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Holistic representation of unit fractions
Dana Ganor-Stern1, Irina Karasik-Rivkin, Joseph Tzelgov
1Achva Academic College, M.P. Shikmim, Israel. danaga@bgu.ac.il
Experimental Psychology
|November 26, 2010
Summary
Understanding unit fractions is context-dependent. This study shows holistic processing of unit fractions when numbers 0 and 1 are included in the context, but not when only fractions are present.
Area of Science:
- Cognitive Psychology
- Numerical Cognition
- Mathematics Education
Background:
- Unit fraction processing is crucial for understanding numerical cognition.
- Previous research suggests potential difficulties in representing fractions holistically.
- The role of context in numerical processing remains an active area of investigation.
Purpose of the Study:
- To investigate the cognitive processing of unit fractions.
- To determine if contextual cues influence the representation of unit fractions.
- To explore the impact of including 0 and 1 in the stimulus set on fraction processing.
Main Methods:
- A numerical comparison task was employed to assess fraction representation.
- Stimulus sets varied to include either only unit fractions or unit fractions alongside 0 and 1.
- Behavioral data were analyzed to identify semantic congruity and distance effects.
Main Results:
- Evidence for holistic representation of unit fractions emerged when 0 and 1 were included in the stimulus set.
- The semantic congruity effect was observed for fraction-pair comparisons in the presence of 0 and 1.
- The distance effect was noted for comparisons involving fractions and 0 or 1.
- No evidence of holistic representation was found when the stimulus set contained only fractions.
Conclusions:
- Fraction processing, particularly for unit fractions, is significantly influenced by the immediate numerical context.
- The inclusion of boundary numbers (0 and 1) facilitates a holistic representation of unit fractions.
- Findings contribute to understanding the broader context-dependent nature of complex number processing.
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