The relevance of basic numerical skills for fraction processing: Evidence from cross-sectional data

PLOS ONE RESEARCH ARTICLE The relevance of basic numerical skills for fraction processing: Evidence from crosssectional data Silke M. Wortha ID1,2,3*, Elise Klein4,5, Katharina Lambert1,6, Tanja Dackermann5, Korbinian Moeller1,5,3,7 a1111111111 a1111111111 a1111111111 a1111111111 a1111111111 1 LEAD Graduate School & Research Network, University of Tuebingen, Tuebingen, Germany, 2 Department of Neurology, University Medicine Greifswald, Greifswald, Germany, 3 Centre for Mathematical Cognition, School of Science, Loughborough University, Loughborough, United Kingdom, 4 University of Paris, LaPsyDÉ, CNRS, Paris, France, 5 Leibniz-Institut für Wissensmedien, Tuebingen, Germany, 6 University of Education, Heidelberg, Germany, 7 Individual Development and Adaptive Education Center, Frankfurt am Main, Germany * Abstract OPEN ACCESS Citation: Wortha SM, Klein E, Lambert K, Dackermann T, Moeller K (2023) The relevance of basic numerical skills for fraction processing: Evidence from cross-sectional data. PLoS ONE 18(1): e0281241. https://doi.org/10.1371/journal. pone.0281241 Editor: Paulo F. Carvalho, Carnegie Mellon University, UNITED STATES Received: September 18, 2021 Accepted: January 18, 2023 Published: January 31, 2023 Copyright: © 2023 Wortha et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability Statement: For reasons of data protection, which was restricted by local school authorities prior to the start of the study, data sharing was not covered by the informed consent. Therefore, and due to the sensitive nature of the data collected for this study (on a vulnerable group of children), data will only be shared upon reasonable request. Requests to share the data set can be directed to the Hector Research Institute of Education Sciences and Psychology (Institute Secretariat: ). Recent research indicated that fraction understanding is an important predictor of later mathematical achievement. In the current study we investigated associations between basic numerical skills and students’ fraction processing. We analyzed data of 939 German secondary school students (age range = 11.92 to 18.00 years) and evaluated the determinants of fraction processing considering basic numerical skills as predictors (i.e., number line estimation, basic arithmetic operations, non-symbolic magnitude comparison, etc.). Additionally, we controlled for general cognitive ability, grade level, and sex. We found that multiplication, subtraction, conceptual knowledge, number line estimation, and basic geometry were significantly associated with fraction processing beyond significant associations of general cognitive ability and sex. Moreover, relative weight analysis revealed that addition and approximate arithmetic should also be considered as relevant predictors for fraction processing. The current results provide food for thought that further research should focus on investigating whether recapitulating basic numerical content in secondary school mathematics education can be beneficial for acquiring more complex mathematical concepts such as fractions. Introduction It has been argued that children’s numerical development is driven by the acquisition of basic numerical skills (e.g., [1, 2]). These basic numerical skills are seen as building blocks for later numerical and mathematical achievement. For successful numerical development different basic numerical skills were found to be important: For instance, symbolic and non-symbolic magnitude knowledge (e.g., [3–5]), as well as a spatial representation of magnitudes as described by the metaphor of the mental number line (e.g., [6, 7]), understanding of the placevalue structure of the Arabic number system (e.g., [8, 9]), acquisition of arithmetic fact PLOS ONE | https://doi.org/10.1371/journal.pone.0281241 January 31, 2023 1 / 15 PLOS ONE Funding: This research was funded and is part of the research program „Netzwerk Bildungsforschung“ (Educational Research Network) of the Baden-Württemberg Stiftung provided to K.L. and was additionally partly funded by the LEAD Graduate School & Research Network [GSC1028], a project of the Excellence Initiative of the German federal and state government. There was no additional external funding received for this study. Competing interests: The authors have declared that no competing interests exist. Basic numerical skills and fraction processing knowledge (i.e., multiplication tables; [3]), as well as skills on procedural and conceptual numerical knowledge (e.g., carry operations, or understanding of the relationship between addition and multiplication [10, 11]). Therefore, it comes with no surprise that the mastery of such basic numerical skills predicts not only future numerical skills and mathematical achievement in school (e.g., [6, 8]), but also more general life prospects (i.e., employment rate; e.g., [12–14]). With regard to educational / mathematical achievement, several studies indicated that mastery of certain basic numerical skills were found to be associated with later mathematical achievement: For instance symbolic and non-symbolic magnitude knowledge (e.g., [15–18])and understanding the place-value structure of the Arabic number system [8]. Therefore, basic numerical skills are seen as highly relevant for children’s development of typical numerical and arithmetical capabilities. Moreover, not only basic numerical skills are critical for children’s numerical development, but also the mastery of more advanced mathematical skills like handling fractions and the ability to successfully calculate with fractions are important steps in children’s mathematical development especially in secondary school [19, 20]. Accordingly, there is evidence that students’ fraction knowledge is a valid predictor of their actual but also future math achievement. For instance, [21] found that children’s early understanding of fractions in 5th or 6th grade predicted their later mathematical achievement and knowledge of algebra in high school even when controlling for IQ, reading achievement, working memory, family education and income, and whole number arithmetic knowledge (see also [22, 23]). As such, understanding fractions provides a critical foundation for later algebra learning (e.g., [24]). In addition, several studies investigated the relevance of domain-general and domain-specific skills for fraction magnitude knowledge and fraction arithmetic (e.g., [23, 25–33]). For instance, [25] observed that knowledge of whole number magnitude and arithmetic in 1st grade predicted knowledge of fraction magnitude and arithmetic in middle school (i.e., 7th and 8th grade) even after controlling for general cognitive abilities, parental education, parental income, race, and gender. Interestingly, however neither whole (...truncated)