The Facilitation Effect of Key-Step Retrieval Practice on Learning One-Variable Quadratic Equations
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| Title: | The Facilitation Effect of Key-Step Retrieval Practice on Learning One-Variable Quadratic Equations |
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| Language: | English |
| Authors: | Kejia Qu (ORCID |
| Source: | Instructional Science: An International Journal of the Learning Sciences. 2026 54(1). |
| Availability: | Springer. Available from: Springer Nature. One New York Plaza, Suite 4600, New York, NY 10004. Tel: 800-777-4643; Tel: 212-460-1500; Fax: 212-460-1700; e-mail: customerservice@springernature.com; Web site: https://link.springer.com/ |
| Peer Reviewed: | Y |
| Publication Date: | 2026 |
| Document Type: | Journal Articles Reports - Research |
| Education Level: | Junior High Schools Middle Schools Secondary Education |
| Descriptors: | Middle School Students, Middle School Mathematics, Mathematics Skills, Problem Solving, Cognitive Processes, Difficulty Level, Equations (Mathematics), Recall (Psychology), Mathematics Tests, Scores |
| DOI: | 10.1007/s11251-025-09759-y |
| ISSN: | 0020-4277 1573-1952 |
| Abstract: | Retrieval practice is a well-established learning strategy. However, the cognitive load involved in retrieving all the steps required for problem solving may hinder its effect in mathematics learning. This study aims to optimize retrieval practice by focusing on key procedural steps to enhance students' learning outcomes in mathematical problem solving. Targeting junior middle school students, the experiment utilized one-variable quadratic equations as learning material. Participants were randomly assigned to one of three groups: a key-step retrieval group, who were instructed to recall only the essential steps in problem solving; a general retrieval group, who retrieved full solution steps; and a relearning group, who restudied the worked examples without retrieval. Results showed that while there was no significant difference in final test scores between the general retrieval practice group and the relearning group, the key-step retrieval practice group significantly outperformed both the general retrieval and relearning groups. Moreover, the key-step retrieval practice group achieved a higher initial retrieval success rate than the general retrieval practice group. These findings indicate that emphasizing key steps during retrieval practice can improve students' transfer performance and lead to more effective learning of mathematical problem solving. |
| Abstractor: | As Provided |
| Entry Date: | 2026 |
| Accession Number: | EJ1497470 |
| Database: | ERIC |
| Abstract: | Retrieval practice is a well-established learning strategy. However, the cognitive load involved in retrieving all the steps required for problem solving may hinder its effect in mathematics learning. This study aims to optimize retrieval practice by focusing on key procedural steps to enhance students' learning outcomes in mathematical problem solving. Targeting junior middle school students, the experiment utilized one-variable quadratic equations as learning material. Participants were randomly assigned to one of three groups: a key-step retrieval group, who were instructed to recall only the essential steps in problem solving; a general retrieval group, who retrieved full solution steps; and a relearning group, who restudied the worked examples without retrieval. Results showed that while there was no significant difference in final test scores between the general retrieval practice group and the relearning group, the key-step retrieval practice group significantly outperformed both the general retrieval and relearning groups. Moreover, the key-step retrieval practice group achieved a higher initial retrieval success rate than the general retrieval practice group. These findings indicate that emphasizing key steps during retrieval practice can improve students' transfer performance and lead to more effective learning of mathematical problem solving. |
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| ISSN: | 0020-4277 1573-1952 |
| DOI: | 10.1007/s11251-025-09759-y |
