Semantic alignment across whole-number arithmetic and rational numbers: evidence from a Russian perspective

Tyumeneva, Yulia; Larina, Galina; Alexandrova, Ekaterina; DeWolf, Melissa; Bassok, Miriam; Holyoak, Keith J.

doi:10.1080/13546783.2017.1374307

Cited by 10 publications

(11 citation statements)

References 19 publications

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“…A similar form of semantic alignment guides the use of different formats for rational numbers-fractions and decimals. Adults in the U.S. and South Korea (Lee et al, 2016), as well as Russia (Tyumeneva et al, 2018), selectively use fractions and decimals to model discrete (i.e., countable) and continuous entities, respectively. Favored semantic alignments may reflect selective similarities between relation vectors that represent mathematical and real-world relations.…”

Section: Limitations and Future Directionsmentioning

confidence: 99%

Probabilistic analogical mapping with semantic relation networks.

Ichien²,

Holyoak³

2022

Psychological Review

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The human ability to flexibly reason using analogies with domain-general content depends on mechanisms for identifying relations between concepts, and for mapping concepts and their relations across analogs. Building on a recent model of how semantic relations can be learned from nonrelational word embeddings, we present a new computational model of mapping between two analogs. The model adopts a Bayesian framework for probabilistic graph matching, operating on semantic relation networks constructed from distributed representations of individual concepts and of relations between concepts. Through comparisons of model predictions with human performance in a novel mapping task requiring integration of multiple relations, as well as in several classic studies, we demonstrate that the model accounts for a broad range of phenomena involving analogical mapping by both adults and children. We also show the potential for extending the model to deal with analog retrieval. Our approach demonstrates that human-like analogical mapping can emerge from comparison mechanisms applied to rich semantic representations of individual concepts and relations.

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Section: Limitations and Future Directionsmentioning

confidence: 99%

Probabilistic analogical mapping with semantic relation networks.

Ichien²,

Holyoak³

2022

Psychological Review

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“…The alignment between real‐world and mathematical knowledge guides the application of abstract mathematical knowledge by both students and textbook writers, not only in the United States (DeWolf, Bassok, & Holyoak, 2015; Rapp, Bassok, DeWolf, & Holyoak, 2015) but also in South Korea (Lee, DeWolf, Bassok, & Holyoak, 2016) and Russia (Tyumeneva et al, 2018). Importantly, alignments and their influence on problem solving procedures likely remain implicit in the mind of the problem solver, as they are not explicitly taught in schools.…”

Section: An Analogical Approach To Teaching: Five Principlesmentioning

confidence: 99%

Teaching by Analogy: From Theory to Practice

Gray

Holyoak

2021

Mind Brain and Education

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Analogy is a powerful tool for fostering conceptual understanding and transfer in STEM and other fields. Well‐constructed analogical comparisons focus attention on the causal‐relational structure of STEM concepts, and provide a powerful capability to draw inferences based on a well‐understood source domain that can be applied to a novel target domain. However, analogy must be applied with consideration to students' prior knowledge and cognitive resources. We briefly review theoretical and empirical support for incorporating analogy into education, and recommend five general principles to guide its application so as to maximize the potential benefits. For analogies to be effective, instructors should use well‐understood source analogs and explain correspondences fully; use visuospatial and verbal supports to emphasize shared structure among analogs; discuss the alignment between semantic and formal representations; reduce extraneous cognitive load imposed by analogical comparison; and encourage generation of inferences when students have some proficiency with the material. These principles can be applied flexibly to topics in a wide variety of domains.

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“…Further, when judging the correspondence between a given ratio and a given rational number, participants performed best when the notation of the number (fraction or decimal) was the one preferred for the given type of ratio. Subsequent studies obtained similar findings in the United States, Korea, and Russia (Lee et al, 2016;Plummer et al, 2017;Rapp et al, 2015;Tyumeneva et al, 2018). Gray et al (2018) found that performance with percentages is similar to that with decimals, and concluded that the conceptual structure of percentages, like that of decimals, is one-dimensional.…”

Section: Suitability Of Rational Number Notations For Representing Di...mentioning

confidence: 76%

Affordances of fractions and decimals for arithmetic.

Liu¹,

Braithwaite²

2023

Journal of Experimental Psychology: Learning, Memory, and Cogni

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Rational numbers are represented by multiple notations: fractions, decimals, and percentages. Whereas previous studies have investigated affordances of these notations for representing different types of information (DeWolf et al., 2015; Tian et al., 2020), the present study investigated their affordances for solving different types of arithmetic problems. We hypothesized that decimals afford addition better than fractions do and that fractions afford multiplication better than decimals do. This hypothesis was tested in two experiments with university students (Ns = 77 and 80). When solving fraction and decimal arithmetic problems, participants converted addition problems from fraction to decimal form more than vice versa, and converted multiplication problems from decimal to fraction form more than vice versa, thus revealing preferences favoring decimals for addition and fractions for multiplication. Accuracies paralleled these revealed preferences: Addition accuracy was higher with decimals than fractions, whereas multiplication accuracy was higher with fractions than decimals. Variations in notation preferences as a function of the types of operands involved (e.g., equal vs. unequal denominator fractions) were more consistent with an explanation based on adaptive strategy choice (Siegler, 1996) than with one based on semantic interpretations associated with each notation.

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Semantic alignment across whole-number arithmetic and rational numbers: evidence from a Russian perspective

Cited by 10 publications

References 19 publications

Probabilistic analogical mapping with semantic relation networks.

Probabilistic analogical mapping with semantic relation networks.

Teaching by Analogy: From Theory to Practice

Affordances of fractions and decimals for arithmetic.

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