type of fraction pair (same denominator or same numerator) and the relationship between the variable fraction components and the subsequent integer pair (spe ...
Implicit priming reveals both holistic and decomposed processing in fraction comparison Jessica Nejman & Thomas J. Faulkenberry Department of Psychological Sciences
Problem
Results - Fraction Task Performance
The primary task used to investigate the mental representation of fractions is the fraction comparison task, where participants are asked to quickly choose which of 2 3 two fractions (e.g., 3 vs. 5 ) is numerically larger. Three competing explanations that account for adults’ performance on this task have emerged:
2100 1825 ms * p = 0.05
1900
Mean RT (ms)
1653 ms
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1500
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The purpose of the present study is to replicate the work of Meert and colleagues [1], who used a priming paradigm to show that while adults do form holistic representations in certain cases, components are automatically processed as well.
2 3.7
(n.s.) p = 0.85
Mean number of errors
- Holistic processing, which involves forming a representation of the fraction’s magnitude [1] - Decomposed processing, which involves separately processing the components (e.g., numerators, denominators) [2] - Hybrid processing, which involves strategic use of both holistic and decomposed processing [3]
3.9
0 Same denominator
Method
Same numerator
Fraction type
We gave 32 participants 128 trials of a two-part numerical decision task, where they were instructed to choose the numerically larger of any presented pair. Every trial began with a fraction pair, followed by an integer pair. We manipulated the type of fraction pair (same denominator or same numerator) and the relationship between the variable fraction components and the subsequent integer pair (specific priming, where the integer pair matched the nonconstant components of the preceding fraction pair, and nonspecific priming, where the integer pair differed from the preceding fraction components).
- Correct responses for same-denominator pairs marginally faster than samenumerator pairs - No difference in error rates between different pair types
Results - Integer Task Performance 750 specific priming nonspecific priming
Mean RT (ms)
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Experimental conditions: 550
a. same denominator / specific priming
Same denominator
Fraction type
b. same denominator / nonspecific priming c. same numerator / specific priming
- Significant interaction between priming type and fraction type - Same denominator pairs with identical components to the preceding integer comparison were compared faster than baseline (e.g., facilitation) - Same numerator pairs with identical components to the preceding integer comparison were compared slower than baseline (e.g., inhibition).
d. same numerator / nonspecific priming
Results - Predictors of Fraction RTs 2200
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r = −0.04
1600
RT (msec)
2200
1200
1200 0.2
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0
4
6
Componential distance
Same numerator fractions
Same numerator fractions
2200
2200
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1600
r = −0.64
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1200
1200 0.2
0.3
0.4
0.5
Holistic distance
0.6
References [1] Meert, G., Grégoire, J., & Noël, M.P. (2009). Rational numbers: Componential versus holistic representation of fractions in a magnitude comparison task. The Quarterly Journal of Experimental Psychology, 62(8), 1598-1616. [2] Bonato, M., Fabbri, S., Umiltà, C., & Zorzi, M. (2007). The mental representation of numerical fractions: Real or integer? Journal of Experimental Psychology: Human Perception and Performance, 33(6), 1410-1419. [3] Faulkenberry, T.J., & Pierce, B.H. (2011). Mental representation in fraction comparison: Holistic versus component-based strategies. Experimental Psychology, 58, 480-489.
r = −0.46
1400
0.1
8
1800
1400
0.0
2
Holistic distance
1800
- We replicated the previous findings of Meert and colleagues [1] - Participants formed holistic representations of same numerator pairs, but integer comparisons primed fraction comparisons, which implies representations of components → support for hybrid model
r = −0.24
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1400
0.1
Take home points
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RT (msec)
Same denominator fractions
RT (msec)
RT (msec)
Same denominator fractions
Same numerator
Acknowledgements 0
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Componential distance
8
This research was partially supported by an Undergraduate Research Assistantship grant awarded to the first author. The authors would like to thank the Tarleton Office of Student Research and Creative Activities for this funding.
