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Matejko AA, Ansari D. The neural association between arithmetic and basic numerical processing depends on arithmetic problem size and not chronological age. Dev Cogn Neurosci 2019; 37:100653. [PMID: 31102959 PMCID: PMC6969316 DOI: 10.1016/j.dcn.2019.100653] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2018] [Revised: 04/16/2019] [Accepted: 04/26/2019] [Indexed: 11/30/2022] Open
Abstract
The intraparietal sulcus (IPS) is thought to be an important region for basic number processing (e.g. symbol-quantity associations) and arithmetic (e.g. addition). Evidence for shared circuitry within the IPS is largely based on comparisons across studies, and little research has investigated number processing and arithmetic in the same individuals. It is also unclear how the neural overlap between number processing and arithmetic is influenced by age and arithmetic problem difficulty. This study investigated these unresolved questions by examining basic number processing (symbol-quantity matching) and arithmetic (addition) networks in 26 adults and 42 children. Number processing and arithmetic elicited overlapping activity in the IPS in children and adults, however, the overlap was influenced by arithmetic problem size (i.e. which modulated the need to use procedural strategies). The IPS was recruited for number processing, and for arithmetic problems more likely to be solved using procedural strategies. We also found that the overlap between number processing and small-problem addition in children was comparable to the overlap between number processing and large-problem addition in adults. This finding suggests that the association between number processing and arithmetic in the IPS is related to the cognitive operation being performed rather than age.
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Affiliation(s)
- Anna A Matejko
- Numerical Cognition Laboratory, Department of Psychology and Brain & Mind Institute, Western University, London, ON, Canada; Center for the Study of Learning, Department of Pediatrics, Building D, Georgetown University, Washington DC, USA.
| | - Daniel Ansari
- Numerical Cognition Laboratory, Department of Psychology and Brain & Mind Institute, Western University, London, ON, Canada.
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Park JY, Cornillie F, van der Maas HLJ, Van Den Noortgate W. A Multidimensional IRT Approach for Dynamically Monitoring Ability Growth in Computerized Practice Environments. Front Psychol 2019; 10:620. [PMID: 30984068 PMCID: PMC6450197 DOI: 10.3389/fpsyg.2019.00620] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/18/2018] [Accepted: 03/06/2019] [Indexed: 11/13/2022] Open
Abstract
Adaptive learning systems have received an increasing attention as they enable to provide personalized instructions tailored to the behaviors and needs of individual learners. In order to reach this goal, it is desired to have an assessment system, monitoring each learner's ability change in real time. The Elo Rating System (ERS), a popular scoring algorithm for paired competitions, has recently been considered as a fast and flexible method that can assess learning progress in online learning environments. However, it has been argued that a standard ERS may be problematic due to the multidimensional nature of the abilities embedded in learning materials. In order to handle this issue, we propose a system that incorporates a multidimensional item response theory model (MIRT) in the ERS. The basic idea is that instead of updating a single ability parameter from the Rasch model, our method allows a simultaneous update of multiple ability parameters based on a compensatory MIRT model, resulting in a multidimensional extension of the ERS ("M-ERS"). To evaluate the approach, three simulation studies were conducted. Results suggest that the ERS that incorrectly assumes unidimensionality has a seriously lower prediction accuracy compared to the M-ERS. Accounting for both speed and accuracy in M-ERS is shown to perform better than using accuracy data only. An application further illustrates the method using real-life data from a popular educational platform for exercising math skills.
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Affiliation(s)
- Jung Yeon Park
- Faculty of Psychology and Educational Sciences, imec–ITEC, KU Leuven, Leuven, Belgium
| | - Frederik Cornillie
- Faculty of Psychology and Educational Sciences, imec–ITEC, KU Leuven, Leuven, Belgium
| | | | - Wim Van Den Noortgate
- Faculty of Psychology and Educational Sciences, imec–ITEC, KU Leuven, Leuven, Belgium
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Li Y, Zhang M, Chen Y, Deng Z, Zhu X, Yan S. Children's Non-symbolic and Symbolic Numerical Representations and Their Associations With Mathematical Ability. Front Psychol 2018; 9:1035. [PMID: 29988580 PMCID: PMC6026675 DOI: 10.3389/fpsyg.2018.01035] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/05/2018] [Accepted: 06/01/2018] [Indexed: 01/29/2023] Open
Abstract
Most empirical evidence supports the view that non-symbolic and symbolic representations are foundations for advanced mathematical ability. However, the detailed development trajectories of these two types of representations in childhood are not very clear, nor are the different effects of non-symbolic and symbolic representations on the development of mathematical ability. We assessed 253 4- to 8-year-old children's non-symbolic and symbolic numerical representations, mapping skills, and mathematical ability, aiming to investigate the developmental trajectories and associations between these skills. Our results showed non-symbolic numerical representation emerged earlier than the symbolic one. Four-year-olds were capable of non-symbolic comparisons but not symbolic comparisons; five-year-olds performed better at non-symbolic comparisons than symbolic comparisons. This performance difference disappeared at age 6. Children at age 6 or older were able to map between symbolic and non-symbolic quantities. However, as children learn more about the symbolic representation system, their advantage in non-symbolic representation disappeared. Path analyses revealed that a direct effect of children's symbolic numerical skills on their math performance, and an indirect effect of non-symbolic numerical skills on math performance via symbolic skills. These results suggest that symbolic numerical skills are a predominant factor affecting math performance in early childhood. However, the influences of symbolic and non-symbolic numerical skills on mathematical performance both declines with age.
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Affiliation(s)
- Yanjun Li
- School of Developmental Psychology, Faculty of Psychology, Beijing Normal University, Beijing, China
- National Innovation Center for Assessment of Basic Education Quality, Beijing Normal University, Beijing, China
| | - Meng Zhang
- Department of Psychology, Rutgers, The State University of New Jersey, New Brunswick, NJ, United States
| | - Yinghe Chen
- School of Developmental Psychology, Faculty of Psychology, Beijing Normal University, Beijing, China
| | - Zhijun Deng
- School of Developmental Psychology, Faculty of Psychology, Beijing Normal University, Beijing, China
| | - Xiaoshuang Zhu
- School of Developmental Psychology, Faculty of Psychology, Beijing Normal University, Beijing, China
| | - Shijia Yan
- China Aerospace Academy of Systems Science and Engineering, Institute of Information Control, China Aerospace Science and Technology Corporation, Beijing, China
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Mutaf Yıldız B, Sasanguie D, De Smedt B, Reynvoet B. Frequency of Home Numeracy Activities Is Differentially Related to Basic Number Processing and Calculation Skills in Kindergartners. Front Psychol 2018; 9:340. [PMID: 29623055 PMCID: PMC5874519 DOI: 10.3389/fpsyg.2018.00340] [Citation(s) in RCA: 32] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2017] [Accepted: 02/28/2018] [Indexed: 11/13/2022] Open
Abstract
Home numeracy has been shown to play an important role in children's mathematical performance. However, findings are inconsistent as to which home numeracy activities are related to which mathematical skills. The present study disentangled between various mathematical abilities that were previously masked by the use of composite scores of mathematical achievement. Our aim was to shed light on the specific associations between home numeracy and various mathematical abilities. The relationships between kindergartners' home numeracy activities, their basic number processing and calculation skills were investigated. Participants were 128 kindergartners (Mage = 5.43 years, SD = 0.29, range: 4.88-6.02 years) and their parents. The children completed non-symbolic and symbolic comparison tasks, non-symbolic and symbolic number line estimation tasks, mapping tasks (enumeration and connecting), and two calculation tasks. Their parents completed a home numeracy questionnaire. Results indicated small but significant associations between formal home numeracy activities that involved more explicit teaching efforts (i.e., identifying numerals, counting) and children's enumeration skills. There was no correlation between formal home numeracy activities and non-symbolic number processing. Informal home numeracy activities that involved more implicit teaching attempts, such as "playing games" and "using numbers in daily life," were (weakly) correlated with calculation and symbolic number line estimation, respectively. The present findings suggest that disentangling between various basic number processing and calculation skills in children might unravel specific relations with both formal and informal home numeracy activities. This might explain earlier reported contradictory findings on the association between home numeracy and mathematical abilities.
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Affiliation(s)
- Belde Mutaf Yıldız
- Brain and Cognition, Faculty of Psychology and Educational Sciences, KU Leuven, Leuven, Belgium
| | - Delphine Sasanguie
- Brain and Cognition, Faculty of Psychology and Educational Sciences, KU Leuven, Leuven, Belgium
- Faculty of Psychology and Educational Sciences, KU Leuven Kulak, Kortrijk, Belgium
| | - Bert De Smedt
- Parenting and Special Education, Faculty of Psychology and Educational Sciences, KU Leuven, Leuven, Belgium
| | - Bert Reynvoet
- Brain and Cognition, Faculty of Psychology and Educational Sciences, KU Leuven, Leuven, Belgium
- Faculty of Psychology and Educational Sciences, KU Leuven Kulak, Kortrijk, Belgium
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Li Y, Zhang M, Chen Y, Zhu X, Deng Z, Yan S. Children's Non-symbolic, Symbolic Addition and Their Mapping Capacity at 4-7 Years Old. Front Psychol 2017; 8:1203. [PMID: 28769845 PMCID: PMC5511823 DOI: 10.3389/fpsyg.2017.01203] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/02/2017] [Accepted: 06/30/2017] [Indexed: 01/29/2023] Open
Abstract
The study aimed to examine the developmental trajectories of non-symbolic and symbolic addition capacities in children and the mapping ability between these two. We assessed 106 4- to 7-year-old children and found that 4-year-olds were able to do non-symbolic addition but not symbolic addition. Five-year-olds and older were able to do symbolic addition and their performance in symbolic addition exceeded non-symbolic addition in grade 1 (approximate age 7). These results suggested non-symbolic addition ability emerges earlier and is less affected by formal mathematical education than symbolic addition. Meanwhile, we tested children's bi-directional mapping ability using a novel task and found that children were able to map between symbolic and non-symbolic representations of number at age 5. Their ability in mapping non-symbolic to symbolic number became more proficient in grade 1 (approximate age 7). This suggests children at age 7 have developed a relatively mature symbolic representation system.
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Affiliation(s)
- Yanjun Li
- Institute of Developmental Psychology, Faculty of Psychology, Bejing Normal UniversityBeijing, China
| | - Meng Zhang
- Department of Psychology, Rutgers, The State University of New Jersey, New BrunswickNJ, United States
| | - Yinghe Chen
- Institute of Developmental Psychology, Faculty of Psychology, Bejing Normal UniversityBeijing, China
| | - Xiaoshuang Zhu
- Institute of Developmental Psychology, Faculty of Psychology, Bejing Normal UniversityBeijing, China
| | - Zhijun Deng
- Institute of Developmental Psychology, Faculty of Psychology, Bejing Normal UniversityBeijing, China
| | - Shijia Yan
- Institute of Information Control, China Aerospace Academy of Systems Science and EngineeringBeijing, China
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