IMPACT OF COMPONENT SIZE AND LENGTH ON BIAS
Description
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.
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Steps to reproduce
Data Collection Methods and Reproduction Guidelines Participants 37 fifth-grade children (M=11.05 years, 20 boys, 17 girls) and 34 college students (M=20.15 years, 17 boys, 17 girls) from Hubei, China. Inclusion criteria: Right-handed, normal/corrected vision, prior instruction on equivalent fractions. Ethics: Approved by Shenzhen University’s Research Ethics Committee; consent obtained from participants/parents/teachers. Compensated with 20 RMB (adults) or small gifts (children). Instruments and Software Hardware: Computer with 1920×1080 screen and standard keyboard. Software: PsychoPy-2023.1.3 Builder (stimulus presentation, response recording). Experimental Design and Tasks Two experiments (2-week interval, same participants) with computer-based tasks: Experiment 1: Equivalent Fraction Knowledge Task Purpose: Assess understanding of equivalent fractions. Stimuli: 40 trials (20 true, 20 false). False trials included 10 "small distance" (difference=0.14) and 10 "large distance" (difference=0.37) pairs. Benchmark fractions (e.g., 1/2) excluded. Procedure: 500-ms fixation cross ("+") → fraction pair (e.g., "1/3=3/9") displayed. Participants pressed "F" (true) or "J" (false); 8 practice trials (with feedback) → 40 formal trials (no feedback, randomized). Recorded: Accuracy (ACC), response time (RT) for correct responses. Experiment 1: Fraction Magnitude Comparison Task Purpose: Measure whole number bias via congruent/incongruent conditions. Stimuli: 40 trials (20 congruent: larger components = larger magnitude; 20 incongruent: larger components = smaller magnitude). Procedure: 500-ms fixation cross → fraction pair displayed. Participants pressed "F" (left larger) or "J" (right larger); 8 practice trials → 40 formal trials (randomized). Recorded: ACC, RT for correct responses. Experiment 2: String Length Manipulation Task Purpose: Isolate component size vs. string length (numerical character count) effects. Stimuli: 40 trials (20 same string length, 20 different string length), each with 10 congruent/incongruent pairs. Procedure: Identical to Experiment 1’s comparison task. Recorded: ACC, RT for correct responses. Data Processing Outliers: RTs ±3 SD from individual means removed. Calculations: Mean ACC, mean correct RT, and "bias" (incongruent RT – congruent RT). Reproduction Steps Recruit participants meeting age/education criteria. Use PsychoPy-2023.1.3 to program tasks with specified stimuli/timing. Administer tasks in a quiet room with 1920×1080 screen; follow practice/formal trial protocols. Apply outlier removal and compute metrics as described. Analyze with repeated-measures ANOVA (covariates: equivalent fraction knowledge) and t-tests.