IMPACT OF COMPONENT SIZE AND LENGTH ON BIAS

Research Hypotheses
The study tested two hypotheses: (1) Whole number bias persists in children and adults even with comparable equivalent fraction knowledge, with children showing stronger bias. (2) Component size (numerator/denominator magnitudes) and string length (number of characters, e.g., "1/10" vs. "10/100") jointly drive this bias, with string length amplifying it.
Data Collection
Participants: 37 fifth graders (M=11.05) and 34 adults (M=20.15) from China, with prior fraction learning.

Experiments:

Exp 1: Equivalent fraction knowledge task (40 trials: 20 true/false) and magnitude comparison task (40 trials: 20 congruent/incongruent, where congruent = larger components → larger fraction). Measured accuracy (ACC) and response time (RT).
Exp 2: 2 weeks later, same participants completed 40 comparison trials manipulating string length (same/different) and congruency.
Key Results
Exp 1: Similar accuracy in equivalent fraction knowledge (children: 97.77%; adults: 96.03%), but children slower (4.75s vs. 3.44s). In comparisons, both groups took longer in incongruent trials (children: 18.45s vs. 11.89s; adults: 7.57s vs. 5.80s), with children’s bias larger (6.56s vs. 1.78s).
Exp 2: Both groups had longer RT in incongruent trials, regardless of string length. Bias was larger with different string lengths (children: 12.42s vs. 8.14s; adults: 3.95s vs. 1.82s), and children’s overall bias was greater.
Interpretation
Bias stems from processing habits, not knowledge deficits. Component size and string length jointly affect judgments, with string length amplifying bias. Children are more susceptible due to immature inhibition of irrelevant cues.

Implications: Teach automated equivalent fraction processing, address visual cues like string length, and enhance inhibitory control in fraction instruction.