A comprehensive model of development on the balance-scale task

Dandurand, Frédéric; Shultz, Thomas R.

doi:10.1016/j.cogsys.2013.10.001

Cited by 7 publications

(7 citation statements)

References 83 publications

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“…Nowadays, this has been solved by augmenting the network structure [41]. For instance, a significant set of experiments replicating children' behavior in the balance beam problem [42][43][44] tested several neural network architectures [37,[45][46][47][48][49][50][51][52][53][54].…”

Section: Related Workmentioning

confidence: 99%

Hierarchical growth in neural networks structure: Organizing inputs by Order of Hierarchical Complexity

Leite,

Mota,

Silva

et al. 2023

PLoS ONE

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Several studies demonstrate that the structure of the brain increases in hierarchical complexity throughout development. We tested if the structure of artificial neural networks also increases in hierarchical complexity while learning a developing task, called the balance beam problem. Previous simulations of this developmental task do not reflect a necessary premise underlying development: a more complex structure can be built out of less complex ones, while ensuring that the more complex structure does not replace the less complex one. In order to address this necessity, we segregated the input set by subsets of increasing Orders of Hierarchical Complexity. This is a complexity measure that has been extensively shown to underlie the complexity behavior and hypothesized to underlie the complexity of the neural structure of the brain. After segregating the input set, minimal neural network models were trained separately for each input subset, and adjacent complexity models were analyzed sequentially to observe whether there was a structural progression. Results show that three different network structural progressions were found, performing with similar accuracy, pointing towards self-organization. Also, more complex structures could be built out of less complex ones without substituting them, successfully addressing catastrophic forgetting and leveraging performance of previous models in the literature. Furthermore, the model structures trained on the two highest complexity subsets performed better than simulations of the balance beam present in the literature. As a major contribution, this work was successful in addressing hierarchical complexity structural growth in neural networks, and is the first that segregates inputs by Order of Hierarchical Complexity. Since this measure can be applied to all domains of data, the present method can be applied to future simulations, systematizing the simulation of developmental and evolutionary structural growth in neural networks.

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Section: Related Workmentioning

confidence: 99%

Hierarchical growth in neural networks structure: Organizing inputs by Order of Hierarchical Complexity

Leite,

Mota,

Silva

et al. 2023

PLoS ONE

View full text Add to dashboard Cite

show abstract

“…Before age 14, children do not typically understand the torque rule (Siegler and Chen, 1998 ; Jansen and van der Maas, 2002 ). Children who resolved the conflict problems could have succeeded by intuition (Messer et al, 2008 ; Dandurand and Shultz, 2009 ; Hofman et al, 2015 ). Children seem to be able to solve the problems without being able to verbalize their reasoning (Messer et al, 2008 ).…”

Section: Discussionmentioning

confidence: 99%

Children's (Mis)understanding of the Balance Beam (Online Edition)

Filion

Sirois

2021

Front. Psychol.

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The balance-scale task, proposed by Inhelder and Piaget, illustrates children understanding of weight-distance relationships. Piaget used the clinical interview method in order to investigate children's reasoning. Over the last five decades, Siegler's Rule-Assessment Approach has been used to explain children reasoning in the balance-scale task according to rules children would use to solve the task. However, this approach does not take into account some key perceptual properties of the task. This study evaluates whether different task demands would alter children's errors. Forty children (twenty children aged 4–5 years and twenty children aged 9–10 years) predicted the movement of both arms of 16 balance-scale problems administered online. Nine 4–5-year-olds produced non-plausible responses whereas none of the 9–10-year-olds provided non-plausible responses. These results seem to indicate a basic misunderstanding of the scale from some younger children, one that eludes traditional measures used with this task.

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“…To make the InI approach compatible with the current results, it would be necessary to incorporate some qualitative rule-based effects, as found in the LCMs of both the paper-and-pencil and Math Garden dataset. The work of Dandurand [ 21 , 52 ] already combines RB effects in an InI approach by including an external learning module in which the model is ‘taught’ RIV—the correct rule where the difference is calculated between multiplication of the weights and distance on each side of the fulcrum. This approach is based on the assumption that children might also learn this rule in an educational setting from instruction instead of from their own experience, which makes it an explicit rule.…”

Section: Discussionmentioning

confidence: 99%

“…Computational models from different research traditions have been proposed: production-rule models [ 9 ], decision-tree models [ 16 ], connectionist models [ 7 , 15 , 17 – 19 ] and ACT-R models [ 20 ]. Although the current models all adopt some characteristics of both theoretical positions, there is still no consensus on the best cognitive processes underlying children’s behavior in the balance-scale task [ 21 ].…”

Section: Introductionmentioning

confidence: 99%

“…It is important to note that the rule model underlying RAM is in fact an instantiation of a restricted confirmatory LCM with fixed conditional probabilities [ 30 ]. Recently [ 21 ] demonstrated in a simulation study that the response probabilities of small classes (N = 20) are characterized by high standard errors. This lack of power due to small class probabilities is indeed problematic for parameter estimation in LCMs.…”

Section: Introductionmentioning

confidence: 99%

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The Balance-Scale Task Revisited: A Comparison of Statistical Models for Rule-Based and Information-Integration Theories of Proportional Reasoning

et al. 2015

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We propose and test three statistical models for the analysis of children’s responses to the balance scale task, a seminal task to study proportional reasoning. We use a latent class modelling approach to formulate a rule-based latent class model (RB LCM) following from a rule-based perspective on proportional reasoning and a new statistical model, the Weighted Sum Model, following from an information-integration approach. Moreover, a hybrid LCM using item covariates is proposed, combining aspects of both a rule-based and information-integration perspective. These models are applied to two different datasets, a standard paper-and-pencil test dataset (N = 779), and a dataset collected within an online learning environment that included direct feedback, time-pressure, and a reward system (N = 808). For the paper-and-pencil dataset the RB LCM resulted in the best fit, whereas for the online dataset the hybrid LCM provided the best fit. The standard paper-and-pencil dataset yielded more evidence for distinct solution rules than the online data set in which quantitative item characteristics are more prominent in determining responses. These results shed new light on the discussion on sequential rule-based and information-integration perspectives of cognitive development.

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A comprehensive model of development on the balance-scale task

Cited by 7 publications

References 83 publications

Hierarchical growth in neural networks structure: Organizing inputs by Order of Hierarchical Complexity

Hierarchical growth in neural networks structure: Organizing inputs by Order of Hierarchical Complexity

Children's (Mis)understanding of the Balance Beam (Online Edition)

The Balance-Scale Task Revisited: A Comparison of Statistical Models for Rule-Based and Information-Integration Theories of Proportional Reasoning

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