대학 신입생들의 미적분학 학습에 관한 연구

Abstract

This study examined and analyzed the difficulties and errors committed by students taking a calculus course at "P" university. The research participants were 599 students who were asked questions about practice problems on calculus, and below is a summary of analysis results. First, there were 302 questions regarding problems on limits and continuities. Among them, 70 were on limits of sequences and 128 were on limits of functions. Second, there were 372 questions on derivatives, where participants expressed difficulties in solving problems related to the mean value theorem, L'Hôpital's rules, and definition of derivatives. Third, there were 445 and 1,074 questions on indefinite integrals and finite integrals, respectively. Participants expressed particular difficulties in solving problems on integration by rational function and integration by substitution in indefinite integrals, and problems related to volumes and integration by parts in finite integrals. Fourth, there were 208 questions on infinite series and power series, where participants struggled the most with the problems related to the integral test for convergence and root test. Fifth, there were 196 and 168 questions on partial differentiation and double integration, respectively. Regarding partial differentiation, participants had difficulties solving problems that asked them to find the limit at a point in a given multivariate function. Regarding double integration, they struggled to find the volume of a surrounded three-dimensional object.