Perceiving Precedence: Order of Operations Errors Are Predicted by Perception of Equivalent Expressions
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 represe...
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| Format: | Article |
| Language: | English |
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PsychOpen GOLD/ Leibniz Insitute for Psychology
2024-12-01
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| Series: | Journal of Numerical Cognition |
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| Online Access: | https://doi.org/10.5964/jnc.14103 |
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| author | Jeffrey Kramer Bye Jenny Yun-Chen Chan Avery H. Closser Ji-Eun Lee Stacy T. Shaw Erin R. Ottmar |
| author_facet | Jeffrey Kramer Bye Jenny Yun-Chen Chan Avery H. Closser Ji-Eun Lee Stacy T. Shaw Erin R. Ottmar |
| author_sort | Jeffrey Kramer Bye |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-8a84699449e4463dab0eabc8c27f9f2c |
| institution | OA Journals |
| issn | 2363-8761 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | PsychOpen GOLD/ Leibniz Insitute for Psychology |
| record_format | Article |
| series | Journal of Numerical Cognition |
| spelling | doaj-art-8a84699449e4463dab0eabc8c27f9f2c2025-08-20T02:16:05ZengPsychOpen GOLD/ Leibniz Insitute for PsychologyJournal of Numerical Cognition2363-87612024-12-011010.5964/jnc.14103jnc.14103Perceiving Precedence: Order of Operations Errors Are Predicted by Perception of Equivalent ExpressionsJeffrey Kramer Bye0https://orcid.org/0000-0002-2636-3657Jenny Yun-Chen Chan1https://orcid.org/0000-0003-1479-5935Avery H. Closser2https://orcid.org/0000-0003-2712-8509Ji-Eun Lee3https://orcid.org/0000-0001-8521-8997Stacy T. Shaw4https://orcid.org/0000-0002-4326-9937Erin R. Ottmar5https://orcid.org/0000-0002-9487-7967Department of Psychology, California State University, Dominguez Hills, Carson, CA, USADepartment of Early Childhood Education, The Education University of Hong Kong, Tai Po, Hong Kong, SAR, ChinaSchool of Teaching and Learning, University of Florida, Gainesville, FL, USADepartment of Social Science & Policy Studies, Worcester Polytechnic Institute, Worcester, MA, USADepartment of Social Science & Policy Studies, Worcester Polytechnic Institute, Worcester, MA, USADepartment of Social Science & Policy Studies, Worcester Polytechnic Institute, Worcester, MA, USAStudents 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.https://doi.org/10.5964/jnc.14103arithmeticprecedenceorder of operationsperceptual learningeducational technologymath equivalenceindividual differences |
| spellingShingle | Jeffrey Kramer Bye Jenny Yun-Chen Chan Avery H. Closser Ji-Eun Lee Stacy T. Shaw Erin R. Ottmar Perceiving Precedence: Order of Operations Errors Are Predicted by Perception of Equivalent Expressions Journal of Numerical Cognition arithmetic precedence order of operations perceptual learning educational technology math equivalence individual differences |
| title | Perceiving Precedence: Order of Operations Errors Are Predicted by Perception of Equivalent Expressions |
| title_full | Perceiving Precedence: Order of Operations Errors Are Predicted by Perception of Equivalent Expressions |
| title_fullStr | Perceiving Precedence: Order of Operations Errors Are Predicted by Perception of Equivalent Expressions |
| title_full_unstemmed | Perceiving Precedence: Order of Operations Errors Are Predicted by Perception of Equivalent Expressions |
| title_short | Perceiving Precedence: Order of Operations Errors Are Predicted by Perception of Equivalent Expressions |
| title_sort | perceiving precedence order of operations errors are predicted by perception of equivalent expressions |
| topic | arithmetic precedence order of operations perceptual learning educational technology math equivalence individual differences |
| url | https://doi.org/10.5964/jnc.14103 |
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