Whole Number Thinking, Learning and Development: Neuro-cognitive, Cognitive and Developmental Approaches

Mulligan, Joanne; Verschaffel, Lieven; Baccaglini-Frank, Anna; Coles, Alf; Gould, Peter; He, Shengqing; Ma, Yunpeng; Milinković, Jasmina; Obersteiner, Andreas; Roberts, Nicole; Sinclair, Nathalie; Wang, Yanling; Shu, Xie; Yang, Der‐Ching

doi:10.1007/978-3-319-63555-2_7

Cited by 7 publications

(4 citation statements)

References 47 publications

(21 reference statements)

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“…Numerical ability refers to knowledge and skills regarding numbers and arithmetic (Andrews & Sayers, 2015; Purpura & Lonigan, 2013), and has been the focus of most research on mathematics in early childhood (Mulligan et al, 2018; Starkey, Klein, & Wakeley, 2004; Verschaffel et al, 2017). It covers several activities with symbolic and non‐symbolic numerosities, including counting, arithmetic, number recognition, and comparison (Andrews & Sayers, 2015; Jordan, Kaplan, Nabors Olah, & Locuniak, 2006; Purpura & Lonigan, 2013).…”

Section: Patterning Numerical Ability and Their Associationmentioning

confidence: 99%

Associations Between Repeating Patterning, Growing Patterning, and Numerical Ability: A Longitudinal Panel Study in 4‐ to 6‐Year Olds

et al. 2021

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The present study aimed to analyze the direction of the associations between repeating patterning, growing patterning, and numerical ability. Participants were 410 children who were annually assessed on their repeating patterning, growing patterning, and numerical ability, at ages 4, 5, and 6 years (i.e., spring 2017, 2018, and 2019). A cross‐lagged panel model identified bidirectional associations between all three abilities from ages 4 to 5 years while taking into account spatial skills. From ages 5 to 6 years, both patterning abilities predicted later numerical ability, but the reverse was no longer true. Associations between performances on both pattern types also disappeared. Results highlight the unique associations between repeating patterning, growing patterning, and numerical ability, above spatial skills.

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Section: Patterning Numerical Ability and Their Associationmentioning

confidence: 99%

Associations Between Repeating Patterning, Growing Patterning, and Numerical Ability: A Longitudinal Panel Study in 4‐ to 6‐Year Olds

et al. 2021

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“…A growing body of research addresses young children's tendency to spontaneously attend to mathematical elements in their environment (Hannula-Sormunen, 2015;Verschaffel, Rathé, Wijns, De Smedt, & Torbeyns, 2018). This research distinguishes between children's spontaneous tendency to think and behave mathematically, and their mathematical ability, i.e., the mathematical knowledge and skills they demonstrate when explicitly guided towards mathematical elements (Mulligan et al, 2018;Verschaffel et al, 2018;Verschaffel, Torbeyns, & De Smedt, 2017). Hannula and Lehtinen (2005) described one such tendency as Spontaneous Focusing On Numerosities (SFON), which is "a separate mental process, one which refers to the child's tendency to spontaneously focus on the aspect of numerosity and utilize his or her enumeration skills in various activity situations" (p. 239).…”

Section: Introductionmentioning

confidence: 99%

“…Researchers have started to explore children's spontaneous tendency to focus on mathematical aspects other than numerosity, including number symbols (SFONS; Rathé, Torbeyns, De Smedt, & Verschaffel, 2019) and quantitative relations (SFOR; Degrande, Verschaffel, & Van Dooren, 2017;McMullen, Hannula-Sormunen, & Lehtinen, 2014). Some researchers suggested the existence of a Spontaneous Focus On Patterns (SFOP) tendency and its role in early mathematical development (Mulligan et al, 2018;Sarama & Clements, 2009;Sharir, Mashal, & Mevarech, 2015;Verschaffel et al, 2018Verschaffel et al, , 2017. The current study focuses on this SFOP concept, which can be described as the tendency to spontaneously look for, notice, or create patterns.…”

Section: Introductionmentioning

confidence: 99%

Are preschoolers who spontaneously create patterns better in mathematics?

Wijns

Smedt

Verschaffel

et al. 2019

Brit J of Edu Psychol

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Background: Early patterning competence has recently been identified as an important precursor of mathematical development. Whereas the focus of this research has been on children's ability regarding repeating patterns, children might also differ in their spontaneous attention to patterns. Aims:The present study aimed to explore four-to five-year olds' Spontaneous Focusing On Patterns (SFOP) and its association with their patterning and mathematical ability. Sample: Participants were 378 children (Mage = 4y10m; 191 boys) from 17 preschools.Methods: SFOP was measured with a construction task in which children had to build a tower with 15 blocks of three different colours. The constructions of the children were grouped into three categories (i.e., pattern, random, and sorting). We additionally SPONTANEOUS CREATION OF PATTERNS 2 administered tasks assessing their patterning ability, mathematical ability, spatial ability, and visuospatial working memory.Results: When building a tower, 37% of the preschoolers spontaneously created a pattern, 49% made a random construction, and 14% sorted the blocks per colour. Preschoolers who spontaneously created a pattern had better patterning and mathematical ability than children in the random group. Group differences in patterning ability and spatial skills accounted for the difference in mathematical ability. Conclusions:The current data suggest that children's spontaneous attention to patterns is an important component of their mathematical ability. Children's spontaneous pattern constructions may provide opportunities to discuss and practice patterns in preschool settings or at home, but more research is required to further analyse the role of SFOP in early mathematical development.

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“…The notion of number sense still lacks a universal interpretation across the communities of cognitive scientists and of mathematics educators, and even within the community of mathematics educators (e.g., Baccaglini-Frank & Maracci, 2015). However, its development is unanimously seen as a necessary condition for gaining arithmetic competence at the early elementary level (Mulligan et al, 2018;Elia, Mulligan, Anderson, Baccaglini-Frank, & Benz, 2018). Moreover, literature from the fields of neuroscience, developmental psychology, and mathematics education agree that a variety of abilities are fundamental for the development of number sense (e.g., Butterworth, 2005;Coles, 2014).…”

Section: The Multiple Faces Of Number Sensementioning

confidence: 99%

Eliciting preschoolers’ number abilities using open, multi-touch environments

Baccaglini-Frank

Carotenuto

Sinclair

2020

ZDM Mathematics Education

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Research has highlighted the potential of digital technology to support the development of children's number sense abilities. However, the main focus of such research has been on apps affording directed interactions, where only one solution strategy is available, and it has targeted mostly cardinality. Little is known, in these terms, about task design and implementation in more open environments where several different solution strategies are available. To explore this direction, we chose to study TouchCounts, an open environment that combines multi-touch affordances with aural, visual and symbolic ones as well.Using tasks that were designed to address different number sense abilities, we experimented with 4-yearold preschoolers. In this paper we present two tasks, their expected potential with respect to strengthening number sense abilities, and analyses of data collected during the preschoolers' interactions with TouchCounts. The analyses reveal that the children used different strategies in response to the two tasks, and that a broad range of abilities related to number sense were elicited, including both cardinality and ordinality. An important contribution of this study is also a theoretical framework capable of identifying children's learning in a multi-touch environment.

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Whole Number Thinking, Learning and Development: Neuro-cognitive, Cognitive and Developmental Approaches

Abstract: The first two authors wrote the chapter with the collaboration of other working group members.

Cited by 7 publications

References 47 publications

Associations Between Repeating Patterning, Growing Patterning, and Numerical Ability: A Longitudinal Panel Study in 4‐ to 6‐Year Olds

Associations Between Repeating Patterning, Growing Patterning, and Numerical Ability: A Longitudinal Panel Study in 4‐ to 6‐Year Olds

Are preschoolers who spontaneously create patterns better in mathematics?

Eliciting preschoolers’ number abilities using open, multi-touch environments

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