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 |
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| Language: | English |
| Authors: | Camilo Andrés Rodríguez-Nieto (ORCID |
| 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 |
| 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. |
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| ISSN: | 2147-0901 2564-8020 |
