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Abreu-Mendoza RA, Powell AB, Renninger KA, Rivera LM, Vulic J, Weimar S, Rosenberg-Lee M. Middle-schoolers' misconceptions in discretized nonsymbolic proportional reasoning explain fraction biases better than their continuous reasoning: Evidence from correlation and cluster analyses. Cogn Psychol 2023; 143:101575. [PMID: 37229979 DOI: 10.1016/j.cogpsych.2023.101575] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2022] [Revised: 04/19/2023] [Accepted: 05/07/2023] [Indexed: 05/27/2023]
Abstract
Early emerging nonsymbolic proportional skills have been posited as a foundational ability for later fraction learning. A positive relation between nonsymbolic and symbolic proportional reasoning has been reported, as well as successful nonsymbolic training and intervention programs enhancing fraction magnitude skills. However, little is known about the mechanisms underlying this relationship. Of particular interest are nonsymbolic representations, which can be in continuous formats that may emphasize proportional relations and in discretized formats that may prompt erroneous whole-number strategies and hamper access to fraction magnitudes. We assessed the proportional comparison skills of 159 middle-school students (mean age = 12.54 years, 43% females, 55% males, 2% other or prefer not to say) across three types of representations: (a) continuous, unsegmented bars, (b) discretized, segmented bars that allowed counting strategies, and (c) symbolic fractions. Using both correlational and cluster approaches, we also examined their relations to symbolic fraction comparison ability. Within each stimulus type, we varied proportional distance, and in the discretized and symbolic stimuli, we also manipulated whole-number congruency. We found that fraction distance across all formats modulated middle-schoolers' performance; however, whole-number information affected discretized and symbolic comparison performance. Further, continuous and discretized nonsymbolic performance was related to fraction comparison ability; however, discretized skills explained variance above and beyond the contributions of continuous skills. Finally, our cluster analyses revealed three nonsymbolic comparison profiles: students who chose the bars with the largest number of segments (whole-number bias), chance-level performers, and high performers. Crucially, students with a whole-number bias profile showed this bias in their fraction skills and failed to show any symbolic distance modulation. Together, our results indicate that the relation between nonsymbolic and symbolic proportional skills may be determined by the (mis)conceptions based on discretized representations, rather than understandings of proportional magnitudes, suggesting that interventions focusing on competence with discretized representations may show dividends for fraction understanding.
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Affiliation(s)
| | - Arthur B Powell
- Department of Urban Education, Rutgers University-Newark, Newark, NJ, United States
| | - K Ann Renninger
- Department of Educational Studies, Swarthmore College, Swarthmore, PA, United States
| | - Luis M Rivera
- Department of Psychology, Rutgers University-Newark, Newark, NJ, United States
| | - John Vulic
- Sydney School of Education and Social Work, The University of Sydney, Australia
| | - Steve Weimar
- 21st Century Partnership for STEM Education, PA, United States
| | - Miriam Rosenberg-Lee
- Department of Psychology, Rutgers University-Newark, Newark, NJ, United States; Behavioral Neuroscience Program Graduate Program, Rutgers University-Newark, Newark, NJ, United States.
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Klein E, Knops A. The two-network framework of number processing: a step towards a better understanding of the neural origins of developmental dyscalculia. J Neural Transm (Vienna) 2023; 130:253-268. [PMID: 36662281 PMCID: PMC10033479 DOI: 10.1007/s00702-022-02580-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/02/2022] [Accepted: 12/23/2022] [Indexed: 01/21/2023]
Abstract
Developmental dyscalculia is a specific learning disorder that persists over lifetime and can have an enormous impact on personal, health-related, and professional aspects of life. Despite its central importance, the origin both at the cognitive and neural level is not yet well understood. Several classification schemas of dyscalculia have been proposed, sometimes together with an associated deficit at the neural level. However, these explanations are (a) not providing an exhaustive framework that is at levels with the observed complexity of developmental dyscalculia at the behavioral level and (b) are largely mono-causal approaches focusing on gray matter deficits. We suggest that number processing is instead the result of context-dependent interaction of two anatomically largely separate, distributed but overlapping networks that function/cooperate in a closely integrated fashion. The proposed two-network framework (TNF) is the result of a series of studies in adults on the neural correlates underlying magnitude processing and arithmetic fact retrieval, which comprised neurofunctional imaging of various numerical tasks, the application of probabilistic fiber tracking to obtain well-defined connections, and the validation and modification of these results using disconnectome mapping in acute stroke patients. Emerged from data in adults, it represents the endpoint of the acquisition and use of mathematical competencies in adults. Yet, we argue that its main characteristics should already emerge earlier during development. Based on this TNF, we develop a classification schema of phenomenological subtypes and their underlying neural origin that we evaluate against existing propositions and the available empirical data.
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Affiliation(s)
- Elise Klein
- LaPsyDÉ, UMR CNRS 8240, Université Paris Cité, La Sorbonne, 46 Rue Saint-Jacques, 75005, Paris, France.
- Leibniz-Institut Fuer Wissensmedien Tuebingen, Tuebingen, Germany.
| | - André Knops
- LaPsyDÉ, UMR CNRS 8240, Université Paris Cité, La Sorbonne, 46 Rue Saint-Jacques, 75005, Paris, France
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Computational complexity explains neural differences in quantifier verification. Cognition 2022; 223:105013. [DOI: 10.1016/j.cognition.2022.105013] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2021] [Revised: 12/29/2021] [Accepted: 01/04/2022] [Indexed: 11/20/2022]
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OUP accepted manuscript. Cereb Cortex 2022; 32:4733-4745. [DOI: 10.1093/cercor/bhab513] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/14/2021] [Revised: 12/15/2021] [Accepted: 12/16/2021] [Indexed: 01/29/2023] Open
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Wortha SM, Bloechle J, Ninaus M, Kiili K, Lindstedt A, Bahnmueller J, Moeller K, Klein E. Neurofunctional plasticity in fraction learning: An fMRI training study. Trends Neurosci Educ 2020; 21:100141. [PMID: 33303106 DOI: 10.1016/j.tine.2020.100141] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/21/2020] [Revised: 08/26/2020] [Accepted: 08/26/2020] [Indexed: 01/05/2023]
Abstract
BACKGROUND Fractions are known to be difficult for children and adults. Behavioral studies suggest that magnitude processing of fractions can be improved via number line estimation (NLE) trainings, but little is known about the neural correlates of fraction learning. METHOD To examine the neuro-cognitive foundations of fraction learning, behavioral performance and neural correlates were measured before and after a five-day NLE training. RESULTS In all evaluation tasks behavioral performance increased after training. We observed a fronto-parietal network associated with number magnitude processing to be recruited in all tasks as indicated by a numerical distance effect. For symbolic fractions, the distance effect on intraparietal activation was only observed after training. CONCLUSION The absence of a distance effect of symbolic fractions before the training could indicate an initially less automatic access to their overall magnitude. NLE training facilitates processing of overall fraction magnitude as indicated by the distance effect in neural activation.
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Affiliation(s)
- Silke M Wortha
- LEAD Graduate School & Research Network, University of Tuebingen, Tuebingen, Germany; Department of Neurology, Universitätsmedizin Greifswald, Greifswald, Germany.
| | - Johannes Bloechle
- Department of Psychiatry and Psychotherapy, University of Tuebingen, Tuebingen, Germany
| | - Manuel Ninaus
- LEAD Graduate School & Research Network, University of Tuebingen, Tuebingen, Germany; Leibniz-Institut für Wissensmedien, Tuebingen, Germany
| | - Kristian Kiili
- Faculty of Education and Culture, Tampere University, Tampere, Finland
| | - Antero Lindstedt
- Faculty of Information Technology and Communication Sciences, Tampere University, Pori, Finland
| | - Julia Bahnmueller
- LEAD Graduate School & Research Network, University of Tuebingen, Tuebingen, Germany; Centre for Mathematical Cognition, School of Science, Loughborough University, United Kingdom
| | - Korbinian Moeller
- LEAD Graduate School & Research Network, University of Tuebingen, Tuebingen, Germany; Leibniz-Institut für Wissensmedien, Tuebingen, Germany; Centre for Mathematical Cognition, School of Science, Loughborough University, United Kingdom; Individual Development and Adaptive Education Center, Frankfurt am Main, Germany
| | - Elise Klein
- Leibniz-Institut für Wissensmedien, Tuebingen, Germany; Université de Paris, LaPsyDÉ, CNRS, Sorbonne Paris Cité, Paris, France
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Kersey AJ, Wakim KM, Li R, Cantlon JF. Developing, mature, and unique functions of the child's brain in reading and mathematics. Dev Cogn Neurosci 2019; 39:100684. [PMID: 31398551 PMCID: PMC6886692 DOI: 10.1016/j.dcn.2019.100684] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2018] [Revised: 07/12/2019] [Accepted: 07/17/2019] [Indexed: 11/07/2022] Open
Abstract
Cognitive development research shows that children use basic "child-unique" strategies for reading and mathematics. This suggests that children's neural processes will differ qualitatively from those of adults during this developmental period. The goals of the current study were to 1) establish whether a within-subjects neural dissociation between reading and mathematics exists in early childhood as it does in adulthood, and 2) use a novel, developmental intersubject correlation method to test for "child-unique", developing, and adult-like patterns of neural activation within those networks. Across multiple tasks, children's reading and mathematics activity converged in prefrontal cortex, but dissociated in temporal and parietal cortices, showing similarities to the adult pattern of dissociation. "Child-unique" patterns of neural activity were observed in multiple regions, including the anterior temporal lobe and inferior frontal gyri, and showed "child-unique" profiles of functional connectivity to prefrontal cortex. This provides a new demonstration that "children are not just little adults" - the developing brain is not only quantitatively different from adults, it is also qualitatively different.
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Affiliation(s)
- Alyssa J Kersey
- Department of Brain and Cognitive Sciences, University of Rochester, Rochester, NY, USA; Department of Psychology, University of Chicago, Chicago, IL, USA.
| | - Kathryn-Mary Wakim
- Neuroscience Graduate Program, University of Rochester Medical Center, Rochester, NY, USA
| | - Rosa Li
- Duke Institute for Brain Sciences, Duke University, Durham, NC, USA
| | - Jessica F Cantlon
- Department of Brain and Cognitive Sciences, University of Rochester, Rochester, NY, USA; Department of Psychology, Carnegie Mellon University, Pittsburgh, PA, USA
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