scholarly journals Same-different judgments with alphabetic characters: The case of literal symbol processing

2019 ◽  
Vol 5 (2) ◽  
pp. 241-259 ◽  
Author(s):  
Courtney Pollack
Keyword(s):  
Numerical Magnitude ◽  
Symbol Processing ◽  
Learning Mathematics ◽  
Distance Effects ◽  
Literal Symbols

Learning mathematics requires fluency with symbols that convey numerical magnitude. Algebra and higher-level mathematics involve literal symbols, such as "x", that often represent numerical magnitude. Compared to other symbols, such as Arabic numerals, literal symbols may require more complex processing because they have strong pre-existing associations in literacy. The present study tested this notion using same-different tasks that produce less efficient judgments for different magnitudes that are closer together compared to farther apart (i.e., same-different distance effects). Twenty-four adolescents completed three same-different tasks using Arabic numerals, literal symbols, and artificial symbols. All three symbolic formats produced same-different distance effects, showing literal and artificial symbol processing of numerical magnitude. Importantly, judgments took longer for literal symbols than artificial symbols on average, suggesting a cost specific to literal symbol processing. Taken together, results suggest that literal symbol processing differs from processing of other symbols that represent numerical magnitude.

scholarly journals Same-Different Judgments with Alphabetic Characters: The Case of Literal Symbol Processing

2019 ◽  
Author(s):  
Courtney Pollack
Keyword(s):  
Numerical Magnitude ◽  
Symbol Processing ◽  
Learning Mathematics ◽  
Distance Effects ◽  
Literal Symbols

Learning mathematics requires fluency with symbols that convey numerical magnitude. Algebra and higher-level mathematics involve literal symbols, such as "x", that often represent numerical magnitude. Compared to other symbols, such as Arabic numerals, literal symbols may require more complex processing because they have strong pre-existing associations in literacy. The present study tested this notion using same-different tasks that produce less efficient judgments for different magnitudes that are closer together compared to farther apart (i.e., same-different distance effects). Twenty-four adolescents completed three same-different tasks using Arabic numerals, literal symbols, and artificial symbols. All three symbolic formats produced same-different distance effects, showing literal and artificial symbol processing of numerical magnitude. Importantly, judgments took longer for literal symbols than artificial symbols on average, suggesting a cost specific to literal symbol processing. Taken together, results suggest that literal symbol processing differs from processing of other symbols that represent numerical magnitude.

Order and Magnitude Share a Common Representation in Parietal Cortex

2009 ◽  
Vol 21 (11) ◽  
pp. 2114-2120 ◽  
Author(s):  
Michael S. Franklin ◽  
John Jonides
Keyword(s):  
Distance Effect ◽  
Number Line ◽  
Judgment Task ◽  
Mental Number Line ◽  
Numerical Magnitude ◽  
Intraparietal Sulcus ◽  
Ordinal Information ◽  
Common Representation ◽  
Distance Effects

The role of the intraparietal sulcus (IPS) in the representation of numerical magnitude is well established. Recently, there has also been speculation that the IPS is involved in the representation of ordinal information as well. These claims, however, overlook the fact that all neuroimaging paradigms in which participants make judgments about either magnitude and/or order result in a behavioral distance effect (i.e., the comparison is easier when the stimuli span a greater distance). This leaves open two possibilities: It may be that activation of the IPS is due to the mechanism that yields distance effects, or it may be that the IPS is involved in the representation of information about both magnitude and order. The current study used fMRI to compare a magnitude task in which participants show distance effects to an order-judgment task that yields reverse-distance effects. The results reveal activation of the IPS for both the magnitude and order tasks that is based on participants' strategies as opposed to the actual distance between the numbers. This leads to the conclusion that the IPS represents a mental number line, and that accessing this line can lead to distance effects when participants compare magnitudes and to reverse-distance effects when participants check for order.

Exploring mental representations for literal symbols using priming and comparison distance effects

ZDM ◽  
2015 ◽  
Vol 48 (3) ◽  
pp. 291-303 ◽  
Author(s):  
Courtney Pollack ◽  
Sibylla Leon Guerrero ◽  
Jon R. Star
Keyword(s):  
Mental Representations ◽  
Distance Effects ◽  
Literal Symbols

scholarly journals Representation of numerical magnitude in math-anxious individuals

2018 ◽  
Vol 72 (3) ◽  
pp. 424-435 ◽  
Author(s):  
Àngels Colomé
Keyword(s):  
Stroop Task ◽  
Size Effects ◽  
Math Anxiety ◽  
Group Differences ◽  
Numerical Magnitude ◽  
Magnitude Representation ◽  
Distance Effects ◽  
Equivalent Distance

Larger distance effects in high math-anxious individuals (HMA) performing comparison tasks have previously been interpreted as indicating less precise magnitude representation in this population. A recent study by Dietrich, Huber, Moeller, and Klein limited the effects of math anxiety to symbolic comparison, in which they found larger distance effects for HMA, despite equivalent size effects. However, the question of whether distance effects in symbolic comparison reflect the properties of the magnitude representation or decisional processes is currently under debate. This study was designed to further explore the relation between math anxiety and magnitude representation through three different tasks. HMA and low math-anxious individuals (LMA) performed a non-symbolic comparison, in which no group differences were found. Furthermore, we did not replicate previous findings in an Arabic digit comparison, in which HMA individuals showed equivalent distance effects to their LMA peers. Lastly, there were no group differences in a counting Stroop task. Altogether, an explanation of math anxiety differences in terms of less precise magnitude representation is not supported.

The Flip Side of the Auditory Spatial Selection Benefit

2015 ◽  
Vol 62 (1) ◽  
pp. 66-74 ◽  
Author(s):  
Iring Koch ◽  
Vera Lawo
Keyword(s):  
Task Switching ◽  
Auditory Task ◽  
Numerical Magnitude ◽  
Attention Shifting ◽  
Gender Selection ◽  
Spatial Selection ◽  
Number Words ◽  
Switch Costs ◽  
Mixing Costs ◽  
Experimental Group

In cued auditory task switching, one of two dichotically presented number words, spoken by a female and a male, had to be judged according to its numerical magnitude. One experimental group selected targets by speaker gender and another group by ear of presentation. In mixed-task blocks, the target-defining feature (male/female vs. left/right) was cued prior to each trial, but in pure blocks it remained constant. Compared to selection by gender, selection by ear led to better performance in pure blocks than in mixed blocks, resulting in larger “global” mixing costs for ear-based selection. Selection by ear also led to larger “local” switch costs in mixed blocks, but this finding was partially mediated by differential cue-repetition benefits. Together, the data suggest that requirements of attention shifting diminish the auditory spatial selection benefit.

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