Pathways to fraction learning: Numerical abilities mediate the relation between early cognitive competencies and later fraction knowledge

Ye, Ai; Resnick, Ilyse; Hansen, Nicole; Rodrigues, Jessica; Rinne, Luke; Jordan, Nancy C.

doi:10.1016/j.jecp.2016.08.001

Cited by 40 publications

(48 citation statements)

References 54 publications

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“…For nonsymbolic comparison, two smaller meta‐analyses found similar correlations (Chen & Li, ; Fazio, Bailey, Thompson, & Siegler, ). Empirical studies (Hansen et al., ; Ye et al., ) and a recent qualitative review of the literature (Schneider, Thompson, & Rittle‐Johnson, ) suggested that the correlation with mathematical competence might be stronger for number line estimation than for magnitude comparison, but this has not been tested meta‐analytically so far. In the following section, we review variables that might moderate the correlation found with the number line estimation task in the current meta‐analysis.…”

Section: Magnitude Comparison As Benchmarkmentioning

confidence: 99%

Associations of Number Line Estimation With Mathematical Competence: A Meta‐analysis

et al. 2018

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The number line estimation task is widely used to investigate mathematical learning and development. The present meta-analysis statistically synthesized the extensive evidence on the correlation between number line estimation and broader mathematical competence. Averaged over 263 effect sizes with 10,576 participants with sample mean ages from 4 to 14 years, this correlation was r = .443. The correlation increased with age, mainly because it was higher for fractions than for whole numbers. The correlation remained stable across a wide range of task variants and mathematical competence measures (i.e., counting, arithmetic, school achievement). These findings demonstrate that the task is a robust tool for diagnosing and predicting broader mathematical competence and should be further investigated in developmental and experimental training studies.

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Section: Magnitude Comparison As Benchmarkmentioning

confidence: 99%

Associations of Number Line Estimation With Mathematical Competence: A Meta‐analysis

et al. 2018

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“…In children, other non-symbolic ratio tasks, such as proportional reasoning or fraction number line estimation, predict later conceptual and procedural fraction knowledge (Hansen et al, 2015;Jordan et al, 2013;Möhring, Newcombe, Levine, & Frick, 2015;Ye et al, 2016) as well as other formal mathematical abilities, such as performance on a standardized mathematics assessment (Resnick et al, 2016). Together, these findings support the idea that the neurocognitive architecture that processes non-symbolic ratios is related to formal, symbolic rational number processing and other forms of mathematical reasoning, but do not provide direct evidence that symbolic fractions elicit an analog internal magnitude representation in children.…”

Section: Architectures For Number Processingmentioning

confidence: 99%

Symbolic fractions elicit an analog magnitude representation in school-age children

Kalra

Binzak

Matthews

et al. 2020

Journal of Experimental Child Psychology

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A fundamental question about fractions is whether they are grounded in an abstract nonsymbolic magnitude code, similar to those postulated for whole numbers. Mounting evidence suggests that symbolic fractions could be grounded in mechanisms for perceiving non-symbolic ratio magnitudes. However, systematic examination of such mechanisms in children has been lacking. We asked second and fifth grade children (prior to and after formal instructions with fractions, respectively) to compare pairs of symbolic fractions, non-symbolic ratios and mixed symbolic/non-symbolic pairs. This paradigm allowed us to test three key questions: 1) whether children show an analog magnitude code for rational numbers, 2) whether that code is compatible with mental representations of symbolic fractions, and 3) how formal education with fractions affects the symbolic-non-symbolic relation. We examined distance effects as a marker of analog ratio magnitude processing and notation effects as a marker of converting across numerical codes. Second and fifth grade children's response times and error rates showed classic distance and notation effects. Non-symbolic ratios were processed most efficiently, with mixed and symbolic notations being relatively slower. Children with more formal instruction in symbolic fractions had a significant advantage in comparing symbolic fractions, but a smaller advantage for non-symbolic ratio stimuli. Supplemental analyses showed that second graders relied on numerator distance more than holistic distance, and fifth graders relied on holistic fraction magnitude distance more than numerator distance. These results suggest that children have a non-symbolic ratio magnitude code, and that symbolic fractions can be translated into that magnitude code.

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“…Additional spatial skills may also be involved. As noted previously, proportional reasoning (Ye et al, 2016) and VSWM (Geary et al, 2007) have also been linked to number line estimation skill. Proportional reasoning may contribute to a proportion judgment strategy, and VSWM may help children to recall locations on number lines they have encountered in school.…”

Section: )mentioning

confidence: 54%

“…In fact, there is evidence that mature performance on a symbolic number line task involves proportion judgments that are biased toward the center of salient categories (such as halves or quarters of the number line), similar to proportion judgments in non-symbolic, visual tasks . Consistent with this, fifth-graders' non-symbolic proportional reasoning skills loaded onto the same factor as number line estimation (Ye, Resnick, Hansen, Rodrigues, Rinne & Jordan, 2016). If proportional reasoning helps children's number line estimation, this may in turn benefit their numeracy skills more broadly.…”

Section: Proportional Reasoning and Spatial Scalingmentioning

confidence: 55%

Spatial Skills, Reasoning, and Mathematics

Newcombe¹,

Booth²,

Gunderson³

2019

The Cambridge Handbook of Cognition and Education

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Chapter for the Cambridge Handbook on Cognition and EducationModern technological societies are built on a foundation of mathematics. We could not have extensive trade without book-keeping-we would be stuck with a barter system. We could not build our long bridges without calculation --we would still be relying on ferries to cross bodies of water. We have made impressive improvements in agricultural science in the past century based in part on experiments using the statistics of "split plots". The examples could be multiplied but the lesson is clear. Given the importance of numeracy, there is good reason for educational systems to strive to teach mathematics effectively. Even though many children in contemporary schools succeed in learning to calculate, many others struggle or progress slowly, and even more never achieve the levels required for full participation in our technological society. There are many reasons for this situation, and many proposed remedies. One potential way to improve mathematics education involves harvesting our growing understanding of how human minds and brains process quantitative information, and how these processes develop.

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Pathways to fraction learning: Numerical abilities mediate the relation between early cognitive competencies and later fraction knowledge

Cited by 40 publications

References 54 publications

Associations of Number Line Estimation With Mathematical Competence: A Meta‐analysis

Associations of Number Line Estimation With Mathematical Competence: A Meta‐analysis

Symbolic fractions elicit an analog magnitude representation in school-age children

Spatial Skills, Reasoning, and Mathematics

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