The discovery and comparison of symbolic magnitudes

Chen, Dawn; Lu, Hongjing; Holyoak, Keith J.

doi:10.1016/j.cogpsych.2014.01.002

Cited by 16 publications

(25 citation statements)

References 98 publications

(181 reference statements)

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“…The main result of this study is in line with reference point models (see Chen et al, 2014;Dehaene, 1989) and it is relevant for theories in which the congruency between magnitude of the stimulus and direction of the comparison affects the strength of the evidence signal (Leth-Steensen & Marley, 2000;Petrusic et al, 2008).…”

Section: Ddm Decomposition Of Semantic Congruity Effect 90supporting

confidence: 86%

A drift diffusion model account of the semantic congruity effect in a classification paradigm

2017

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The semantic congruity effect refers to the facilitation of judgements (i) when the direction of the comparison of two items coincides with the relative position of the items along the dimension comparison or (ii) when the relative size of a standard and a target stimulus coincides. For example, people are faster in judging 'which is bigger?' for two large items, than judging 'which is smaller?' for two large items (selection paradigm). Also, people are faster in judging a target stimulus as smaller when compared to a small standard, than when compared to a large standard, and vice versa (classification paradigm). We use the Drift Diffusion Model (DDM) to explain the time course of a semantic congruity effect in a classification paradigm. Formal modelling of semantic congruity allows the time course of the decision process to be described, using an established model of decision making. Moreover, although there have been attempts to explain the semantic congruity effect within evidence accumulation models, two possible accounts for the congruity effect have been proposed but their specific predictions have not been compared directly, using a model that could quantitatively account for both; a shift in the starting point of evidence accumulation or a change in the rate at which evidence is accumulated. With our computational investigation we provide evidence for the latter, while controlling for other possible explanations such as a variation in non-decision time or boundary separation, that have not been taken into account in the explanation of this phenomenon. When subjects are required to judge two stimuli that differ on a single contrastive polar continuum (e.g., 'big' vs.'small'), subjects are faster to judge which of the two stimuli is higher on that continuum, when the stimuli are high on that particular dimension, and they are faster to judge which of the two stimuli is lower on that continuum, when the stimuli are low on that particular dimension. Furthermore, when subjects are required to judge whether a target stimulus is bigger or smaller than a standard stimulus, subjects are faster when the relative size of the standard and of the target coincides (see Dehaene, 1989). Dehaene (1989) defined the first paradigm (i.e., chose the bigger/smaller of two stimuli) as a selection paradigm, and the second paradigm (i.e., is the target bigger/smaller than a standard) as a classification paradigm. The result that characterises these two paradigms is referred to as the semantic congruity effect. The semantic congruity effect has been replicated in perceptual and symbolic judgements across different domains, including surface area (Moyer & Bayer,

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Section: Ddm Decomposition Of Semantic Congruity Effect 90supporting

confidence: 86%

A drift diffusion model account of the semantic congruity effect in a classification paradigm

2017

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“…(MATLAB code for the BART model is available at cvl.psych.ucla.edu/BART2code.zip.) An earlier version of this model had the limited function of learning comparative relations (e.g., “larger,” “smarter”) (10, 20, 21). BART takes as inputs feature vectors for pairs of words that constitute positive or negative examples of a semantic relation.…”

Section: Model Of Relation Learningmentioning

confidence: 99%

Emergence of analogy from relation learning

Holyoak

2019

Proc. Natl. Acad. Sci. U.S.A.

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By middle childhood, humans are able to learn abstract semantic relations (e.g., antonym, synonym, category membership) and use them to reason by analogy. A deep theoretical challenge is to show how such abstract relations can arise from nonrelational inputs, thereby providing key elements of a protosymbolic representation system. We have developed a computational model that exploits the potential synergy between deep learning from “big data” (to create semantic features for individual words) and supervised learning from “small data” (to create representations of semantic relations between words). Given as inputs labeled pairs of lexical representations extracted by deep learning, the model creates augmented representations by remapping features according to the rank of differences between values for the two words in each pair. These augmented representations aid in coping with the feature alignment problem (e.g., matching those features that make “love-hate” an antonym with the different features that make “rich-poor” an antonym). The model extracts weight distributions that are used to estimate the probabilities that new word pairs instantiate each relation, capturing the pattern of human typicality judgments for a broad range of abstract semantic relations. A measure of relational similarity can be derived and used to solve simple verbal analogies with human-level accuracy. Because each acquired relation has a modular representation, basic symbolic operations are enabled (notably, the converse of any learned relation can be formed without additional training). Abstract semantic relations can be induced by bootstrapping from nonrelational inputs, thereby enabling relational generalization and analogical reasoning.

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“…The instructional implication is that learning would benefit from teachers and textbooks presenting well-chosen analogies that highlight that the same reasoning applies to DD as to WD problems. Instruction based on structurally sound analogies has often proved effective in improving numerical understanding (e.g., Chen, Lu, & Holyoak, 2014;Opfer & Siegler, 2007;Sullivan & Barner, 2014). The clear parallels between multiplication of a whole number and a rational number between zero and one, and two rational numbers between zero and one, suggest that promoting analogies from the easier to the harder case could improve learning.…”

Section: Implications For Instructionmentioning

confidence: 99%

Conceptual knowledge of decimal arithmetic.

Lortie‐Forgues

Siegler

2017

Journal of Educational Psychology

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In two studies (N's = 55 and 54), we examined a basic form of conceptual understanding of rational number arithmetic, the direction of effect of decimal arithmetic operations, at a level of detail useful for informing instruction. Middle school students were presented tasks examining knowledge of the direction of effects (e.g., "True or false: 0.77 * 0.63 > 0.77), number line estimation of decimal magnitudes, and knowledge of decimal arithmetic procedures. Their confidence in their direction of effect judgments was also assessed. We found (1) most students incorrectly predicted the direction of effect of multiplication and division with decimals below one; (2) this pattern held for students who accurately estimated the magnitudes of individual decimals and correctly executed decimal arithmetic operations; (3) explanations of direction of effect judgments that cited both the arithmetic operation and the numbers' magnitudes were strongly associated with accurate judgments; and (4) judgments were more accurate when multiplication problems involved a whole number and a decimal below one than with two decimals below one. Implications of the findings for instruction are discussed.

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The discovery and comparison of symbolic magnitudes

Cited by 16 publications

References 98 publications

A drift diffusion model account of the semantic congruity effect in a classification paradigm

A drift diffusion model account of the semantic congruity effect in a classification paradigm

Emergence of analogy from relation learning

Conceptual knowledge of decimal arithmetic.

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