Conceptual Knowledge of Fraction Arithmetic

Understanding an arithmetic operation implies, at minimum, knowing the direction of effects that the operation produces. However, many children and adults, even those who execute arithmetic procedures correctly, may lack this knowledge on some operations and types of numbers. To test this hypothesis...

Full description

Saved in:
Bibliographic Details
Published in:Journal of educational psychology 2015-08, Vol.107 (3), p.909-918
Main Authors: Siegler, Robert S., Lortie-Forgues, Hugues
Format: Article
Language:English
Subjects:
Accuracy
Arithmetic
Cognition
College Students
Comparative Analysis
Computation
Educational Experiments
Educational psychology
Female
Foreign Countries
Fractions
Human
Hypothesis Testing
Knowledge Level
Majors (Students)
Male
Mathematical Ability
Mathematics
Mathematics (Concepts)
Mathematics Achievement
Mathematics Education
Mathematics Skills
Middle School Students
Middle Schools
Prediction
Preservice Teachers
Problem Solving
Sciences
Statistical Analysis
Student teachers
Task Analysis
University students
Citations: Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Understanding an arithmetic operation implies, at minimum, knowing the direction of effects that the operation produces. However, many children and adults, even those who execute arithmetic procedures correctly, may lack this knowledge on some operations and types of numbers. To test this hypothesis, we presented preservice teachers (Study 1), middle school students (Study 2), and math and science majors at a selective university (Study 3) with a novel direction of effects task with fractions. On this task, participants were asked to predict without calculating whether the answer to an inequality would be larger or smaller than the larger fraction in the problem (e.g., "True or false: 31/56 * 17/42 > 31/56"). Both preservice teachers and middle school students correctly answered less often than chance on problems involving multiplication and division of fractions below 1, though they were consistently correct on all other types of problems. In contrast, the math and science students from the selective university were consistently correct on all items. Interestingly, the weak understanding of multiplication and division of fractions below 1 was present even among middle school students and preservice teachers who correctly executed the fraction arithmetic procedures and had highly accurate knowledge of the magnitudes of individual fractions, which ruled out several otherwise plausible interpretations of the findings. Theoretical and educational implications of the findings are discussed.
ISSN:0022-0663
1939-2176
DOI:10.1037/edu0000025