Correlation analysis of students' success in solving analytic geometry and multiple integral problems

Aleksandar Milenković, Radoslav Božić, Djurdjica Takači

In this paper, we aim to contribute to the planning and implementation of education in higher mathematics education for students from non-mathematics study programs, specifically focusing on multivariable calculus, i.e., multiple integrals. Indeed, the outcomes of various empirical studies indicate that students from non-mathematical faculties struggle to grasp and comprehend multiple integrals and multivariable functions in general. The research presented in this paper aims to ascertain whether there is a significant correlation between students' achievements in multiple integrals and their achievements in applying knowledge and skills from analytical geometry (to define sets of points in the plane and space, determined by lines, curves, planes and surfaces). Additionally, the study investigates whether this correlation potentially varies based on the various instructional teaching approaches. The presented empirical research was conducted at the Faculty of Engineering, University of Kragujevac, with 72 second-year students, divided into two groups. The results indicate that the given linear correlation is statistically significant and positive. Moreover, the differences in correlation coefficients calculated for two groups of students who acquired knowledge in multiple integrals through different instructional approaches are not statistically significant. These findings underscore the need to devote substantial attention to the teaching of multiple integrals, especially in devising methods that enable students to visualize specific mathematical concepts in both plane and space. Additionally, a precise definition of integration domains, and an accurate specification of variable bounds, should be emphasized in the multiple integrals teaching and learning process.