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Engineering Students' Mathematical Understanding Based on the Quality of Mathematical Connections Activated to Solve Tasks about Function's Graph and Its Derivative

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Title: Engineering Students' Mathematical Understanding Based on the Quality of Mathematical Connections Activated to Solve Tasks about Function's Graph and Its Derivative
Language: English
Authors: Camilo Andrés Rodríguez-Nieto (ORCID 0000-0001-9922-4079), Flor Monserrat Rodríguez-Vásquez (ORCID 0000-0002-9596-4253), Vicenç Font Moll (ORCID 0000-0003-1405-0458), Sudirman Sudirman (ORCID 0000-0002-1696-5160), Benilda María Cantillo-Rudas (ORCID 0009-0006-6431-3526)
Source: Educational Process: International Journal. Article e2025394 2025 17.
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: 38
Publication Date: 2025
Document Type: Journal Articles
Reports - Research
Education Level: Higher Education
Postsecondary Education
Descriptors: Knowledge Level, Problem Solving, Graphs, Mathematics Instruction, Engineering Education, College Students, Student Attitudes, Symbols (Mathematics), Mathematical Concepts, Foreign Countries
Geographic Terms: Colombia
ISSN: 2147-0901
2564-8020
Abstract: Background/purpose. One of the current problems facing mathematics students, graduates in mathematics, and engineering is the disconnection between the meanings, symbolic representations, and graphics of derivatives when solving problems, which hinders their understanding. This article analyzes engineering students' understanding activated by connections made to solve tasks on derivatives in a graphical context. To do so, networking between the Extended Theory of Connections and the Onto-semiotic Approach will be used. Materials/methods. The methodology was qualitative and exploratory. A questionnaire was designed with three tasks on the meaning of the derivative and the graphs of the function f and the derivative f'. This questionnaire was administered in the context of participant observation to nineteen engineering students who volunteered. The collected and video-recorded data were analyzed using the theoretical tool from an onto-semiotic view. Results. The results show that students who have a level 2 understanding of the derivative (graphically) because they sketch the graph of f' given the graph of f and sketch the graph of f from the graph of f', establishing mathematical connections of implication, different representations, meaning, procedural, part-whole and the main connection of reversibility that allowed them to make the two graphs. Students who have level 1 understanding establish consistent connections, but do not argue or have details to correct in the graphs. Conclusion. Other students have level 0 understanding because they did not make the graphs of f and f' because they did not activate mathematical connections but personal connections, assuming that the graph of the derivative is a reflection of the graph of the original function, they do not locate the relative extremes, inflection points, monotony due to poor conceptual understanding.
Abstractor: As Provided
Entry Date: 2025
Accession Number: EJ1483768
Database: ERIC
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  Availability: 0
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  – Url: https://eric.ed.gov/contentdelivery/servlet/ERICServlet?accno=EJ1483768
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  Data: Engineering Students' Mathematical Understanding Based on the Quality of Mathematical Connections Activated to Solve Tasks about Function's Graph and Its Derivative
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  Data: <searchLink fieldCode="AR" term="%22Camilo+Andrés+Rodríguez-Nieto%22">Camilo Andrés Rodríguez-Nieto</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0001-9922-4079">0000-0001-9922-4079</externalLink>)<br /><searchLink fieldCode="AR" term="%22Flor+Monserrat+Rodríguez-Vásquez%22">Flor Monserrat Rodríguez-Vásquez</searchLink> (ORCID <externalLink term="http://orcid.org/0000-0002-9596-4253">0000-0002-9596-4253</externalLink>)<br /><searchLink fieldCode="AR" term="%22Vicenç+Font+Moll%22">Vicenç Font Moll</searchLink> (ORCID <externalLink term="http://orcid.org/0000-0003-1405-0458">0000-0003-1405-0458</externalLink>)<br /><searchLink fieldCode="AR" term="%22Sudirman+Sudirman%22">Sudirman Sudirman</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0002-1696-5160">0000-0002-1696-5160</externalLink>)<br /><searchLink fieldCode="AR" term="%22Benilda+María+Cantillo-Rudas%22">Benilda María Cantillo-Rudas</searchLink> (ORCID <externalLink term="https://orcid.org/0009-0006-6431-3526">0009-0006-6431-3526</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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  Label: Abstract
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  Data: Background/purpose. One of the current problems facing mathematics students, graduates in mathematics, and engineering is the disconnection between the meanings, symbolic representations, and graphics of derivatives when solving problems, which hinders their understanding. This article analyzes engineering students' understanding activated by connections made to solve tasks on derivatives in a graphical context. To do so, networking between the Extended Theory of Connections and the Onto-semiotic Approach will be used. Materials/methods. The methodology was qualitative and exploratory. A questionnaire was designed with three tasks on the meaning of the derivative and the graphs of the function f and the derivative f'. This questionnaire was administered in the context of participant observation to nineteen engineering students who volunteered. The collected and video-recorded data were analyzed using the theoretical tool from an onto-semiotic view. Results. The results show that students who have a level 2 understanding of the derivative (graphically) because they sketch the graph of f' given the graph of f and sketch the graph of f from the graph of f', establishing mathematical connections of implication, different representations, meaning, procedural, part-whole and the main connection of reversibility that allowed them to make the two graphs. Students who have level 1 understanding establish consistent connections, but do not argue or have details to correct in the graphs. Conclusion. Other students have level 0 understanding because they did not make the graphs of f and f' because they did not activate mathematical connections but personal connections, assuming that the graph of the derivative is a reflection of the graph of the original function, they do not locate the relative extremes, inflection points, monotony due to poor conceptual understanding.
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    Languages:
      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 38
    Subjects:
      – SubjectFull: Knowledge Level
        Type: general
      – SubjectFull: Problem Solving
        Type: general
      – SubjectFull: Graphs
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      – SubjectFull: Mathematics Instruction
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      – SubjectFull: Engineering Education
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      – SubjectFull: College Students
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      – SubjectFull: Student Attitudes
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      – SubjectFull: Symbols (Mathematics)
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      – SubjectFull: Mathematical Concepts
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      – SubjectFull: Foreign Countries
        Type: general
      – SubjectFull: Colombia
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    Titles:
      – TitleFull: Engineering Students' Mathematical Understanding Based on the Quality of Mathematical Connections Activated to Solve Tasks about Function's Graph and Its Derivative
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            NameFull: Camilo Andrés Rodríguez-Nieto
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              Y: 2025
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