View in EDS

The Facilitation Effect of Key-Step Retrieval Practice on Learning One-Variable Quadratic Equations

Saved in:
Bibliographic Details
Title: The Facilitation Effect of Key-Step Retrieval Practice on Learning One-Variable Quadratic Equations
Language: English
Authors: Kejia Qu (ORCID 0000-0001-5534-1492), Ruiqian Ma, Yadi Yu
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
FullText Text:
  Availability: 0
Header DbId: eric
DbLabel: ERIC
An: EJ1497470
AccessLevel: 3
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: The Facilitation Effect of Key-Step Retrieval Practice on Learning One-Variable Quadratic Equations
– Name: Language
  Label: Language
  Group: Lang
  Data: English
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Kejia+Qu%22">Kejia Qu</searchLink> (ORCID <externalLink term="http://orcid.org/0000-0001-5534-1492">0000-0001-5534-1492</externalLink>)<br /><searchLink fieldCode="AR" term="%22Ruiqian+Ma%22">Ruiqian Ma</searchLink><br /><searchLink fieldCode="AR" term="%22Yadi+Yu%22">Yadi Yu</searchLink>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="SO" term="%22Instructional+Science%3A+An+International+Journal+of+the+Learning+Sciences%22"><i>Instructional Science: An International Journal of the Learning Sciences</i></searchLink>. 2026 54(1).
– Name: Avail
  Label: Availability
  Group: Avail
  Data: 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/
– Name: PeerReviewed
  Label: Peer Reviewed
  Group: SrcInfo
  Data: Y
– 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="%22Junior+High+Schools%22">Junior High Schools</searchLink><br /><searchLink fieldCode="EL" term="%22Middle+Schools%22">Middle Schools</searchLink><br /><searchLink fieldCode="EL" term="%22Secondary+Education%22">Secondary Education</searchLink>
– Name: Subject
  Label: Descriptors
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Middle+School+Students%22">Middle School Students</searchLink><br /><searchLink fieldCode="DE" term="%22Middle+School+Mathematics%22">Middle School Mathematics</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+Skills%22">Mathematics Skills</searchLink><br /><searchLink fieldCode="DE" term="%22Problem+Solving%22">Problem Solving</searchLink><br /><searchLink fieldCode="DE" term="%22Cognitive+Processes%22">Cognitive Processes</searchLink><br /><searchLink fieldCode="DE" term="%22Difficulty+Level%22">Difficulty Level</searchLink><br /><searchLink fieldCode="DE" term="%22Equations+%28Mathematics%29%22">Equations (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Recall+%28Psychology%29%22">Recall (Psychology)</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+Tests%22">Mathematics Tests</searchLink><br /><searchLink fieldCode="DE" term="%22Scores%22">Scores</searchLink>
– Name: DOI
  Label: DOI
  Group: ID
  Data: 10.1007/s11251-025-09759-y
– Name: ISSN
  Label: ISSN
  Group: ISSN
  Data: 0020-4277<br />1573-1952
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: 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.
– Name: AbstractInfo
  Label: Abstractor
  Group: Ab
  Data: As Provided
– Name: DateEntry
  Label: Entry Date
  Group: Date
  Data: 2026
– Name: AN
  Label: Accession Number
  Group: ID
  Data: EJ1497470
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=eric&AN=EJ1497470
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1007/s11251-025-09759-y
    Languages:
      – Text: English
    Subjects:
      – SubjectFull: Middle School Students
        Type: general
      – SubjectFull: Middle School Mathematics
        Type: general
      – SubjectFull: Mathematics Skills
        Type: general
      – SubjectFull: Problem Solving
        Type: general
      – SubjectFull: Cognitive Processes
        Type: general
      – SubjectFull: Difficulty Level
        Type: general
      – SubjectFull: Equations (Mathematics)
        Type: general
      – SubjectFull: Recall (Psychology)
        Type: general
      – SubjectFull: Mathematics Tests
        Type: general
      – SubjectFull: Scores
        Type: general
    Titles:
      – TitleFull: The Facilitation Effect of Key-Step Retrieval Practice on Learning One-Variable Quadratic Equations
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Kejia Qu
      – PersonEntity:
          Name:
            NameFull: Ruiqian Ma
      – PersonEntity:
          Name:
            NameFull: Yadi Yu
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 06
              Type: published
              Y: 2026
          Identifiers:
            – Type: issn-print
              Value: 0020-4277
            – Type: issn-electronic
              Value: 1573-1952
          Numbering:
            – Type: volume
              Value: 54
            – Type: issue
              Value: 1
          Titles:
            – TitleFull: Instructional Science: An International Journal of the Learning Sciences
              Type: main
ResultId 1