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Error Patterns in Ordering Fractions Among At-Risk Fourth-Grade Students.
Amelia S Malone1, Lynn S Fuchs1
11 Department of Special Education, Vanderbilt University, Nashville, TN, USA.
Journal of Learning Disabilities
|March 12, 2016
Summary
Fourth-grade students struggle with ordering fractions, often misapplying whole number logic. Fraction magnitude estimation, not part-whole understanding, predicted these common ordering errors.
Area of Science:
- Mathematics Education
- Cognitive Psychology
Background:
- Fractional understanding is crucial for advanced mathematics.
- Fourth-grade students often exhibit difficulties with fraction concepts.
Purpose of the Study:
- Describe fraction ordering errors in at-risk fourth graders.
- Assess the impact of part-whole understanding and magnitude estimation on errors.
- Examine how explaining comparisons affects error probability.
Main Methods:
- Administered a nine-item fraction ordering test to 227 at-risk fourth-grade students.
- Analyzed error types, focusing on misapplication of whole number logic.
- Used regression analysis to identify predictors of errors.
Main Results:
- 81% of problems were answered incorrectly.
- 65% of errors stemmed from applying whole number logic to fractions.
- Fraction magnitude estimation accuracy significantly predicted errors, while part-whole understanding did not.
Conclusions:
- At-risk fourth graders make frequent fraction ordering errors, primarily due to whole number logic.
- Fraction magnitude estimation is a key factor in avoiding these errors.
- Instruction should focus on developing accurate fraction magnitude estimation skills.
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