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Gouet C, Jin W, Naiman DQ, Peña M, Halberda J. Bias and noise in proportion estimation: A mixture psychophysical model. Cognition 2021; 213:104805. [PMID: 34172265 DOI: 10.1016/j.cognition.2021.104805] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/15/2020] [Revised: 06/04/2021] [Accepted: 06/05/2021] [Indexed: 01/29/2023]
Abstract
The importance of proportional reasoning has long been recognized by psychologists and educators, yet we still do not have a good understanding of how humans mentally represent proportions. In this paper we present a psychophysical model of proportion estimation, extending previous approaches. We assumed that proportion representations are formed by representing each magnitude of a proportion stimuli (the part and its complement) as Gaussian activations in the mind, which are then mentally combined in the form of a proportion. We next derived the internal representation of proportions, including bias and internal noise parameters -capturing respectively how our estimations depart from true values and how variable estimations are. Methodologically, we introduced a mixture of components to account for contaminating behaviors (guessing and reversal of responses) and framed the model in a hierarchical way. We found empirical support for the model by testing a group of 4th grade children in a spatial proportion estimation task. In particular, the internal density reproduced the asymmetries (skewedness) seen in this and in previous reports of estimation tasks, and the model accurately described wide variations between subjects in behavior. Bias estimates were in general smaller than by using previous approaches, due to the model's capacity to absorb contaminating behaviors. This property of the model can be of especial relevance for studies aimed at linking psychophysical measures with broader cognitive abilities. We also recovered higher levels of noise than those reported in discrimination of spatial magnitudes and discuss possible explanations for it. We conclude by illustrating a concrete application of our model to study the effects of scaling in proportional reasoning, highlighting the value of quantitative models in this field of research.
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Affiliation(s)
- Camilo Gouet
- Department of Psychological and Brain Sciences, The Johns Hopkins University, Baltimore, MD 21218, USA; Laboratorio de Neurociencias Cognitivas, Escuela de Psicología, Pontificia Universidad Católica de Chile, Avenida Vicuña Mackenna 4860, Macul, Santiago, Chile.
| | - Wei Jin
- Department of Applied Mathematics and Statistics, The Johns Hopkins University, Baltimore, MD 21218, USA.
| | - Daniel Q Naiman
- Department of Applied Mathematics and Statistics, The Johns Hopkins University, Baltimore, MD 21218, USA.
| | - Marcela Peña
- Laboratorio de Neurociencias Cognitivas, Escuela de Psicología, Pontificia Universidad Católica de Chile, Avenida Vicuña Mackenna 4860, Macul, Santiago, Chile.
| | - Justin Halberda
- Department of Psychological and Brain Sciences, The Johns Hopkins University, Baltimore, MD 21218, USA.
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Gouet C, Carvajal S, Halberda J, Peña M. Training nonsymbolic proportional reasoning in children and its effects on their symbolic math abilities. Cognition 2020; 197:104154. [PMID: 31945678 DOI: 10.1016/j.cognition.2019.104154] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/28/2017] [Revised: 12/03/2019] [Accepted: 12/05/2019] [Indexed: 01/29/2023]
Abstract
Our understanding of proportions can be both symbolic, as when doing calculations in school mathematics, or intuitive, as when folding a bed sheet in half. While an understanding of symbolic proportions is crucial for school mathematics, the cognitive foundations of this ability remain unclear. Here we implemented a computerized training game to test a causal link from intuitive (nonsymbolic) to symbolic proportional reasoning and other math abilities in 4th grade children. An experimental group was trained in nonsymbolic proportional reasoning (PR) with continuous extents, and an active control group was trained on a remarkably similar nonsymbolic magnitude comparison. We found that the experimental group improved at nonsymbolic PR across training sessions, showed near transfer to a paper-and-pencil nonsymbolic PR test, transfer to symbolic proportions, and far transfer to geometry. The active control group showed only a predicted far transfer to geometry. In a second experiment, these results were replicated with an independent cohort of children. Overall this study extends previous correlational evidence, suggesting a functional link between nonsymbolic PR on one hand and symbolic PR and geometry on the other.
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Affiliation(s)
- Camilo Gouet
- Laboratorio de Neurociencias Cognitivas, Escuela de Psicología, Pontificia Universidad Católica de Chile, Avenida Vicuña Mackenna 4860, Macul, Santiago, Chile.
| | - Salvador Carvajal
- Laboratorio de Neurociencias Cognitivas, Escuela de Psicología, Pontificia Universidad Católica de Chile, Avenida Vicuña Mackenna 4860, Macul, Santiago, Chile
| | - Justin Halberda
- Department of Psychological and Brain Sciences, The Johns Hopkins University, Baltimore, MD 21218, USA.
| | - Marcela Peña
- Laboratorio de Neurociencias Cognitivas, Escuela de Psicología, Pontificia Universidad Católica de Chile, Avenida Vicuña Mackenna 4860, Macul, Santiago, Chile.
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Gouet C, Gutiérrez Silva CA, Guedes B, Peña M. Cognitive and Neural Effects of a Brief Nonsymbolic Approximate Arithmetic Training in Healthy First Grade Children. Front Integr Neurosci 2018; 12:28. [PMID: 30065636 PMCID: PMC6056658 DOI: 10.3389/fnint.2018.00028] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2018] [Accepted: 06/11/2018] [Indexed: 11/30/2022] Open
Abstract
Recent studies with children and adults have shown that the abilities of the Approximate Number System (ANS), which operates from early infancy and allows estimating the number of elements in a set without symbols, are trainable and transferable to symbolic arithmetic abilities. Here we investigated the brain correlates of these training effects, which are currently unknown. We trained two Groups of first grade children, one in performing nonsymbolic additions with dot arrays (Addition-Group) and another one in performing color comparisons of the same arrays (Color-Group). The training program was computerized, throughout seven sessions and had a pretest-posttest design. To evaluate cognitive gains, we measured math skills before and after the training. To measure the brain changes, we used electroencephalogram (EEG) recordings in the first and the last training sessions. We explored the changes in N1 and P2p, which are two electrophysiological components sensitive to nonsymbolic numeric computations. A passive Control-Group receiving no intervention also had their math skills evaluated. We found that the two training Groups had similarly gain in math skills, suggesting no specific transfer of the nonsymbolic addition training to math skills at the behavioral level. In contrast, at the brain level, we found that only in the Addition-Group the P2p amplitude significantly increased across sessions. Notably, the gain in P2p amplitude positively correlated with the gain in math abilities. Together, our results showed that first graders rapidly gained in math skills by different interventions. However, number-related brain networks seem to be particularly sensitive to nonsymbolic arithmetic training.
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Affiliation(s)
- Camilo Gouet
- Cognitive Neuroscience Laboratory, Pontificia Universidad Católica de Chile, Santiago, Chile
| | - César A Gutiérrez Silva
- Cognitive Neuroscience Laboratory, Pontificia Universidad Católica de Chile, Santiago, Chile.,Department of Neuroscience, King's College of London, London, United Kingdom
| | - Bruno Guedes
- Cognitive Neuroscience Laboratory, Pontificia Universidad Católica de Chile, Santiago, Chile
| | - Marcela Peña
- Cognitive Neuroscience Laboratory, Pontificia Universidad Católica de Chile, Santiago, Chile
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Dresler T, Bugden S, Gouet C, Lallier M, Oliveira DG, Pinheiro-Chagas P, Pires AC, Wang Y, Zugarramurdi C, Weissheimer J. A Translational Framework of Educational Neuroscience in Learning Disorders. Front Integr Neurosci 2018; 12:25. [PMID: 30022931 PMCID: PMC6039789 DOI: 10.3389/fnint.2018.00025] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/14/2017] [Accepted: 05/22/2018] [Indexed: 12/12/2022] Open
Abstract
Neuroimaging has undergone enormous progress during the last two and a half decades. The combination of neuroscientific methods and educational practice has become a focus of interdisciplinary research in order to answer more applied questions. In this realm, conditions that hamper learning success and have deleterious effects in the population - such as learning disorders (LD) - could especially profit from neuroimaging findings. At the moment, however, there is an ongoing debate about how far neuroscientific research can go to inform the practical work in educational settings. Here, we put forward a theoretical translational framework as a method of conducting neuroimaging and bridging it to education, with a main focus on dyscalculia and dyslexia. Our work seeks to represent a theoretical but mainly empirical guide on the benefits of neuroimaging, which can help people working with different aspects of LD, who need to act collaboratively to reach the full potential of neuroimaging. We provide possible ideas regarding how neuroimaging can inform LD at different levels within our multidirectional framework, i.e., mechanisms, diagnosis/prognosis, training/intervention, and community/education. In addition, we discuss methodological, conceptual, and structural limitations that need to be addressed by future research.
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Affiliation(s)
- Thomas Dresler
- LEAD Graduate School & Research Network, University of Tübingen, Tübingen, Germany
- Department of Psychiatry and Psychotherapy, University of Tübingen, Tübingen, Germany
| | - Stephanie Bugden
- Department of Psychology, University of Pennsylvania, Philadelphia, PA, United States
- The Numerical Cognition Lab, Department of Psychology, Brain and Mind Institute, University of Western Ontario, London, ON, Canada
| | - Camilo Gouet
- Laboratorio de Neurociencias Cognitivas, Escuela de Psicología, Pontificia Universidad Católica de Chile, Santiago, Chile
| | - Marie Lallier
- Basque Center on Cognition, Brain and Language, San Sebastián, Spain
| | - Darlene G. Oliveira
- Instituto Presbiteriano Mackenzie, Universidade Presbiteriana Mackenzie, São Paulo, Brazil
| | - Pedro Pinheiro-Chagas
- Cognitive Neuroimaging Unit, Institut National de la Santé et de la Recherche Médicale, Paris, France
- Laboratory of Behavioral and Cognitive Neuroscience, Stanford Human Intracranial Cognitive Electrophysiology Program, Department of Neurology and Neurological Sciences, Stanford University, Stanford, CA, United States
| | - Ana C. Pires
- Centro de Investigación Básica en Psicología, Facultad de Psicología, Universidad de la República, Montevideo, Uruguay
| | - Yunqi Wang
- School of International Studies, Zhejiang University, Hangzhou, China
| | - Camila Zugarramurdi
- Basque Center on Cognition, Brain and Language, San Sebastián, Spain
- Centro de Investigación Básica en Psicología, Facultad de Psicología, Universidad de la República, Montevideo, Uruguay
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