Students' Conception on Multiple Integrals of a Function of Several Variables: A Case of Adama Science and Technology University

Abstract

The study was conducted at Adama Science and Technology University to investigate students' conceptual understanding in learning Applied Mathematics II in general and multiple integrals in particular. A case study research design was employed on a Mechanical engineering group one student. This group was randomly selected through simple random sampling techniques. The number of students involved in this study was 50. Qualitative data were collected through reasoning part of the multiple choice items of the pre-test and interview items of the post-test were analyzed using APOS analysis based on proposed genetic decompositions. These tools were intended to investigate the conceptual understanding of students and the way they justify their answers. The study shows that the majority of the students' conception of multiple integrals could be categorized under action level whereas a few students were categorized under process conception. Students' conceptual understanding on multiple integrals of a function of two variables is a straight forward as that of a function of a single variable, which reveals that students have not developed a new schema for a function of two variables, as different from a function of a single variable. The majority of the respondents was poor at extending previous concepts to the new concept and had difficulty to represent multiple integrals using graph. Thus; the researchers recommended the utilization of an appropriate instructional approach in order to scaffold students' conceptual understanding of multiple integrals.