EXPRESS: Operator Positions and Perceptual Cues: Unpacking Their Effects on Middle School Students' Performance and Errors in Order-of-Operations Problems.

Many middle school students struggle to recognize the structure of arithmetic problems, which often leads to mathematical errors. This study investigated the effects of operator positions and perceptual supports (e.g., color, spacing) on the performance and mathematical errors of U.S. middle school students (N = 578) when solving online arithmetic problems with one higher-order operator (multiplication) and two lower-order operators (addition, subtraction). The results of mixed-effect models revealed that students' accuracy decreased as the location of the multiplication moved from left to middle or right, while their response time increased. Furthermore, the types and rates of errors students made significantly differed by perceptual cue. Students provided with color cues were less likely to make "left-to-right operation" errors compared to those without perceptual cues. However, students who received the color cue were more likely to make "performing multiplication-only" errors than those without perceptual cues. These findings suggest that although providing perceptual cues like color can reduce "left-to-right" errors, they may introduce new types of errors to some students. Therefore, clear instructions and examples need to accompany the use of perceptual cues in problem-solving tasks.