Analysis of Students' Mistakes in Solving Integrals to Minimize their Mistakes

Document Type : بنیادی - نظری


1 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.

2 Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashahad, Iran

3 , Department of Statistics, Science and Research Branch, Islamic Azad University, Tehran, Iran



Experiences of teaching Integral have indicated that the vast majorities of Iranian university students commit numerous errors while solving integral problems and have weak skills in this field; we might even say that they hide away from integral and consider it the nightmare of mathematics‎. ‎On the other hand, Integral is the base of pure and applied mathematics for all students of science‎, ‎especially engineering‎, ‎which some of their lessons are dependent on it directly or indirectly‎, ‎so it is important to pay attention to it‎. ‎Through descriptive method-exposed factor, ‎an exam has been conducted in the form of three questions‎, ‎the first of which is consisted of 4 sections on fifty students from different fields, and then interviews were conducted with a few of those students about their answers in order to study the students' behaviors when solving integral problems and to determine the type of their errors‎. ‎By analyzing the performance of students in this test‎, ‎we can see that students often struggle with integral and mostly have a feeble performance in solving trigonometric integrals‎. ‎They want to learn computational integral instead of how to conceptualize integral in their minds correctly‎. ‎The error most committed by university students was procedural errors‎, ‎which arise from using derivative instead of integral‎. ‎Besides most of the mistakes happen in solving definite integrals‎, ‎and calculating finite areas between two curves‎. ‎This is due to a lack of understanding of integrals and a lack of information in other areas of mathematics.


Main Subjects

‎Adi Wibawa K.‎, ‎Nusantara T.‎, ‎Subanji Parta N‎. ‎(2017)‎. ‎``Fragmentation of Thinking‎
‎Structure's Students to Solving the Problem of Application Definite Integral in Area''‎, ‎International Education Studies‎, ‎10(5)‎, ‎48-60‎.
‎Allen D‎. ‎(2001)‎. ‎``Learning integral calculus tee rough non-template''‎, ‎Problem-solving‎, ‎XI(2)‎, ‎147-160‎.
‎Apostol T.M‎. ‎(1967)‎. ‎``Calculus‎. ‎Xerox Corporation''‎, ‎Waltham‎: ‎Massachusetts‎.
‎Baki M‎. ‎Cekmez E‎. ‎(2012)‎. ‎``Prospective elementary mathematics teachers' understandings about the formal definition of limit''‎, ‎Turkish Journal of Computer and Mathematics Education‎, ‎3(2)‎, ‎81-98‎.
‎Biber A‎. ا., ‎Arg"{u}n Z‎. ‎(2015)‎. ‎``The relations between concept knowledge related to the limits concepts in one and two variables functions of mathematics teachers candidates''‎, ‎Bartin University Journal of Faculty of Education‎, ‎4(2)‎, ‎501-515‎.
‎Cetin F."{O}.‎, ‎Dane A.‎, ‎Bekdemir M‎. ‎(2012)‎. ‎``A concept of accumulation point and its usage''‎, ‎Necatibey Faculty of Education Electronic Journal of Science and Mathematics Education‎, ‎6(2)‎, ‎217-233‎.
‎Dan A.‎, ‎Faruk Cetin O.‎, ‎Ba F.‎, ‎"{O}zturan Sa$v{rm g}$ırulilı‎ , ‎M‎. ‎(2016)‎. ‎``A Conceptual and Procedural Research on the Hierarchical Structure of Mathematics Emerging in the Minds of University Students‎: ‎An Example of Limit-Continuity-Integral-Derivative''‎, ‎International Journal of Higher Education‎, ‎5(2)‎, ‎82-91‎.
‎Dancis J.(2001)‎. ‎``Student modeling of physical phenomena as they derive standard integral formulae‎: ‎One way to reduce proof phobia''‎, ‎PRIMUS‎, ‎XI(2)‎, ‎124-146‎.
‎Kula S.‎, ‎Bukova G"{u}zel E‎. ‎(2015)‎. ‎``Reflections of Mathematics Student Teachers' Knowledge Related to the Purposes of the Curriculum on Their Limit Teaching''‎, ‎Journal of Theoretical Educational Science‎, ‎8(1)‎, ‎28-49‎.
‎Jonse S.R‎. ‎(2013)‎. ‎``Understanding the integral‎: ‎Students symbolic forms''‎, ‎Journal of mathematical behavior‎, ‎32‎, ‎122-141‎.
‎Kiat S.E‎. ‎(2005) ``Analysis of student difficulties in solving integration problems''‎, ‎9(1)‎, ‎39-59‎.
‎Orton A‎. ‎(1983)‎. ‎``Student's understanding of integration''‎, ‎Educational studies in mathematics‎, ‎14‎, ‎1-18‎.
‎"{O}zkaya M.‎, ‎Isık A.‎, ‎Konyalıo$v{rm g}$lu A‎. ‎(2014)‎. ‎``Proofing and counter-exampling performances of students in the elementary mathematics education department for continuous functions''‎, ‎Middle Eastern & African Journal of Educational Research‎, ‎11‎, ‎26-42‎.
‎Thomas M.‎, ‎& Hong Y.Y‎. ‎(1996)‎. ‎``The Riemann Integral in Calculus‎: ‎Student's Processes and Concepts‎, ‎In P‎. ‎C‎. ‎Clarkson (Ed.)‎, ‎Proceeding of the ${19}^{th}$ Annual Conference of the Mathematics Education Research Group of Australia''‎, ‎Melbourne‎, ‎Victoria‎, ‎Australia‎.
‎Ubuz B‎. ‎(2011)‎. ‎``Factors associated with success in a calculus course‎: ‎An examination of personal variables''‎, ‎International journal of mathematical education in science and technology‎, ‎42(1)‎, ‎1-12‎.