Error Patterns with Fraction Calculations at Fourth Grade as a Function of Students' Mathematics Achievement Status.

Area of Science:

• Mathematics Education
• Cognitive Psychology

Background:

• Fraction calculation is a key skill in upper elementary grades.
• Students often exhibit whole number bias when solving fraction problems.

Purpose of the Study:

• To describe fraction-calculation errors in 4th graders.
• To determine how error patterns vary by problem type, orientation, and achievement status.
• To investigate the relationship between achievement status and whole number bias.

Main Methods:

• Analysis of fraction-calculation errors across different problem types and orientations.
• Comparison of error patterns among low-, average-, and high-achieving students.
• Evaluation of two instructional approaches (part-whole vs. magnitude understanding) for low-performing students.

Main Results:

• Whole number bias was more prevalent with unlike denominators.
• Low- and average-achieving students in core instruction showed more whole number bias than low-achieving students in magnitude-focused tutoring.
• Magnitude understanding instruction positively impacted fraction calculation for low-performing students.

Conclusions:

• Instruction emphasizing magnitude understanding is crucial for improving fraction skills.
• Targeted interventions can mitigate whole number bias in fraction calculation.
• Magnitude-based instruction benefits diverse learners in upper elementary grades.