The approximate number system and mathematics achievement: it's complicated. A thorough investigation of different ANS measures and executive functions in mathematics achievement in children

Coolen, Ilse; Riggs, Kevin J.; Bugler, Myfanwy; Castronovo, Julie

doi:10.1080/20445911.2022.2044338

Cited by 9 publications

(9 citation statements)

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“…They also form a reasonable basis for acquiring proximal prerequisites, such as knowledge of multiplication and division, symbolic proportional reasoning skills or informal fraction knowledge. Beyond WNLE and different spontaneous focusing tendencies, other aspects of basic number processing, such as the approximate number system (ANS), showed low correlations with fraction knowledge previously (Jordan et al, 2013) and seemed not to be strong predictors of formal mathematics learning in secondary education (Coolen et al, 2022; Libertus et al, 2013) so that they are not focused on in the present study.…”

Section: Predictors Of Fraction Knowledgementioning

confidence: 63%

Mathematical knowledge and skills as longitudinal predictors of fraction learning among sixth-grade students.

Schadl,

Ufer

2023

Journal of Educational Psychology

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It is well known that fraction knowledge is relevant for later success in mathematics. However, many students still face difficulties when dealing with fractions. Predictors of fraction knowledge have been widely examined. Systematizing mathematical predictors, whether their predictive contributions are direct or indirectly mediated via other mathematical knowledge and skills, could reveal how mathematics teachers could support students' fraction learning. The present longitudinal study investigates these roles for six mathematical prerequisites of fraction knowledge that differ in their connection to the multiplicative field. N = 363 students' skills regarding six prerequisites were measured at the beginning of Grade 6. For three of these prerequisites ("distal prerequisites," e.g., whole number line estimation), possible indirect effects via one or more of the other three prerequisites ("proximal prerequisites," e.g., symbolic proportional reasoning skills) can be argued. After the systematic introduction of fractions in class, students worked on tests for three central facets of fraction knowledge (knowledge of fraction subconstructs, fraction arithmetic skills, and fraction word problem-solving). All prerequisites predicted later fraction knowledge but in different roles. The three proximal prerequisites directly predicted all facets of fraction knowledge, even when controlling for all other prerequisites. As assumed, the distal prerequisites indirectly predicted all facets of fraction knowledge, with the three proximal prerequisites as mediators. The results extend previous findings on the effects of indirect predictors on fraction learning and highlight their role in building up necessary direct predictors before fraction teaching. Educational Impact and Implications StatementThis study provides evidence that a range of mathematical knowledge and skills is relevant for fraction learning in different roles. Based on the present results, acquiring prerequisites for fraction learning begins early during school and should also be considered via indirect mechanisms. It is essential to ensure several prerequisites directly before introducing fractions in class, particularly more proximal prerequisites such as knowledge of multiplication and division, symbolic proportional reasoning skills, and informal fraction knowledge. If students have problems acquiring these prerequisites, focusing on more distal prerequisites, such as whole number line estimation and different spontaneous focusing tendencies in interventions to support students' fraction learning, might be helpful.

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Section: Predictors Of Fraction Knowledgementioning

confidence: 63%

Mathematical knowledge and skills as longitudinal predictors of fraction learning among sixth-grade students.

Schadl,

Ufer

2023

Journal of Educational Psychology

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“… Soltész et al (2010) looked at different numerical abilities in 4-to-7-year-olds and found that non-symbolic numerical magnitude discrimination did not correlate significantly with verbal counting or arithmetic even during that age range. Coolen et al (2022) gave children two computerized Approximate Number System tasks, two executive function tasks, a verbal skills task, two intelligence subscales, and a mathematics achievement task (involving global, formal, and informal mathematics achievement). Results demonstrated that, when controlling for intelligence and visuospatial memory, the relation between ANS acuity and mathematics achievement ceased to exist.…”

Section: Non-symbolic Magnitude Approximation and Comparisonmentioning

confidence: 99%

The componential nature of arithmetical cognition: some important questions

Dowker

2023

Front. Psychol.

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Research on typically developing children and adults and people with developmental and acquired dyscalculia converges in indicating that arithmetical ability is not unitary but is made up of many different components. Categories of components include non-symbolic quantity representation and processing; symbolic quantity representation and processing; counting procedures and principles; arithmetic operations; arithmetical knowledge and understanding; multiple forms and applications of conceptual knowledge of arithmetic; and domain-general abilities such as attention, executive functions and working memory. There is much evidence that different components can and often do show considerable functional independence, not only in developmental and acquired dyscalculia, but in typically achieving children and adults. At the same time, it is possible to find complex interactions and bidirectional relationships between the different components, including between domain-specific and apparently domain-general abilities. There is a great deal that still needs to be discovered. In particular, we need to learn more about the origins in infancy of subitizing and approximate magnitude comparison, the extent to which these interact, the extent to which they may be further divisible, and the extent and ways in which they themselves may develop with age and the extent to which they may influence later-developing components. There also needs to be a lot more research on exactly how domain-general and domain-specific abilities contribute to mathematical development, and how they interact with one another.

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“…Furthermore, not all studies have replicated a correlation between ANS acuity and mathematics achievement (e.g., Castronovo & Göbel, 2012;Iuculano et al, 2008;Vanbinst et al, 2012). More recently, research found that the nature of the correlation between the ANS and mathematics achievement might change with age, mathematics experience, and the development of other important cognitive precursors of mathematics (Coolen et al, 2022). Indeed, the ANS has been found to be more correlated to informal mathematics achievement and at the start of mathematics learning (Coolen et al, 2022;Libertus et al, 2013).…”

Section: Domain-specific Precursors Of Mathematicsmentioning

confidence: 99%

“…More recently, research found that the nature of the correlation between the ANS and mathematics achievement might change with age, mathematics experience, and the development of other important cognitive precursors of mathematics (Coolen et al, 2022). Indeed, the ANS has been found to be more correlated to informal mathematics achievement and at the start of mathematics learning (Coolen et al, 2022;Libertus et al, 2013). It has therefore been suggested that the importance of domain-general skills gradually increases when mathematical concepts become more complex with the beginning of formal schooling (e.g., Gimbert et al, 2019).…”

Section: Domain-specific Precursors Of Mathematicsmentioning

confidence: 99%

“…This suggests that while approximate arithmetic could be causally related to symbolic arithmetic, this is not necessarily the case for the magnitude comparison task, which is expected to play a bigger role in emerging informal mathematics skills (Libertus et al, 2013). Moreover, some research suggests that tasks measuring nonsymbolic magnitude comparisons and non-symbolic arithmetic are in part separable as they show poor construct validity and both tasks might be measuring different ANS-related skills (Coolen et al, 2022;Gilmore et al, 2011). Indeed, non-symbolic magnitude comparison is expected to be more predictive of early mathematical development for which the acquisition of number concepts is central, while non-symbolic arithmetic is expected to be more predictive of symbolic arithmetic skill acquisition.…”

Section: Domain-specific Precursors Of Mathematicsmentioning

confidence: 99%

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Now you see it, now you don’t - Cognitive skills and their contributions to mathematics across early development

Coolen,

Omont-Lescieux,

Knops

2023

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A broad variety of domain-specific (e.g., non-symbolic magnitude comparison and arithmetic) and domain-general (e.g., spatial skills and inhibition) skills have been identified as precursors to mathematics achievement. However, due to the increasing complexity of mathematics education with age and the associated increase in cognitive demands, it can be assumed that a divergent set of skills is predictive of mathematics achievement at different ages. This cross-sectional study in children aged 3, 5, and 7 years aims at identifying the differential contribution of domain-specific and domain-general contributors to mathematics and delineating their developmental dynamics. Our results reveal a consistent role for non-symbolic magnitude comparison across all age groups, non-symbolic arithmetic starting from the age of 5 years and visuospatial memory only in 5-year-olds. These findings support the notion that mathematics cannot be conceived as a unitary cognitive skill and provide a fine-grained analysis of the cognitive requirements of mathematical skills at different ages. On a more general note, they are in line with the idea that the ANS provides a critical scaffold for the development of mathematical skills but challenge the view that all ANS measures tap into the same underlying process.

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The approximate number system and mathematics achievement: it's complicated. A thorough investigation of different ANS measures and executive functions in mathematics achievement in children

Cited by 9 publications

References 97 publications

Mathematical knowledge and skills as longitudinal predictors of fraction learning among sixth-grade students.

Mathematical knowledge and skills as longitudinal predictors of fraction learning among sixth-grade students.

The componential nature of arithmetical cognition: some important questions

Now you see it, now you don’t - Cognitive skills and their contributions to mathematics across early development

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