Student errors and concept images in multiple integrals

The Analysis (Calculus) course provided to mathematics, engineering and science students is one of the sub-branches of mathematics that is founded by Newton and Leibniz in 17th Century. Analysis deals with the immeasurably small quantities in the rates of change in the area of a specific region or volume of objects that are determined by means of a function. When the literature regarding the student errors in Analysis course is scanned, it is observed that the carried out studies are usually focused on single variable functions while the studies focused on multi-variable functions are rather less. In this study, it is intended to see the errors made by the students and to find out about the learning difficulties they experience in the name of offering an insight into different teaching techniques that may be developed in order to teach the subject of integral in multi-variable functions in an effective manner. This study is carried out in order to see and identify the errors of students regarding the concept of integral, therefore is a case study since the behaviors of students are not interfered. An open end test comprising ten questions has been used in the research. Obtained data have been analyzed quantitatively and qualitatively. In the quantitative part, the solution of each question has been divided into sub-phases, whereas correctly completed phases have been coded as 1, while the phases left blank or completed wrongly have been coded as 0. The students have been divided into sub-groups according to such codes. Formed groups have been tabularized with the student frequency and percentage presentations. In the qualitative part, however, the student errors regarding the researched outcome have been presented. As a result of the research, it is observed that the region is perceived by the students as a circular area when the functional structures that reminds of the polar coordinates are given at integral limits. On the other hand, it is observed that the students designate the region of which the integral is taken with wrong criteria during double integral calculations. It is established that the students were not able to comprehend the meanings of area and volume of double integral. In consideration of the findings obtained, it is concluded that the students have insufficiencies in terms of conceptual learning with regard to the subject of multiple integrals.