View in EDS

How Students Think about a Reverse Problem of Derivative: A Study of Arnon's Coordination in Mental Mechanism

Saved in:
Bibliographic Details
Title: How Students Think about a Reverse Problem of Derivative: A Study of Arnon's Coordination in Mental Mechanism
Language: English
Authors: Fara Virgianita Pangadongan, Toto Nusantara, I Made Sulandra
Source: Mathematics Teaching Research Journal. 2025 17(6):42-73.
Availability: City University of New York. Creative Commons. 205 East 42 Street, New York, NY 10017. Web site: https://mtrj.commons.gc.cuny.edu/
Peer Reviewed: Y
Page Count: 32
Publication Date: 2025
Document Type: Journal Articles
Reports - Research
Education Level: Higher Education
Postsecondary Education
Descriptors: Problem Solving, Cognitive Processes, Coordination, Mathematics Education, College Students, Mathematics
ISSN: 2573-4377
Abstract: Mental mechanism of coordination is indispensable in the construction of certain objects, contributing to problem-solving. Although Arnon et al. hypothesized about how two processes are coordinated mentally, which is referred to as Arnon's Coordination, further analysis is required. Studies related to coordination had explored its emergence in reflective abstraction during problem-solving. Generally, descriptions of coordination focused exclusively on the outcomes and application to problem-solving, particularly direct problems. Therefore, this study aimed to describe how students performed coordination between two processes in reverse problem-solving, focusing mainly on derivative and antiderivative graphs. Data were collected from 4 of the 44 third-year mathematics education students through answer sheets, think-aloud, and semi-structured interviews to examine mental mechanisms. The results showed that students coordinated the two processes by adopting three cognitive actions, namely determining processes, transforming it into an object through encapsulation, and integration through assimilation or accommodation. This also included the challenges students experienced with each cognitive action. In conclusion, this study served as a reference for educators when designing mathematical problem-solving exercises and lessons.
Abstractor: As Provided
Entry Date: 2026
Accession Number: EJ1507449
Database: ERIC
FullText Text:
  Availability: 0
CustomLinks:
  – Url: https://eric.ed.gov/contentdelivery/servlet/ERICServlet?accno=EJ1507449
    Name: ERIC Full Text
    Category: fullText
    Text: Full Text from ERIC
Header DbId: eric
DbLabel: ERIC
An: EJ1507449
AccessLevel: 3
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: How Students Think about a Reverse Problem of Derivative: A Study of Arnon's Coordination in Mental Mechanism
– Name: Language
  Label: Language
  Group: Lang
  Data: English
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Fara+Virgianita+Pangadongan%22">Fara Virgianita Pangadongan</searchLink><br /><searchLink fieldCode="AR" term="%22Toto+Nusantara%22">Toto Nusantara</searchLink><br /><searchLink fieldCode="AR" term="%22I+Made+Sulandra%22">I Made Sulandra</searchLink>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="SO" term="%22Mathematics+Teaching+Research+Journal%22"><i>Mathematics Teaching Research Journal</i></searchLink>. 2025 17(6):42-73.
– Name: Avail
  Label: Availability
  Group: Avail
  Data: City University of New York. Creative Commons. 205 East 42 Street, New York, NY 10017. Web site: https://mtrj.commons.gc.cuny.edu/
– Name: PeerReviewed
  Label: Peer Reviewed
  Group: SrcInfo
  Data: Y
– Name: Pages
  Label: Page Count
  Group: Src
  Data: 32
– Name: DatePubCY
  Label: Publication Date
  Group: Date
  Data: 2025
– 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="%22Higher+Education%22">Higher Education</searchLink><br /><searchLink fieldCode="EL" term="%22Postsecondary+Education%22">Postsecondary Education</searchLink>
– Name: Subject
  Label: Descriptors
  Group: Su
  Data: <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="%22Coordination%22">Coordination</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+Education%22">Mathematics Education</searchLink><br /><searchLink fieldCode="DE" term="%22College+Students%22">College Students</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics%22">Mathematics</searchLink>
– Name: ISSN
  Label: ISSN
  Group: ISSN
  Data: 2573-4377
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Mental mechanism of coordination is indispensable in the construction of certain objects, contributing to problem-solving. Although Arnon et al. hypothesized about how two processes are coordinated mentally, which is referred to as Arnon's Coordination, further analysis is required. Studies related to coordination had explored its emergence in reflective abstraction during problem-solving. Generally, descriptions of coordination focused exclusively on the outcomes and application to problem-solving, particularly direct problems. Therefore, this study aimed to describe how students performed coordination between two processes in reverse problem-solving, focusing mainly on derivative and antiderivative graphs. Data were collected from 4 of the 44 third-year mathematics education students through answer sheets, think-aloud, and semi-structured interviews to examine mental mechanisms. The results showed that students coordinated the two processes by adopting three cognitive actions, namely determining processes, transforming it into an object through encapsulation, and integration through assimilation or accommodation. This also included the challenges students experienced with each cognitive action. In conclusion, this study served as a reference for educators when designing mathematical problem-solving exercises and lessons.
– 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: EJ1507449
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=eric&AN=EJ1507449
RecordInfo BibRecord:
  BibEntity:
    Languages:
      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 32
        StartPage: 42
    Subjects:
      – SubjectFull: Problem Solving
        Type: general
      – SubjectFull: Cognitive Processes
        Type: general
      – SubjectFull: Coordination
        Type: general
      – SubjectFull: Mathematics Education
        Type: general
      – SubjectFull: College Students
        Type: general
      – SubjectFull: Mathematics
        Type: general
    Titles:
      – TitleFull: How Students Think about a Reverse Problem of Derivative: A Study of Arnon's Coordination in Mental Mechanism
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Fara Virgianita Pangadongan
      – PersonEntity:
          Name:
            NameFull: Toto Nusantara
      – PersonEntity:
          Name:
            NameFull: I Made Sulandra
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2025
          Identifiers:
            – Type: issn-electronic
              Value: 2573-4377
          Numbering:
            – Type: volume
              Value: 17
            – Type: issue
              Value: 6
          Titles:
            – TitleFull: Mathematics Teaching Research Journal
              Type: main
ResultId 1