The Hierarchical Relations Among Mathematical Competencies: From Fundamental Numeracy to Complex Mathematical Skills
Mathematical competencies can be conceptualized as layers of knowledge, with numeracy skills as the foundational core and more complex mathematical skills as the additional layers over the core. In this study, we tested an expanded hierarchical symbol integration (HSI) model by examining the hierarc...
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| Published in | Canadian journal of experimental psychology Vol. 77; no. 4; pp. 284 - 295 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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Canada
Educational Publishing Foundation
01.12.2023
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| Subjects | |
| Online Access | Get full text |
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| Abstract | Mathematical competencies can be conceptualized as layers of knowledge, with numeracy skills as the foundational core and more complex mathematical skills as the additional layers over the core. In this study, we tested an expanded hierarchical symbol integration (HSI) model by examining the hierarchical relations among mathematical skills. Undergraduate students (N = 236) completed order judgement, simple arithmetic, fraction arithmetic, algebra, and verbal working memory tasks. In a series of hierarchical multiple regressions, we found support for the hierarchical model: Additive skills (i.e., addition and subtraction) predicted unique variance in multiplicative skills (i.e., multiplication and division); multiplicative skills predicted unique variance in fraction arithmetic; and fraction skills predicted unique variance in algebra. These results support the framework of the HSI model in which mathematical competencies are related hierarchically, capturing the increasing complexity of symbolic mathematical skills.
Les compétences mathématiques peuvent être conceptualisées comme des couches de connaissances, les compétences en numératie constituant le noyau de base et les compétences mathématiques plus complexes étant les couches supplémentaires enveloppant le noyau. Dans cette étude, nous avons testé un modèle élargi d'intégration hiérarchique des symboles (HSI) en examinant les relations hiérarchiques entre les compétences mathématiques. Des étudiants de premier cycle (N = 236) ont effectué des tâches de jugement d'ordre, d'arithmétique simple, d'arithmétique fractionnaire, d'algèbre et de mémoire de travail verbale. Une série de régressions multiples hiérarchiques a permis de confirmer le modèle hiérarchique : les compétences additives (c'est-à-dire l'addition et la soustraction) prédisent une variance unique dans les compétences multiplicatives (c'est-à-dire la multiplication et la division); les compétences multiplicatives prédisent une variance unique dans l'arithmétique fractionnaire; et les compétences fractionnaires prédisent une variance unique dans l'algèbre. Ces résultats soutiennent le cadre du modèle HSI dans lequel les compétences mathématiques sont liées de manière hiérarchique, ce qui permet de saisir la complexité croissante des compétences mathématiques symboliques.
Public Significance Statement
In this study, we test a hierarchical model of mathematics skills and find that adults' addition and subtraction skills predict their multiplication and division skills, their multiplication and division skills predict their fraction performance, and fraction performance predicts algebra. These findings support the value of learners developing strong foundational skills in mathematics to support success in more advanced mathematics skills. |
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| AbstractList | Mathematical competencies can be conceptualized as layers of knowledge, with numeracy skills as the foundational core and more complex mathematical skills as the additional layers over the core. In this study, we tested an expanded hierarchical symbol integration (HSI) model by examining the hierarchical relations among mathematical skills. Undergraduate students (N = 236) completed order judgement, simple arithmetic, fraction arithmetic, algebra, and verbal working memory tasks. In a series of hierarchical multiple regressions, we found support for the hierarchical model: Additive skills (i.e., addition and subtraction) predicted unique variance in multiplicative skills (i.e., multiplication and division); multiplicative skills predicted unique variance in fraction arithmetic; and fraction skills predicted unique variance in algebra. These results support the framework of the HSI model in which mathematical competencies are related hierarchically, capturing the increasing complexity of symbolic mathematical skills.
Les compétences mathématiques peuvent être conceptualisées comme des couches de connaissances, les compétences en numératie constituant le noyau de base et les compétences mathématiques plus complexes étant les couches supplémentaires enveloppant le noyau. Dans cette étude, nous avons testé un modèle élargi d'intégration hiérarchique des symboles (HSI) en examinant les relations hiérarchiques entre les compétences mathématiques. Des étudiants de premier cycle (N = 236) ont effectué des tâches de jugement d'ordre, d'arithmétique simple, d'arithmétique fractionnaire, d'algèbre et de mémoire de travail verbale. Une série de régressions multiples hiérarchiques a permis de confirmer le modèle hiérarchique : les compétences additives (c'est-à-dire l'addition et la soustraction) prédisent une variance unique dans les compétences multiplicatives (c'est-à-dire la multiplication et la division); les compétences multiplicatives prédisent une variance unique dans l'arithmétique fractionnaire; et les compétences fractionnaires prédisent une variance unique dans l'algèbre. Ces résultats soutiennent le cadre du modèle HSI dans lequel les compétences mathématiques sont liées de manière hiérarchique, ce qui permet de saisir la complexité croissante des compétences mathématiques symboliques.
Public Significance Statement
In this study, we test a hierarchical model of mathematics skills and find that adults' addition and subtraction skills predict their multiplication and division skills, their multiplication and division skills predict their fraction performance, and fraction performance predicts algebra. These findings support the value of learners developing strong foundational skills in mathematics to support success in more advanced mathematics skills. Mathematical competencies can be conceptualized as layers of knowledge, with numeracy skills as the foundational core and more complex mathematical skills as the additional layers over the core. In this study, we tested an expanded (HSI) model by examining the hierarchical relations among mathematical skills. Undergraduate students ( = 236) completed order judgement, simple arithmetic, fraction arithmetic, algebra, and verbal working memory tasks. In a series of hierarchical multiple regressions, we found support for the hierarchical model: Additive skills (i.e., addition and subtraction) predicted unique variance in multiplicative skills (i.e., multiplication and division); multiplicative skills predicted unique variance in fraction arithmetic; and fraction skills predicted unique variance in algebra. These results support the framework of the HSI model in which mathematical competencies are related hierarchically, capturing the increasing complexity of symbolic mathematical skills. (PsycInfo Database Record (c) 2023 APA, all rights reserved). Mathematical competencies can be conceptualized as layers of knowledge, with numeracy skills as the foundational core and more complex mathematical skills as the additional layers over the core. In this study, we tested an expanded hierarchical symbol integration (HSI) model by examining the hierarchical relations among mathematical skills. Undergraduate students (N = 236) completed order judgement, simple arithmetic, fraction arithmetic, algebra, and verbal working memory tasks. In a series of hierarchical multiple regressions, we found support for the hierarchical model: Additive skills (i.e., addition and subtraction) predicted unique variance in multiplicative skills (i.e., multiplication and division); multiplicative skills predicted unique variance in fraction arithmetic; and fraction skills predicted unique variance in algebra. These results support the framework of the HSI model in which mathematical competencies are related hierarchically, capturing the increasing complexity of symbolic mathematical skills. (PsycInfo Database Record (c) 2023 APA, all rights reserved).Mathematical competencies can be conceptualized as layers of knowledge, with numeracy skills as the foundational core and more complex mathematical skills as the additional layers over the core. In this study, we tested an expanded hierarchical symbol integration (HSI) model by examining the hierarchical relations among mathematical skills. Undergraduate students (N = 236) completed order judgement, simple arithmetic, fraction arithmetic, algebra, and verbal working memory tasks. In a series of hierarchical multiple regressions, we found support for the hierarchical model: Additive skills (i.e., addition and subtraction) predicted unique variance in multiplicative skills (i.e., multiplication and division); multiplicative skills predicted unique variance in fraction arithmetic; and fraction skills predicted unique variance in algebra. These results support the framework of the HSI model in which mathematical competencies are related hierarchically, capturing the increasing complexity of symbolic mathematical skills. (PsycInfo Database Record (c) 2023 APA, all rights reserved). Mathematical competencies can be conceptualized as layers of knowledge, with numeracy skills as the foundational core and more complex mathematical skills as the additional layers over the core. In this study, we tested an expanded hierarchical symbol integration (HSI) model by examining the hierarchical relations among mathematical skills. Undergraduate students ( N = 236) completed order judgement, simple arithmetic, fraction arithmetic, algebra, and verbal working memory tasks. In a series of hierarchical multiple regressions, we found support for the hierarchical model: Additive skills (i.e., addition and subtraction) predicted unique variance in multiplicative skills (i.e., multiplication and division); multiplicative skills predicted unique variance in fraction arithmetic; and fraction skills predicted unique variance in algebra. These results support the framework of the HSI model in which mathematical competencies are related hierarchically, capturing the increasing complexity of symbolic mathematical skills. (PsycInfo Database Record (c) 2024 APA, all rights reserved) (Source: journal abstract) |
| Author | LeFevre, Jo-Anne Xu, Chang Di Lonardo Burr, Sabrina |
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| Keywords | symbol integration arithmétique mathematics algèbre intégration de symboles mathématiques arithmetic algebra fractions |
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| Title | The Hierarchical Relations Among Mathematical Competencies: From Fundamental Numeracy to Complex Mathematical Skills |
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