Perceiving Precedence: Order of Operations Errors Are Predicted by Perception of Equivalent Expressions
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| Title: | Perceiving Precedence: Order of Operations Errors Are Predicted by Perception of Equivalent Expressions |
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| Language: | English |
| Authors: | Jeffrey Kramer Bye (ORCID |
| Source: | Journal of Numerical Cognition. Article e14103 2024 10. |
| Availability: | Leibniz Institute for Psychology. Universitatsring 15, Trier, 54296, Germany. e-mail: support@psychopen.eu; Web site: https://jnc.psychopen.eu |
| Peer Reviewed: | Y |
| Page Count: | 23 |
| Publication Date: | 2024 |
| Document Type: | Journal Articles Reports - Research |
| Education Level: | Junior High Schools Middle Schools Secondary Education |
| Descriptors: | Middle School Students, Middle School Mathematics, Arithmetic, Mathematics Skills, Problem Solving, Computation, Algebra, Mathematics Anxiety, Predictor Variables, Error Patterns, Individual Differences, Educational Games, Perceptual Development, Perceptual Motor Learning |
| ISSN: | 2363-8761 |
| Abstract: | Students often perform arithmetic using rigid problem-solving strategies that involve left-to-right-calculations. However, as students progress from arithmetic to algebra, entrenchment in rigid problem-solving strategies can negatively impact performance as students experience varied problem representations that sometimes conflict with the order of precedence (the order of operations). Research has shown that the syntactic structure of problems, and students' perceptual processes, are involved in mathematics performance and developing fluency with precedence. We examined 837 U.S. middle schoolers' propensity for precedence errors on six problems in an online mathematics game. We included an algebra knowledge assessment, math anxiety measure, and a perceptual math equivalence task measuring quick detection of equivalent expressions as predictors of students' precedence errors. We found that students made more precedence errors when the leftmost operation was invalid (addition followed by multiplication). Individual difference analyses revealed that students varied in propensity for precedence errors, which was better predicted by students' performance on the perceptual math equivalence task than by their algebra knowledge or math anxiety. Students' performance on the perceptual task and interactive game provide rich insights into their real-time understanding of precedence and the role of perceptual processes in equation solving. |
| Abstractor: | As Provided |
| Entry Date: | 2025 |
| Accession Number: | EJ1459951 |
| Database: | ERIC |
| Abstract: | Students often perform arithmetic using rigid problem-solving strategies that involve left-to-right-calculations. However, as students progress from arithmetic to algebra, entrenchment in rigid problem-solving strategies can negatively impact performance as students experience varied problem representations that sometimes conflict with the order of precedence (the order of operations). Research has shown that the syntactic structure of problems, and students' perceptual processes, are involved in mathematics performance and developing fluency with precedence. We examined 837 U.S. middle schoolers' propensity for precedence errors on six problems in an online mathematics game. We included an algebra knowledge assessment, math anxiety measure, and a perceptual math equivalence task measuring quick detection of equivalent expressions as predictors of students' precedence errors. We found that students made more precedence errors when the leftmost operation was invalid (addition followed by multiplication). Individual difference analyses revealed that students varied in propensity for precedence errors, which was better predicted by students' performance on the perceptual math equivalence task than by their algebra knowledge or math anxiety. Students' performance on the perceptual task and interactive game provide rich insights into their real-time understanding of precedence and the role of perceptual processes in equation solving. |
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| ISSN: | 2363-8761 |
