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Students' Problem-Solving Behavior in Differential Calculus Based on Mathematical Prior Knowledge

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Title: Students' Problem-Solving Behavior in Differential Calculus Based on Mathematical Prior Knowledge
Language: English
Authors: Dwi Sulistyaningsih (ORCID 0000-0003-1757-437X), Stevanus Budi Waluya (ORCID 0000-0002-8834-1138), Isnarto (ORCID 0009-0001-3877-6512), Sugiman (ORCID 0000-0002-1656-6661)
Source: Educational Process: International Journal. Article e2025565 2025 19.
Availability: UNIVERSITEPARK Limited. iTOWER Plaza (No61, 9th floor) Merkez Mh Akar Cd No3, Sisli, Istanbul, Turkey 34382. e-mail: editor@edupij.com; Web site: http://www.edupij.com/
Peer Reviewed: Y
Page Count: 19
Publication Date: 2025
Document Type: Journal Articles
Reports - Research
Education Level: Higher Education
Postsecondary Education
Descriptors: College Students, Mathematics Education, Calculus, College Mathematics, Problem Solving, Student Behavior, Prior Learning, Mathematical Models, Foreign Countries
Geographic Terms: Indonesia
ISSN: 2147-0901
2564-8020
Abstract: Background/purpose: This study aims to analyze students' ability to solve differential calculus problems in relation to their prior mathematical knowledge (PMK). Materials/methods: A qualitative research design method was employed. Participants in this study were 103 third-semester students at the university enrolled in the Differential Calculus course. They were divided into three groups, i.e., high, medium, and low, based on their PMK scores. They were given the same real-life problems to solve using differential calculus. In-depth interviews were conducted to identify and clarify things written and not written on the answer sheets. Data were analyzed using the Miles and Huberman model, while the process stages were analyzed according to the Bransford and Stein stages. Results: The results showed that the real number course was the most mastered, indicated by the highest average PRK test score. The majority of students, namely 50.49%, were at the medium PMK level. Only the best group at the high PMK level could achieve correct final results and follow the Bradford and Stein stages. The group that excelled most at solving differential calculus problems was those with high limit course scores, not those with high real number course scores. It was also found that converting real-life problems into mathematical models was the most difficult stage. Conclusion: Students who included problem scenario images during this phase performed better than those who did not. The most challenging problem was transforming a real-life problem into a mathematical model. Therefore, it is recommended to add a phase of transforming a real-life problem into a mathematical problem after the problem identification phase in Bransford and Stein's stages.
Abstractor: As Provided
Entry Date: 2025
Accession Number: EJ1489886
Database: ERIC
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  Data: Students' Problem-Solving Behavior in Differential Calculus Based on Mathematical Prior Knowledge
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  Data: <searchLink fieldCode="AR" term="%22Dwi+Sulistyaningsih%22">Dwi Sulistyaningsih</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0003-1757-437X">0000-0003-1757-437X</externalLink>)<br /><searchLink fieldCode="AR" term="%22Stevanus+Budi+Waluya%22">Stevanus Budi Waluya</searchLink> (ORCID <externalLink term="http://orcid.org/0000-0002-8834-1138">0000-0002-8834-1138</externalLink>)<br /><searchLink fieldCode="AR" term="%22Isnarto%22">Isnarto</searchLink> (ORCID <externalLink term="https://orcid.org/0009-0001-3877-6512">0009-0001-3877-6512</externalLink>)<br /><searchLink fieldCode="AR" term="%22Sugiman%22">Sugiman</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0002-1656-6661">0000-0002-1656-6661</externalLink>)
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  Data: UNIVERSITEPARK Limited. iTOWER Plaza (No61, 9th floor) Merkez Mh Akar Cd No3, Sisli, Istanbul, Turkey 34382. e-mail: editor@edupij.com; Web site: http://www.edupij.com/
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  Data: 2147-0901<br />2564-8020
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Background/purpose: This study aims to analyze students' ability to solve differential calculus problems in relation to their prior mathematical knowledge (PMK). Materials/methods: A qualitative research design method was employed. Participants in this study were 103 third-semester students at the university enrolled in the Differential Calculus course. They were divided into three groups, i.e., high, medium, and low, based on their PMK scores. They were given the same real-life problems to solve using differential calculus. In-depth interviews were conducted to identify and clarify things written and not written on the answer sheets. Data were analyzed using the Miles and Huberman model, while the process stages were analyzed according to the Bransford and Stein stages. Results: The results showed that the real number course was the most mastered, indicated by the highest average PRK test score. The majority of students, namely 50.49%, were at the medium PMK level. Only the best group at the high PMK level could achieve correct final results and follow the Bradford and Stein stages. The group that excelled most at solving differential calculus problems was those with high limit course scores, not those with high real number course scores. It was also found that converting real-life problems into mathematical models was the most difficult stage. Conclusion: Students who included problem scenario images during this phase performed better than those who did not. The most challenging problem was transforming a real-life problem into a mathematical model. Therefore, it is recommended to add a phase of transforming a real-life problem into a mathematical problem after the problem identification phase in Bransford and Stein's stages.
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  Data: EJ1489886
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RecordInfo BibRecord:
  BibEntity:
    Languages:
      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 19
    Subjects:
      – SubjectFull: College Students
        Type: general
      – SubjectFull: Mathematics Education
        Type: general
      – SubjectFull: Calculus
        Type: general
      – SubjectFull: College Mathematics
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      – SubjectFull: Problem Solving
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      – SubjectFull: Student Behavior
        Type: general
      – SubjectFull: Prior Learning
        Type: general
      – SubjectFull: Mathematical Models
        Type: general
      – SubjectFull: Foreign Countries
        Type: general
      – SubjectFull: Indonesia
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    Titles:
      – TitleFull: Students' Problem-Solving Behavior in Differential Calculus Based on Mathematical Prior Knowledge
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            NameFull: Dwi Sulistyaningsih
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            NameFull: Stevanus Budi Waluya
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            NameFull: Sugiman
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              M: 01
              Type: published
              Y: 2025
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            – TitleFull: Educational Process: International Journal
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