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

Document Type : بنیادی - نظری

Authors

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

10.30473/coam.2020.55039.1148

Abstract

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.

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Main Subjects


‎bibitem{a4-1}‎
‎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.
 
‎bibitem{a4-2}‎
‎Allen D‎. ‎(2001)‎. ‎``Learning integral calculus tee rough non-template''‎, ‎Problem-solving‎, ‎XI(2)‎, ‎147-160‎.
 
‎bibitem{a4-3}‎
‎Apostol T.M‎. ‎(1967)‎. ‎``Calculus‎. ‎Xerox Corporation''‎, ‎Waltham‎: ‎Massachusetts‎.
 
‎bibitem{a4-4}‎
‎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.
 
‎bibitem{a4-5}‎
‎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.
 
‎bibitem{a4-6}‎
‎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.
 
‎bibitem{a4-7}‎
‎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.
 
‎bibitem{a4-8}‎
‎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.
 
‎bibitem{a4-9}‎
‎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.
 
‎bibitem{a4-10}‎
‎Jonse S.R‎. ‎(2013)‎. ‎``Understanding the integral‎: ‎Students symbolic forms''‎, ‎Journal of mathematical behavior‎, ‎32‎, ‎122-141‎.
 
‎bibitem{a4-11}‎
‎Kiat S.E‎. ‎(2005) ``Analysis of student difficulties in solving integration problems''‎, ‎9(1)‎, ‎39-59‎.
 
‎bibitem{a4-12}‎
‎Orton A‎. ‎(1983)‎. ‎``Student's understanding of integration''‎, ‎Educational studies in mathematics‎, ‎14‎, ‎1-18‎.
 
‎bibitem{a4-13}‎
‎"{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.
 
‎bibitem{a4-14}‎
‎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.
 
‎bibitem{a4-15}‎
‎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.