Representations of the Magnitudes of Fractions

We tested whether adults can use integrated, analog, magnitude representations to compare the values of fractions. The only previous study on this question concluded that even college students cannot form such representations and instead compare fraction magnitudes by representing numerators and den...

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Bibliographic Details
Published in:Journal of experimental psychology. Human perception and performance 2010-10, Vol.36 (5), p.1227-1238
Main Authors: Schneider, Michael, Siegler, Robert S
Format: Article
Language:English
Subjects:
Adult
Adults
Biological and medical sciences
Cognition & reasoning
Cognition. Intelligence
College Students
Community Colleges
Comparative Analysis
Concept Formation
Decision Making
Distance Perception
Educational Strategies
Experimental psychology
Female
Fractions
Fundamental and applied biological sciences. Psychology
Human
Humans
Judgment
Logical Thinking
Magnitude
Magnitude Estimation
Male
Mathematical functions
Mathematics
Mathematics Instruction
Mental imagery. Mental representation
Numbers (Numerals)
Problem Solving
Psychology. Psychoanalysis. Psychiatry
Psychology. Psychophysiology
Strategies
Student Behavior
Tests
Undergraduate students
Universities
Young Adult
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Summary:We tested whether adults can use integrated, analog, magnitude representations to compare the values of fractions. The only previous study on this question concluded that even college students cannot form such representations and instead compare fraction magnitudes by representing numerators and denominators as separate whole numbers. However, atypical characteristics of the presented fractions might have provoked the use of atypical comparison strategies in that study. In our 3 experiments, university and community college students compared more balanced sets of single-digit and multi-digit fractions and consistently exhibited a logarithmic distance effect. Thus, adults used integrated, analog representations, akin to a mental number line, to compare fraction magnitudes. We interpret differences between the past and present findings in terms of different stimuli eliciting different solution strategies.
ISSN:0096-1523
1939-1277
DOI:10.1037/a0018170