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Classification of Abstract Thinking in Solving Mathematical Problems

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Title: Classification of Abstract Thinking in Solving Mathematical Problems
Language: English
Authors: Muhammad Noor Kholid (ORCID 0000-0002-7215-3239), Noviani Nur Aisyah (ORCID 0009-0003-6767-101X)
Source: Educational Process: International Journal. Article e2025194 2025 16.
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: 21
Publication Date: 2025
Document Type: Journal Articles
Reports - Research
Education Level: Higher Education
Postsecondary Education
Descriptors: Abstract Reasoning, Thinking Skills, Mathematics Skills, Problem Solving, College Mathematics, College Students, Foreign Countries, Reflection, Logical Thinking, Visual Learning, Equations (Mathematics)
Geographic Terms: Indonesia
ISSN: 2147-0901
2564-8020
Abstract: Background/purpose: This research aims to classify and show the characteristics of the types of abstract thinking students use when solving mathematical problems. Materials/methods: This descriptive qualitative research was conducted in a structured manner on students of the University of Muhammadiyah Surakarta, Faculty of Teacher Training and Education, Mathematics Education Study Program, semesters 3, 5, and 7. The instruments of this research include a two-variable linear equation (SELTV), story questions, and audio-visual recording tools. Data collection is carried out through tests. The data is analyzed through data reduction, presentation, and conclusion. Results: This research finds a way to solve problems directly from the subject's thinking. Its findings are in the form of three classifications of abstract thinking: reflective abstraction, connected abstraction, and visual abstraction. Conclusion: This research identifies and classifies the types of abstract thinking students use in solving mathematical problems, such as symbolic, logical, connective, and visual thinking. Every kind of abstract thinking plays an important role in solving various mathematical problems, including systems of linear equations in two variables.
Abstractor: As Provided
Entry Date: 2025
Accession Number: EJ1483384
Database: ERIC
FullText Text:
  Availability: 0
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  Data: Classification of Abstract Thinking in Solving Mathematical Problems
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  Data: English
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  Data: <searchLink fieldCode="AR" term="%22Muhammad+Noor+Kholid%22">Muhammad Noor Kholid</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0002-7215-3239">0000-0002-7215-3239</externalLink>)<br /><searchLink fieldCode="AR" term="%22Noviani+Nur+Aisyah%22">Noviani Nur Aisyah</searchLink> (ORCID <externalLink term="https://orcid.org/0009-0003-6767-101X">0009-0003-6767-101X</externalLink>)
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  Data: <searchLink fieldCode="SO" term="%22Educational+Process%3A+International+Journal%22"><i>Educational Process: International Journal</i></searchLink>. Article e2025194 2025 16.
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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: Y
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  Data: 21
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  Data: 2025
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  Data: Journal Articles<br />Reports - Research
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  Data: <searchLink fieldCode="EL" term="%22Higher+Education%22">Higher Education</searchLink><br /><searchLink fieldCode="EL" term="%22Postsecondary+Education%22">Postsecondary Education</searchLink>
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  Data: <searchLink fieldCode="DE" term="%22Abstract+Reasoning%22">Abstract Reasoning</searchLink><br /><searchLink fieldCode="DE" term="%22Thinking+Skills%22">Thinking Skills</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="%22College+Mathematics%22">College Mathematics</searchLink><br /><searchLink fieldCode="DE" term="%22College+Students%22">College Students</searchLink><br /><searchLink fieldCode="DE" term="%22Foreign+Countries%22">Foreign Countries</searchLink><br /><searchLink fieldCode="DE" term="%22Reflection%22">Reflection</searchLink><br /><searchLink fieldCode="DE" term="%22Logical+Thinking%22">Logical Thinking</searchLink><br /><searchLink fieldCode="DE" term="%22Visual+Learning%22">Visual Learning</searchLink><br /><searchLink fieldCode="DE" term="%22Equations+%28Mathematics%29%22">Equations (Mathematics)</searchLink>
– Name: Subject
  Label: Geographic Terms
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Indonesia%22">Indonesia</searchLink>
– Name: ISSN
  Label: ISSN
  Group: ISSN
  Data: 2147-0901<br />2564-8020
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Background/purpose: This research aims to classify and show the characteristics of the types of abstract thinking students use when solving mathematical problems. Materials/methods: This descriptive qualitative research was conducted in a structured manner on students of the University of Muhammadiyah Surakarta, Faculty of Teacher Training and Education, Mathematics Education Study Program, semesters 3, 5, and 7. The instruments of this research include a two-variable linear equation (SELTV), story questions, and audio-visual recording tools. Data collection is carried out through tests. The data is analyzed through data reduction, presentation, and conclusion. Results: This research finds a way to solve problems directly from the subject's thinking. Its findings are in the form of three classifications of abstract thinking: reflective abstraction, connected abstraction, and visual abstraction. Conclusion: This research identifies and classifies the types of abstract thinking students use in solving mathematical problems, such as symbolic, logical, connective, and visual thinking. Every kind of abstract thinking plays an important role in solving various mathematical problems, including systems of linear equations in two variables.
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  Data: 2025
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  Data: EJ1483384
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RecordInfo BibRecord:
  BibEntity:
    Languages:
      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 21
    Subjects:
      – SubjectFull: Abstract Reasoning
        Type: general
      – SubjectFull: Thinking Skills
        Type: general
      – SubjectFull: Mathematics Skills
        Type: general
      – SubjectFull: Problem Solving
        Type: general
      – SubjectFull: College Mathematics
        Type: general
      – SubjectFull: College Students
        Type: general
      – SubjectFull: Foreign Countries
        Type: general
      – SubjectFull: Reflection
        Type: general
      – SubjectFull: Logical Thinking
        Type: general
      – SubjectFull: Visual Learning
        Type: general
      – SubjectFull: Equations (Mathematics)
        Type: general
      – SubjectFull: Indonesia
        Type: general
    Titles:
      – TitleFull: Classification of Abstract Thinking in Solving Mathematical Problems
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            NameFull: Muhammad Noor Kholid
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            NameFull: Noviani Nur Aisyah
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          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2025
          Identifiers:
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              Value: 2147-0901
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              Value: 2564-8020
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              Value: 16
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            – TitleFull: Educational Process: International Journal
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