Analysis of student´s challenges and performances in solving integral´s problems


  • Mohammad Darvishzadeh Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
  • Ahmad Shahvarani Department of mathematics, science and research branch, Islamic Azad University, Tehran, Iran
  • Hassan Alamolhodaei Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashahad, Iran
  • Mohammad Hassan Behzadi Department of Statistics, Science and Research Branch, Islamic Azad University, Tehran, Iran


Integral is the base of pure and applied mathematics for all students of science, especially engineering, which some of their lessons are dependent to it directly or indirectly. In fact, Integral is an indisputable concept for solve practical and executive problems of students, so it is important to pay attention to it. On the other hand, experiences of teaching Integral have indicated that most students have weakness in solve Integral problems. Through case study, an exam has been conducted in the form of six problems on six good experienced students in order to study the students' behaviors in coping with the integral problems and also to reach a proposed method for teaching the integral concept, in which each question has in turn two parts. The analysis of their responses and discussion with them have led some light on more details about the integral, how to teach it and also the problems as a result of the teaching method and the problems to which they would encounter, so that by their citation, an appropriate teaching method could be presented in order to maximally conceptualize the integral in students. On the other hand, these studies reveal that in order to solve the integral-related problems, most students first refer to the initial function approach and try to solve the problem by the direct method rather than spending their time learning conceptually and meaningfully. But those students who have used Riemann concept and infinite collection in solve Integral problems were successful in compare to others