View in EDS

A Longitudinal Investigation of the Codevelopment and Bidirectional Relations among Whole Number Arithmetic and Conceptual and Procedural Fraction Knowledge

Saved in:
Bibliographic Details
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 0000-0002-6702-3958), Sabrina Di Lonardo Burr, Lisa Jane Rodgers, Judith Wylie, Jiwei Si, Bijuan Huang, Kaiyue Guo, Hongxia Li
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
FullText Text:
  Availability: 0
Header DbId: eric
DbLabel: ERIC
An: EJ1507476
AccessLevel: 3
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: A Longitudinal Investigation of the Codevelopment and Bidirectional Relations among Whole Number Arithmetic and Conceptual and Procedural Fraction Knowledge
– Name: Language
  Label: Language
  Group: Lang
  Data: English
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Chang+Xu%22">Chang Xu</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0002-6702-3958">0000-0002-6702-3958</externalLink>)<br /><searchLink fieldCode="AR" term="%22Sabrina+Di+Lonardo+Burr%22">Sabrina Di Lonardo Burr</searchLink><br /><searchLink fieldCode="AR" term="%22Lisa+Jane+Rodgers%22">Lisa Jane Rodgers</searchLink><br /><searchLink fieldCode="AR" term="%22Judith+Wylie%22">Judith Wylie</searchLink><br /><searchLink fieldCode="AR" term="%22Jiwei+Si%22">Jiwei Si</searchLink><br /><searchLink fieldCode="AR" term="%22Bijuan+Huang%22">Bijuan Huang</searchLink><br /><searchLink fieldCode="AR" term="%22Kaiyue+Guo%22">Kaiyue Guo</searchLink><br /><searchLink fieldCode="AR" term="%22Hongxia+Li%22">Hongxia Li</searchLink>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="SO" term="%22Journal+of+Educational+Psychology%22"><i>Journal of Educational Psychology</i></searchLink>. 2026 118(2):224-239.
– Name: Avail
  Label: Availability
  Group: Avail
  Data: 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
– Name: PeerReviewed
  Label: Peer Reviewed
  Group: SrcInfo
  Data: Y
– Name: Pages
  Label: Page Count
  Group: Src
  Data: 16
– Name: DatePubCY
  Label: Publication Date
  Group: Date
  Data: 2026
– Name: TypeDocument
  Label: Document Type
  Group: TypDoc
  Data: Journal Articles<br />Reports - Research
– Name: Audience
  Label: Education Level
  Group: Audnce
  Data: <searchLink fieldCode="EL" term="%22Elementary+Education%22">Elementary Education</searchLink><br /><searchLink fieldCode="EL" term="%22Grade+4%22">Grade 4</searchLink><br /><searchLink fieldCode="EL" term="%22Intermediate+Grades%22">Intermediate Grades</searchLink><br /><searchLink fieldCode="EL" term="%22Grade+5%22">Grade 5</searchLink><br /><searchLink fieldCode="EL" term="%22Middle+Schools%22">Middle Schools</searchLink>
– Name: Subject
  Label: Descriptors
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Foreign+Countries%22">Foreign Countries</searchLink><br /><searchLink fieldCode="DE" term="%22Elementary+Education%22">Elementary Education</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+Education%22">Mathematics Education</searchLink><br /><searchLink fieldCode="DE" term="%22Arithmetic%22">Arithmetic</searchLink><br /><searchLink fieldCode="DE" term="%22Fractions%22">Fractions</searchLink><br /><searchLink fieldCode="DE" term="%22Longitudinal+Studies%22">Longitudinal Studies</searchLink><br /><searchLink fieldCode="DE" term="%22Grade+4%22">Grade 4</searchLink><br /><searchLink fieldCode="DE" term="%22Grade+5%22">Grade 5</searchLink><br /><searchLink fieldCode="DE" term="%22Thinking+Skills%22">Thinking Skills</searchLink><br /><searchLink fieldCode="DE" term="%22Sequential+Learning%22">Sequential Learning</searchLink><br /><searchLink fieldCode="DE" term="%22Learning+Strategies%22">Learning Strategies</searchLink>
– Name: Subject
  Label: Geographic Terms
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22China%22">China</searchLink>
– Name: DOI
  Label: DOI
  Group: ID
  Data: 10.1037/edu0000942
– Name: ISSN
  Label: ISSN
  Group: ISSN
  Data: 0022-0663<br />1939-2176
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: 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.
– Name: AbstractInfo
  Label: Abstractor
  Group: Ab
  Data: As Provided
– Name: Note
  Label: Notes
  Group: Note
  Data: https://osf.io/yspb6
– Name: DateEntry
  Label: Entry Date
  Group: Date
  Data: 2026
– Name: AN
  Label: Accession Number
  Group: ID
  Data: EJ1507476
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=eric&AN=EJ1507476
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1037/edu0000942
    Languages:
      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 16
        StartPage: 224
    Subjects:
      – SubjectFull: Foreign Countries
        Type: general
      – SubjectFull: Elementary Education
        Type: general
      – SubjectFull: Mathematics Education
        Type: general
      – SubjectFull: Arithmetic
        Type: general
      – SubjectFull: Fractions
        Type: general
      – SubjectFull: Longitudinal Studies
        Type: general
      – SubjectFull: Grade 4
        Type: general
      – SubjectFull: Grade 5
        Type: general
      – SubjectFull: Thinking Skills
        Type: general
      – SubjectFull: Sequential Learning
        Type: general
      – SubjectFull: Learning Strategies
        Type: general
      – SubjectFull: China
        Type: general
    Titles:
      – TitleFull: A Longitudinal Investigation of the Codevelopment and Bidirectional Relations among Whole Number Arithmetic and Conceptual and Procedural Fraction Knowledge
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Chang Xu
      – PersonEntity:
          Name:
            NameFull: Sabrina Di Lonardo Burr
      – PersonEntity:
          Name:
            NameFull: Lisa Jane Rodgers
      – PersonEntity:
          Name:
            NameFull: Judith Wylie
      – PersonEntity:
          Name:
            NameFull: Jiwei Si
      – PersonEntity:
          Name:
            NameFull: Bijuan Huang
      – PersonEntity:
          Name:
            NameFull: Kaiyue Guo
      – PersonEntity:
          Name:
            NameFull: Hongxia Li
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 02
              Type: published
              Y: 2026
          Identifiers:
            – Type: issn-print
              Value: 0022-0663
            – Type: issn-electronic
              Value: 1939-2176
          Numbering:
            – Type: volume
              Value: 118
            – Type: issue
              Value: 2
          Titles:
            – TitleFull: Journal of Educational Psychology
              Type: main
ResultId 1