Bridging the gap: Fraction understanding is central to mathematics achievement in students from three different continents

Torbeyns, Joke; Schneider, Michael; Xin, Ziqiang; Siegler, Robert S.

doi:10.1016/j.learninstruc.2014.03.002

Cited by 155 publications

(139 citation statements)

References 45 publications

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“…Moreover, as noted earlier, both concurrent and predictive relations are present for symbolic rational and whole numbers between overall mathematics achievement and magnitude knowledge, even after statistically controlling for many relevant variables, and the relations are present in Europe and East Asia as well as North America (e.g. Bailey et al ., ; Hallet, Nunes & Bryant, ; Siegler et al ., ; Torbeyns, Schneider, Xin & Siegler, ).…”

Section: From Whole To Rational Numbersmentioning

confidence: 99%

Magnitude knowledge: the common core of numerical development

Siegler

2016

Developmental Science

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The integrated theory of numerical development posits that a central theme of numerical development from infancy to adulthood is progressive broadening of the types and ranges of numbers whose magnitudes are accurately represented. The process includes four overlapping trends: (1) representing increasingly precisely the magnitudes of non-symbolic numbers, (2) connecting small symbolic numbers to their non-symbolic referents, (3) extending understanding from smaller to larger whole numbers, and (4) accurately representing the magnitudes of rational numbers. The present review identifies substantial commonalities, as well as differences, in these four aspects of numerical development. With both whole and rational numbers, numerical magnitude knowledge is concurrently correlated with, longitudinally predictive of, and causally related to multiple aspects of mathematical understanding, including arithmetic and overall math achievement. Moreover, interventions focused on increasing numerical magnitude knowledge often generalize to other aspects of mathematics. The cognitive processes of association and analogy seem to play especially large roles in this development. Thus, acquisition of numerical magnitude knowledge can be seen as the common core of numerical development. Research highlights• The integrated theory of numerical development posits that the unifying theme of numerical development is children's growing understanding of numerical magnitudes.• The theory focuses on four aspects of numerical development: representing increasingly precisely the magnitudes of non-symbolic numbers, connecting small symbolic numbers to their non-symbolic referents, extending understanding from smaller to larger whole numbers, and accurately representing the magnitudes of rational numbers.• For both whole and rational numbers, knowledge of numerical magnitudes is correlated with, predictive of, and causally related to other crucial aspects of mathematics, including arithmetic and overall math achievement.• Interventions that emphasize acquisition of numerical magnitude knowledge have yielded a broad range of positive effects with both whole and rational numbers.

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Section: From Whole To Rational Numbersmentioning

confidence: 99%

Magnitude knowledge: the common core of numerical development

Siegler

2016

Developmental Science

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194

167

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“…A mature understanding of fractions emerges as children integrate their understanding of fraction magnitudes with their understanding of whole number magnitudes (Siegler et al, 2011; Siegler & Lortie-Forgues, 2014; Torbeyns, Schneider, Xin, & Siegler, 2015). Children with a strong grasp of whole numbers should then be better situated to make this integration than other children.…”

Section: Introductionmentioning

confidence: 99%

Developmental foundations of children’s fraction magnitude knowledge

Mou

Hoard

et al. 2016

Cognitive Development

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The conceptual insight that fractions represent magnitudes is a critical yet daunting step in children’s mathematical development, and the knowledge of fraction magnitudes influences children’s later mathematics learning including algebra. In this study, longitudinal data were analyzed to identify the mathematical knowledge and domain-general competencies that predicted 8th and 9th graders’ (n=122) knowledge of fraction magnitudes and its cross-grade gains. Performance on the fraction magnitude measures predicted 9th grade algebra achievement. Understanding and fluently identifying the numerator-denominator relation in 7th grade emerged as the key predictor of later fraction magnitudes knowledge in both 8th and 9th grades. Competence at using fraction procedures, knowledge of whole number magnitudes, and the central executive contributed to 9th but not 8th graders’ fraction magnitude knowledge, and knowledge of whole number magnitude contributed to cross-grade gains. The key results suggest fluent processing of numerator-denominator relations presages students’ understanding of fractions as magnitudes and that the integration of whole number and fraction magnitudes occurs gradually.

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“…Among the reasons for the widespread use of the task is that studies found correlations between task performance and a wide range of other, more complex and advanced mathematical competence measures (see Siegler, , for a review). For example, number line estimation has been found to correlate with counting (Östergren & Träff, ), arithmetic (Torbeyns, Schneider, Xin, & Siegler, ), and standardized school achievement tests (Ashcraft & Moore, ). In several studies, the correlation remained significant after controlling for potential confounding variables, such as parental income and education, race, ethnicity, working memory, intelligence, reading achievement, nonsymbolic numerical knowledge, proportional reasoning, and arithmetic proficiency (Bailey, Siegler, & Geary, ; Geary, ; Hansen et al., ; Hornung, Schiltz, Brunner, & Martin, ; Jordan et al., ; Östergren & Träff, ; Vukovic et al., ).…”

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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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Bridging the gap: Fraction understanding is central to mathematics achievement in students from three different continents

Cited by 155 publications

References 45 publications

Magnitude knowledge: the common core of numerical development

Magnitude knowledge: the common core of numerical development

Developmental foundations of children’s fraction magnitude knowledge

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

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