A Longitudinal Investigation of the Codevelopment and Bidirectional Relations among Whole Number Arithmetic and Conceptual and Procedural Fraction Knowledge
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| Title: | A Longitudinal Investigation of the Codevelopment and Bidirectional Relations among Whole Number Arithmetic and Conceptual and Procedural Fraction Knowledge |
|---|---|
| Language: | English |
| Authors: | Chang Xu (ORCID |
| Source: | Journal of Educational Psychology. 2026 118(2):224-239. |
| Availability: | American Psychological Association. Journals Department, 750 First Street NE, Washington, DC 20002. Tel: 800-374-2721; Tel: 202-336-5510; Fax: 202-336-5502; e-mail: order@apa.org; Web site: http://www.apa.org |
| Peer Reviewed: | Y |
| Page Count: | 16 |
| Publication Date: | 2026 |
| Document Type: | Journal Articles Reports - Research |
| Education Level: | Elementary Education Grade 4 Intermediate Grades Grade 5 Middle Schools |
| Descriptors: | Foreign Countries, Elementary Education, Mathematics Education, Arithmetic, Fractions, Longitudinal Studies, Grade 4, Grade 5, Thinking Skills, Sequential Learning, Learning Strategies |
| Geographic Terms: | China |
| DOI: | 10.1037/edu0000942 |
| ISSN: | 0022-0663 1939-2176 |
| Abstract: | How do conceptual and procedural fraction knowledge influence the development of each other over time? Is their pattern of development a reflection of instruction? In the present study, we conducted a four-wave longitudinal investigation of the co- and bidirectional development of whole number arithmetic, and conceptual and procedural fraction knowledge during a critical phase of fraction learning. Chinese students (N = 1,055, M[subscript age] = 9.8, SD = 0.7) educated through a linear curriculum completed whole number arithmetic, and conceptual and procedural fraction assessments during the first and second terms in Grade 4 and Grade 5. Cross-lagged panel analysis, controlling for students' nonverbal reasoning skills, revealed that conceptual and procedural fraction knowledge did not influence the development of one another prior to Grade 5. However, starting in Grade 5, a unidirectional pattern emerged, where conceptual fraction knowledge supported the development of procedural fraction knowledge. This unilateral conceptual-to-procedural pattern of development contrasts with findings from studies with students in the United States, suggesting that educational experiences may shape the codevelopment of these two types of fraction knowledge. Furthermore, proficiency in whole number arithmetic predicted the development in both conceptual and procedural fraction knowledge, highlighting its important role alongside conceptual knowledge in supporting the acquisition of fraction procedures. Our findings emphasize the need to consider educational experiences and foster meaningful connections between concepts and procedures during fraction instruction while promoting mastery of whole number arithmetic to promote students' development of fraction knowledge. |
| Abstractor: | As Provided |
| Notes: | https://osf.io/yspb6 |
| Entry Date: | 2026 |
| Accession Number: | EJ1507476 |
| Database: | ERIC |
| Abstract: | How do conceptual and procedural fraction knowledge influence the development of each other over time? Is their pattern of development a reflection of instruction? In the present study, we conducted a four-wave longitudinal investigation of the co- and bidirectional development of whole number arithmetic, and conceptual and procedural fraction knowledge during a critical phase of fraction learning. Chinese students (N = 1,055, M[subscript age] = 9.8, SD = 0.7) educated through a linear curriculum completed whole number arithmetic, and conceptual and procedural fraction assessments during the first and second terms in Grade 4 and Grade 5. Cross-lagged panel analysis, controlling for students' nonverbal reasoning skills, revealed that conceptual and procedural fraction knowledge did not influence the development of one another prior to Grade 5. However, starting in Grade 5, a unidirectional pattern emerged, where conceptual fraction knowledge supported the development of procedural fraction knowledge. This unilateral conceptual-to-procedural pattern of development contrasts with findings from studies with students in the United States, suggesting that educational experiences may shape the codevelopment of these two types of fraction knowledge. Furthermore, proficiency in whole number arithmetic predicted the development in both conceptual and procedural fraction knowledge, highlighting its important role alongside conceptual knowledge in supporting the acquisition of fraction procedures. Our findings emphasize the need to consider educational experiences and foster meaningful connections between concepts and procedures during fraction instruction while promoting mastery of whole number arithmetic to promote students' development of fraction knowledge. |
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| ISSN: | 0022-0663 1939-2176 |
| DOI: | 10.1037/edu0000942 |
