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

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Publication Details

Journal
Quarterly Journal of Experimental Psychology
Published
2026-09-04
DOI
https://doi.org/10.1177/17470218261488305
Primary Topic
Cognitive and developmental aspects of mathematical skills
Type
article
Field-Weighted Citation Impact
0.00

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article

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

Jeffrey K. Bye, Caroline Byrd Hornburg, Alena Egorova, Ji‐Eun Lee et al.
Quarterly Journal of Experimental Psychology
Cognitive and developmental aspects of mathematical skills
article

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

Jeffrey K. Bye, Caroline Byrd Hornburg, Alena Egorova, Ji‐Eun Lee, Carly Siegel Thorp, Arba Kamberi, Erin Ottmar, Avery H. Closser, Heidy Rodriguez
article en

Abstract

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.

Quarterly Journal of Experimental Psychology
Worcester Polytechnic Institute (US), Harvard University Press (US), California State University, Dominguez Hills (US), University of Florida (US), Virginia Tech (US)
Division of Research on Learning in Formal and Informal Settings
Quality Education
Openalex Percentile: Top 7%
Cognitive and developmental aspects of mathematical skills
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