Towards a mathematically more correct understanding of rational numbers: A longitudinal study with upper elementary school learners

Hoof, Jo Van; Degrande, Tine; Ceulemans, Eva; Verschaffel, Lieven; Dooren, Wim Van

doi:10.1016/j.lindif.2017.11.010

Cited by 60 publications

(56 citation statements)

References 26 publications

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“…For instance, measures of inhibition have been shown to predict false-belief understanding, a component of theory of mind [69], and a composite of executive functions tasks have been associated with children’s understanding of vitalist biology (understanding of life, death, and body functions) [70]. Using assessments that tap into conceptual understandings [71,72], future studies could explore more comprehensively the role of executive functions in mathematical knowledge, not only in childhood but in adolescence as well.…”

Section: Discussionmentioning

confidence: 99%

The contributions of executive functions to mathematical learning difficulties and mathematical talent during adolescence

et al. 2018

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Are mathematical learning difficulties caused by impairment of the abilities that underlie mathematical talent? Or are mathematical difficulties and talent qualitatively different? The main goal of this study was to determine whether mathematical learning difficulties are explained by the same executive functions as mathematical talent. We screened a pool of 2,682 first-year high school students and selected 48 for evaluation, dividing them into three groups: those with mathematical learning difficulties (n = 16), those with typical performance (n = 16), and those with mathematical talent (n = 16). Adolescents from the learning difficulties and talented groups had age, reading skills, and verbal and non-verbal intelligence that were similar to those of the typical performance group. Participants were administered a suite of tasks to evaluate verbal and visual short-term memory and executive functions of inhibition, shifting, and updating. Different executive functions showed different contributions at the two ends of the math ability continuum: lower levels of performance in updating visual information were related to mathematical learning difficulties, while greater shifting abilities were related to mathematical talent. Effect sizes for the differences in performance between groups were large (Hedges' g > 0.8). These results suggest that different executive functions are associated with mathematical learning difficulties and mathematical talent. We discuss how these differences in executive functions could be related to the different types of mathematical abilities that distinguish the three groups.

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Section: Discussionmentioning

confidence: 99%

The contributions of executive functions to mathematical learning difficulties and mathematical talent during adolescence

et al. 2018

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“…This NNB in fraction comparison seems to be very persistent. It has been documented in younger and older students (e.g., Van Hoof et al, 2018) as well as in college students (e.g., DeWolf and Vosniadou, 2011), university students (Gómez et al, 2017) and-in some types of problems-even in academic mathematicians (Obersteiner et al, 2013).…”

Section: The Natural Number Bias As a Source Of Individual Errors In mentioning

confidence: 98%

“…Overall, the strong individual differences in NNB patterns suggest that research on the NNB in particular and research on the development of fraction knowledge in general should utilize person-oriented approaches to account for individual differences (see Rinne et al, 2017;Van Hoof et al, 2018;Gómez and Dartnell, 2019;González-Forte et al, 2019).…”

Section: Individual Profiles With and Without A Natural Number Biasmentioning

confidence: 99%

The Interplay Between the Natural Number Bias and Fraction Magnitude Processing in Low-Achieving Students

et al. 2020

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Research has identified two core difficulties many students have with fractions: first, they often struggle with processing fraction magnitudes, and second, they rely on natural number concepts in fraction problems ["Natural Number Bias" (NNB)]. Yet, the relation between these two difficulties is not well-understood. Moreover, while most studies of the NNB relied on analyses of whole samples, there is empirical evidence that the occurrence of the NNB differs between student subgroups. In the present study, we investigate individual students' profiles of the occurrence of the NNB and their ability to process fraction magnitude, using a dynamic assessment that utilizes continuous diagrams on touchscreen devices. We analyze data of 234 low-achieving 6th-grade students from Germany who completed a symbolic fraction comparison task, and a fraction magnitude estimation task with continuous circle and tape diagrams. A cluster analysis on the comparison task revealed three distinct clusters: a Typical Bias cluster (better performance on symbolic fraction comparison items congruent to natural number-based reasoning), a Reverse Bias cluster (better performance on items incongruent to natural number-based reasoning), and a No Bias cluster (similar performance on congruent and incongruent items). Only students in the No Bias cluster but not students in the other clusters demonstrated a distance effect in symbolic fraction comparison, suggesting fraction magnitude processing. Linear mixed models on the percent absolute error in the magnitude estimation task revealed significantly lower percent absolute error for students in the No Bias cluster compared to students in the other two clusters. Students in the No Bias cluster were significantly slower to solve both fraction comparison and fraction magnitude estimation tasks than students in the other clusters. The results of this study suggest that the occurrence of the natural number bias and the ability to process fraction magnitude are closely related. The continuous representations used in our digital assessment tools appeared to be suitable for assessing both the natural number bias and fraction magnitude processing.

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“…Latent variable mixture models are particularly powerful in measuring unseen developmental patterns (e.g. Van Hoof, Degrande, Ceulemans, Verschaffel, & Van Dooren, 2018), and additionally useful in testing the specific effects of educational interventions on learning (e.g. Schneider & Hardy, 2013).…”

Section: Structure Of the Special Issuementioning

confidence: 99%

Latent variable mixture models in research on learning and individual differences

McMullen

Hickendorff

2018

Learning and Individual Differences

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License: Article 25fa pilot End User Agreement This publication is distributed under the terms of Article 25fa of the Dutch Copyright Act (Auteurswet) with explicit consent by the author. Dutch law entitles the maker of a short scientific work funded either wholly or partially by Dutch public funds to make that work publicly available for no consideration following a reasonable period of time after the work was first published, provided that clear reference is made to the source of the first publication of the work. This publication is distributed under The Association of Universities in the Netherlands (VSNU) 'Article 25fa implementation' pilot project. In this pilot research outputs of researchers employed by Dutch Universities that comply with the legal requirements of Article 25fa of the Dutch Copyright Act are distributed online and free of cost or other barriers in institutional repositories. Research outputs are distributed six months after their first online publication in the original published version and with proper attribution to the source of the original publication. You are permitted to download and use the publication for personal purposes. All rights remain with the author(s) and/or copyrights owner(s) of this work. Any use of the publication other than authorised under this licence or copyright law is prohibited. If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons.

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Towards a mathematically more correct understanding of rational numbers: A longitudinal study with upper elementary school learners

Cited by 60 publications

References 26 publications

The contributions of executive functions to mathematical learning difficulties and mathematical talent during adolescence

The contributions of executive functions to mathematical learning difficulties and mathematical talent during adolescence

The Interplay Between the Natural Number Bias and Fraction Magnitude Processing in Low-Achieving Students

Latent variable mixture models in research on learning and individual differences

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