, negotiations and activities that appeared relevant to each didactical episode in the activity (Van Nes & Van Eerde, 2010;Andrews, 2004;Powell, Francisco, & Maher, 2003). During the learning activity, we also make some notes based on some important moments.…”

Section: Data Collection and Data Analysismentioning

confidence: 99%

On Developing Students’ Spatial Visualisation Ability

Risma¹,

Putri²,

Hartono³

2013

IES

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This research aims at studying on how students develop their spatial visualisation abilities. In this paper, one of five activities in an ongoing classroom activity is discussed. This paper documents students' learning activity in exploring the building blocks. The goal of teaching experiment is to support the development of students' spatial visualisation ability and to study about how students visualise and interpret the building blocks. The analysis of the activity is focused on exploring how the building blocks activity develop students' spatial visualisation, various way of students' interpretation and visualisation of building blocks, and how teacher affect the way students visualise and interpret the building blocks. The results of this study show that the building blocks activity supports the development of students' spatial visualisation ability.

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Spatial structuring and the development of number sense: A case study of young children working with blocks

Cited by 22 publications

References 28 publications

Identifying Opportunities for Grade One Children to Acquire Foundational Number Sense: Developing a Framework for Cross Cultural Classroom Analyses

Identifying Opportunities for Grade One Children to Acquire Foundational Number Sense: Developing a Framework for Cross Cultural Classroom Analyses

The Role of Conceptual Subitising in the Development of Foundational Number Sense

On Developing Students’ Spatial Visualisation Ability

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