Evaluation of Students' Conceptual Understanding of Double Integral Using APOS Theory

Subject Areas : Educational Management

Zahra Jafaribehbahani ¹ , mohsen roodaki ²

1 - Assistant Professor, Department of Mathematics, Marvdasht Branch, Islamic Azad University, Marvdasht, Iran
2 - Department of Mathematics, Marvdasht Branch, Islamic Azad University, Marvdasht, Iran

Received: 2025-01-16 Accepted : 2025-02-10 Published : 2025-02-12

Keywords: APOS theory, Conceptual understanding, Bivariate functions, Double integrals. ,

Abstract :

Introduction: One of the important topics that plays an important role in the education of engineering students is double integral. The present research has investigated the level of conceptual understanding of undergraduate engineering students of the double integral by using the APOS theory.
Methodology: The sample was 127 undergraduate students of engineering fields and generally students of the second semester. After teaching the subject of double integral to the students, a test consisting of questions corresponding to the topics taught to the students was held. Evaluation of the level of conceptual understanding and examination of students' challenges was done by analyzing their answers to this test based on the four levels of APOS.
Findings: More than 60% of the students didn’t deeply understand the consept of double integral. Most of the students' understanding of the double integral does not rise above the level of the process, and their biggest challenge was changing the order of integration. Few of them had reached the surface of the object. The examining students' answers and interviewing them after the test showed that a large number of them have learned this important topic in a procedural way.
Conclusion: The results showed the lack of deep and conceptual understanding of a large number of undergraduate engineering students on the topic of double integral. Due to the importance of conceptual understanding of this topic and the inability of the traditional method to create this deep understanding, the need to improve educational strategies and use more suitable teaching methods for learning this topic is felt. One of the weaknesses of the students that had a negative effect on their performance was the weakness in drawing the integration area when necessary, which shows the lack of deep learning of related basic topics. To solve this problem, education can be developed using appropriate software, as well as solving more problems and generally using active teaching methods in math classes.

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