Individual Differences in Detecting and Correcting Logical Errors in Mathematical Texts

This study explored individual differences among senior high school students in detecting and correcting logical errors in mathematical reasoning. Eight participants with high and average mathematical abilities each were recruited from a key high school in Shanghai to solve three error-detecting tasks by thinking aloud; they were then interviewed. Results showed that high ability students performed better in answering time, validation judgment, detection, explanation, and correction of logical errors. The cognitive processes for detecting and correcting logical errors were a combination of five types of cognitive behaviors-read, analyze, check, judge and correct. Although their specific combination methods were different, the two groups exhibited two different detecting styles. Error detection of high ability students was more active and effective, and their thinking processes were smooth and concise. The average ability group was more passive in error detection, more dependent on mathematical texts, and more stuck in the thinking process. Both groups agreed on the value of logical error-detecting tasks, although the high ability group had a more positive attitude toward them.