String Length Amplifies the Whole Number Bias in Fraction Comparison: Evidence from Children and Adults
Description
Research Hypothesis: This study investigated whether string length (the number of digits in a fraction, e.g., "1/2" vs. "10/20") amplifies the "whole number bias" in fraction comparison. A key preliminary aim was to first establish that participants possessed a solid conceptual understanding of fraction equivalence, ensuring that any observed biases in the main task were due to perceptual interference, not a lack of knowledge. Data & Methodology: Data was gathered from 37 fifth-grade children and 34 adults. The study involved two key tasks: Equivalent Fraction Knowledge Task (Screening): This task measured participants' conceptual understanding. They judged whether fraction equations were true or false (e.g., "20/36 = 5/9"). Accuracy was recorded. The results showed that both children (97.8% accuracy) and adults (96.0% accuracy) performed significantly better than chance, confirming they had strong underlying knowledge of equivalent fractions. Fraction Magnitude Comparison Task (Main Experiment): Only with the above knowledge established, participants then completed the critical task. They quickly selected the larger of two equivalent fractions in a design that manipulated: Congruency: Congruent (larger components = larger value) vs. Incongruent (larger components = smaller value). String Length: Different string lengths vs. Same string length. The primary data were Accuracy (%) and Response Time (ms). The key metric for bias was the RT difference between incongruent and congruent trials. Key Findings & Interpretation: Conceptual Knowledge Was High and Controlled: The high accuracy on the Equivalent Fraction Knowledge Task is crucial. It confirms that participants understood fraction equivalence, ruling out ignorance as an explanation for subsequent biases. Persistent Perceptual Interference: Despite this strong knowledge, both groups showed significant congruency effects (slower RTs on incongruent trials) in the comparison task. This demonstrates that component size automatically interferes with magnitude judgments even when conceptual understanding is intact. String Length Amplifies Bias: The critical finding was that the RT bias was significantly larger in the different string-length condition. This shows that string length acts as a powerful perceptual cue that amplifies the whole number bias, over and above the effect of component size alone. Children are More Susceptible: Children exhibited a significantly larger overall RT bias than adults, indicating their less-developed inhibitory control makes them more vulnerable to these misleading perceptual cues.
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Steps to reproduce
1. Participants: Recruited 71 participants (37 fifth-graders, 34 adults) from China. All had normal vision and prior fraction instruction. Power analysis (η² = 0.25) determined minimum sample size. 2. Stimuli & Tasks: Equivalent Fraction Knowledge Task: 40 true/false equations (e.g., 20/36 = 5/9) controlled for distance from equivalence Fraction Comparison Task: 40 fraction pairs in 2×2 design: String Length (Different/Same) Congruency (Congruent/Incongruent) All pairs used equivalent fractions with small numerical distances 3. Procedure: Computerized tasks programmed in PsychoPy 2023.1.3 Standardized instructions + 8 practice trials with feedback 500ms fixation → stimulus until response → mask Response keys: F/J for left/right or true/false No feedback during main experiment 4. Data Recording: Accuracy (%) and response time (ms) recorded trial-by-trial RT outliers excluded (>±3 SD from individual mean) 5. Analysis: Bias score = RT_incongruent - RT_congruent Repeated-measures ANOVA (String Length × Congruency) Paired t-tests comparing bias across conditions This protocol ensures controlled measurement of whole number bias while accounting for equivalent fraction knowledge. Reproduction requires precise recreation of the fraction pairs and experimental timing.
Institutions
- Shenzhen University