Concept Images of University Students for Geometric Representation of the Double Integral Concept

Year 2023, Volume: 17 Issue: 1, 66 - 98, 30.06.2023

Mustafa Özbey Şenol Dost

https://doi.org/10.17522/balikesirnef.1274911

Abstract

This study has focused on how university students understand the geometric representation of double integral. For this purpose, six participants have been asked six questions. Later, semi-structured interviews were conducted with the participants. In this study, the data obtained from questionnaire form and interviews were analyzed with open and axial coding. As a result of this research, it was observed that the concept images of university students were grouped into two categories as “area” and “volume”. It was determined that the participants acted with an intuitive approach without having to establish a relationship between the concept definition and the concept image, the ∬ in the symbol of the double integral caused the participants to think of it as a two-dimensional geometric structure and their image of the concept of the single integral was very active. The findings obtained in this research shows that there are problems in understanding the concept of the double integral, which is the first step of generalizing to multiple integrals, and that educator should produce solutions for this subject.

Keywords

Double integral, concept image, concept definition, university students

Matematik Öğretmeni Adaylarının Çift İntegral Kavramının Geometrik Temsiline Yönelik Kavram Görselleri

Abstract

Bu çalışmada matematik öğretmen adaylarının çift katlı integralin geometrik temsilini nasıl anladıklarına odaklanılmıştır. Araştırmanın amacı doğrultusunda bu çalışmanın araştırma deseni, temel nitel araştırma yöntemi olarak benimsenmiştir. Altı katılımcıya altı soru sorulmuştur. Daha sonra katılımcılarla yarı yapılandırılmış görüşmeler yapılmıştır. Anket formu ve görüşmelerden elde edilen veriler açık ve eksensel kodlama ile analiz edilmiştir. Araştırma sonucunda matematik öğretmen adaylarının kavram imajlarının “alan” ve “hacim” olmak üzere iki kategoride toplandığı görülmüştür. Araştırmadan elde edilen veriler doğrultusunda, katılımcıların kavram tanımı ile kavram imajı arasında ilişki kurmak zorunda kalmadan sezgisel bir yaklaşımla hareket ettikleri, çift katlı integral sembolünü ∬ iki boyutlu geometrik bir yapı gibi düşündükleri ve tek katlı integral kavramına ilişkin imajları etkin olduğuna ulaşılmıştır. Bu araştırmada elde edilen bulgular, çoklu integrali genellemenin ilk adımı olan çift katlı integral kavramının anlaşılmasında zorluklar olduğunu ve eğitimcilerin bu konuya yönelik çözümler üretmesi gerektiğini göstermektedir.

Keywords

Çift katlı integral, kavram imajı, kavram tanımı, matematik öğretmen adayları.

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