How abstract is symbolic thought?

Landy, David; Goldstone, Robert L.

doi:10.1037/0278-7393.33.4.720

Cited by 153 publications

(178 citation statements)

References 56 publications

Supporting

Mentioning

153

Contrasting

Unclassified

Order By: Relevance

“…This pattern of alignments suggests that people view the symbolic notations of rational numbers as either discrete (fractions) or continuous (decimals). Although this hypothesis has yet to be tested directly (e.g., by asking people to select continuous or discrete representations for numbers without specifying their units), it is consistent with recent work showing the impact of notational tools on mathematical reasoning (Braithwaite & Goldstone, 2013;Fisher, Borchert, & Bassok, 2011;Landy & Goldstone, 2007;Zahner & Corter, 2010).…”

Section: Discussionsupporting

confidence: 77%

Modeling discrete and continuous entities with fractions and decimals.

Rapp¹,

Bassok²,

DeWolf³

et al. 2015

Journal of Experimental Psychology: Applied

View full text Add to dashboard Cite

When people use mathematics to model real-life situations, their use of mathematical expressions is often mediated by semantic alignment (Bassok, Chase, & Martin, 1998): The entities in a problem situation evoke semantic relations (e.g., tulips and vases evoke the functionally asymmetric “contain” relation), which people align with analogous mathematical relations (e.g., the noncommutative division operation, tulips/vases). Here we investigate the possibility that semantic alignment is also involved in the comprehension and use of rational numbers (fractions and decimals). A textbook analysis and results from two experiments revealed that both mathematic educators and college students tend to align the discreteness versus continuity of the entities in word problems (e.g., marbles vs. distance) with distinct symbolic representations of rational numbers—fractions versus decimals, respectively. In addition, fractions and decimals tend to be used with nonmetric units and metric units, respectively. We discuss the importance of the ontological distinction between continuous and discrete entities to mathematical cognition, the role of symbolic notations, and possible implications of our findings for the teaching of rational numbers.

show abstract

Section: Discussionsupporting

confidence: 77%

Modeling discrete and continuous entities with fractions and decimals.

Rapp¹,

Bassok²,

DeWolf³

et al. 2015

Journal of Experimental Psychology: Applied

View full text Add to dashboard Cite

show abstract

“…In our study, instead of content (e.g., objects, story line) the surface cue was the format of the algebraic equations. In some respects, college students' tendency to follow the linear layout of standard-form algebraic models (i.e., engage in direct translation of word to equations) is similar to recent findings of Landy and Goldstone (2007). These researchers found that the physical layout of algebraic equations affects the way college students apply a well-known mathematical rule.…”

Section: Discussionsupporting

confidence: 73%

Following the standard form: Effects of equation format on algebraic modeling

2010

View full text Add to dashboard Cite

When people construct algebraic equations to represent quantitative relations, they often reverse the roles of the variables (6S = P instead of 6P = S). Results from three experiments show that a major reason for such reversal errors is people's adherence to, and interpretation of, the Standard Form of algebraic models. College students constructed, selected, and interpreted algebraic models that either had the standard multiplication format (MF: ax = y), or the mathematically equivalent division format (DF: y/a = x). A large minority of participants constructed reversed MF models, whereas most participants who were instructed to use DF equations constructed correct models (Experiment 1). Most participants understood that MF and DF models of the same relation should be mathematically equivalent (Experiment 2), but they drew a conceptual distinction between these models (Experiment 3). The authors discuss the impact of notational conventions on people's interpretation and use of representational tools.

show abstract

“…No such difference, however, was found for students who has been taught algebra with a representation system which eliminated these saliency features. Complementary results were published by Landy and Goldstone (2007), who found that the internal spacing of algebraic expressions can affect their opaqueness/transparency.…”

Section: The Affirmative Premise Effectsupporting

confidence: 67%

Conditional inference and advanced mathematical study

Inglis

Simpson

2007

Educ Stud Math

View full text Add to dashboard Cite

. (2008) 'Conditional inference and advanced mathematical study.', Educational studies in mathematics., 67 (3). pp. 187-204. Further information on publisher's website:http://dx.doi.org/10.1007/s10649-007-9098-9Publisher's copyright statement: NOTICE: this is the author's version of a work that was accepted for publication in Educational studies in mathematics.Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details.

show abstract

How abstract is symbolic thought?

Cited by 153 publications

References 56 publications

Modeling discrete and continuous entities with fractions and decimals.

Modeling discrete and continuous entities with fractions and decimals.

Following the standard form: Effects of equation format on algebraic modeling

Conditional inference and advanced mathematical study

Contact Info

Product

Resources

About