Learning correspondences between magnitudes, symbols and words: Evidence for a triple code model of arithmetic development

Heron-Delaney, Michelle; Burgoyne, Kelly; Hulme, Charles

doi:10.1016/j.cognition.2018.11.016

Cited by 29 publications

(30 citation statements)

References 47 publications

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“…While present in infancy (Xu & Spelke, 2000), approximate representations of numerosities increase in precision into adulthood (Halberda & Feigenson, 2008). Although the ability to discriminate between quantities is considered a primitive system shared by humans and nonhuman animals (e.g., Brannon, 2002; Cantlon & Brannon, 2006), the development of culturally specific verbal number systems allows for these imprecise ANS representations to be mapped onto exact symbolic representations (e.g., “eight” or 8; Dehaene & Cohen, 1995; Gilmore, Attridge, & Inglis, 2011; Malone, Heron-Delaney, Burgoyne, & Hulme, 2019; Núñez, 2017). In turn, this exact number system provides the foundation for precise arithmetical calculations.…”

Section: The Approximate Number System and Non-verbal Numerosity Repr...mentioning

confidence: 99%

Number knowledge and the approximate number system are two critical foundations for early arithmetic development.

Hulme

Burgoyne

Hulme

2020

Journal of Educational Psychology

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We assessed a range of theoretically critical predictors (numerosity discrimination, number knowledge, counting, language, executive function and finger gnosis) of early arithmetic development in a large unselected sample of 569 children at school entry. Assessments were repeated 12 months later. Although all predictors (except finger gnosis) were moderate to strong correlates of arithmetic, a latent variable path model showed that only number knowledge and numerosity discrimination were unique predictors of arithmetic development over the 1st year of formal education. These findings are consistent with the Triple Code Model (Dehaene & Cohen, 1995) suggesting that both nonsymbolic representations of numerosity and visual symbolic representations of number are critical for the development of arithmetic. Our results suggest that the assessment of numerosity judgments and Arabic number knowledge at school entry may be useful for identifying children at risk of difficulties in acquiring arithmetic skills.

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Section: The Approximate Number System and Non-verbal Numerosity Repr...mentioning

confidence: 99%

Number knowledge and the approximate number system are two critical foundations for early arithmetic development.

Hulme

Burgoyne

Hulme

2020

Journal of Educational Psychology

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“…visuospatial skills (Butterworth 2005); mental number line precision (Praet & Desoete, 2014;Reeve, Paul, & Butterworth, 2015); innate number competence (Duncan et al, 2007;Jordan, Kaplan, Ramineni, & Locuniak, 2009); counting skills (Jordan et al, 2007;Muldoon, Towse, Simms, Perra, & Menzies, 2013); and linguistic skills (Praet, Titeca, Ceulemans, & Desoete, 2013 Support for the triple code model has however been found in recent studies Malone, Heron-Delaney, Burgoyne, & Hulme, 2019). A latent variable path model showed that early number knowledge and numerosity discrimination were unique predictors of arithmetical development , and another study showed that tasks involving mapping magnitudes onto verbal or visual stimuli predicted arithmetic performance over and beyond predictors such as age and IQ (Malone, Heron-Delaney, et al, 2019). Arabic digits.…”

Section: The Triple Code Model Of Numerical Processingmentioning

confidence: 99%

“…Thus, to examine the ANS hypothesis, we need to look at longitudinal studies and intervention studies. As for longitudinal studies, some show support for this hypothesis (Chu, vanMarle, & Geary, 2016;Halberda et al, 2008;Malone, Heron-Delaney, et al, 2019;Toll, Van Viersen, Kroesbergen, & Van Luit, 2015). However, these results are inconclusive.…”

Section: Components Of Early Numeracy Skillsmentioning

confidence: 99%

Validation of an Early Numeracy Screener for First Graders

Lopez-Pedersen

Mononen

Korhonen

et al. 2020

Scandinavian Journal of Educational Research

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The development of well-functioning numeracy skills is a foundation for further mathematical skills. Mathematical skills develop in a cumulative fashion, and to help children establish these skills, we need to better understand how they in fact develop, how to identify children who are at risk of developing mathematical learning difficulties, and last but not least how we can help remedy these difficulties. To better understand and ultimately support these children, we need to apply different methods and research designs. We need to make sure we raise questions that are detailed enough in order to avoid brevity, and help to answer the major question which iswhich are the most important skills to help children who struggle in mathematics? Which particular skills might be more relevant to be assessed in order to identify children who are at risk of developing mathematical learning difficulties? The first study examined the developmental relationship between the approximate number system and early mathematical skills, in two different datasets. The main objective was to further investigate the theory that the approximate number system has a potential casual influence on mathematical development. First, we reanalyzed the dataset from a recent study by Elliott, Feigenson, Halberda, and Libertus (2019). Using cross-lagged panel model Elliott et al. (2019) claimed a reciprocal relationship between the approximate number system and early mathematics, however when reanalyzing this dataset by using a novel methodological approach, a random-intercept cross-lagged panel model, no evidence of a reciprocal relationship was found. Second, in a 1-year longitudinal study with three time points we examined the developmental relationship of the approximate number system and addition skills with the same methodological approach as in the reanalysis of Elliott et al.'s (2019) data. Here, the results did not show any evidence supporting a reciprocal relationship between the approximate number system and mathematical development either. Combined, this questions the idea that the approximate number system plays a vital role in the development of early mathematics, and vice versa. Moreover, this study displayed how different methodological approaches lead to different results. The second study is a validation study. The psychometric properties of the Early Numeracy Screener that was developed from a theoretical model, the core numerical skills model by Aunio and Räsänen (2016). The Early Numeracy Screener aims to detect children who are at risk of developing mathematical learning difficulties later on, and furthermore aims to identify three sets of early numeracy skills; namely counting skills, numerical relational skills, and basic arithmetic skills. Confirmatory factor analysis found evidence for a never getting tired of watching Harry Potter with me. To paraphrase Bess Streeter Aldrich, there is neither subtraction nor division in my love for you, only addition and multiplication.

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“…For this, the system collects learners’ emotional cues (e.g., brainwaves) and analyses the data to provide the students with the best-fitted teaching materials according to their skills, requirements, characteristics and capacities (Shao et al, 2019 ). In other words, they aim to keep the learners connected and engaged and enhance their attention and satisfaction during lectures (Malone et al, 2019 ). They have the capacity to offer T&L several benefits -mainly support diversity and inclusion.…”

Section: Introductionmentioning

confidence: 99%