Funda AYDIN GÜÇ
(Giresun Üniversitesi, Giresun, Türkiye)
Derya AYGÜN
(Milli Eğitim Bakanlığı, Ankara, Türkiye)
Yıl: 2021Cilt: 8Sayı: 2ISSN: 2148-225XSayfa Aralığı: 1106 - 1126İngilizce

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ERRORS AND MISCONCEPTIONS OF EIGHTH-GRADE STUDENTS REGARDING OPERATIONS WITH ALGEBRAIC EXPRESSIONS
The study aimed to determine the mistakes of students in operations with algebraic expressions, and their misconceptions that may lead to errors. The study adopted case study method, one of the qualitative research models. The participants were composed of 48 (24 boys, 24 girls) randomly selected among 8th grade students in three different classes from three different schools that were selected via convenience sampling method. To determine students’ errors and misconceptions, the “Misconceptions Diagnostic Test for Operationswith Algebraic Expressions” was developed by the researchers, considering the curriculum, relevant literature, and researchers’ teaching experience. The diagnostic test included 10 open-ended questions. In addition, clinical interviews were conducted with all students on their wrong answers. Results indicated that the most common misconception was that the minus at the beginning of the algebraic expression had no meaning and that half of the students had this misconception. It was also observed that the number of students with the following misconceptions were close to each other: “The operation on one side of the equation should also be applied to the other side so that the equality is not broken”, “we should take into account the order of operation priority in integers while writing the sentences as algebraic expressions,” and “everything before the parenthesis is distributed to the parentheses.” The reasons for the emergence of these misconceptions were found to beepistemological barriers and over-generalization of information in arithmetic.
DergiAraştırma MakalesiErişime Açık
  • Akkaya, R., & Durmuş, S. (2006). Misconceptions of elementary school students in grades 6- 8 on learning algebra. Hacettepe University Journal of Education, 31(31), 1-12.
  • Akyüz, G., & Hangül, T. (2014). A study on overcoming misconceptions of 6th graders about equations. Journal of Theoretical Educational Science, 7(1), 16-43.
  • Arnawa, I. M., & Nita, S. (2019, October). Errors and misconceptions in learning elementary linear algebra. Journal of Physics: Conference Series, 1321(2).
  • Booth, J. L., & Koedinger, K. R. (2008). Key misconceptions in algebraic problem solving. In Proceedings of the Annual Meeting of the Cognitive Science Society, 30(30).
  • Cohen, E., & Kanim, S. E. (2005). Factors influencing the algebra “reversal error”. American Journal of Physics, 73(11), 1072-1078.
  • Cortes, A., & Pfaff, N. (2000). Solving equations and inequations: operational invariants and methods constructed by students. In PME Conference, 2(2), 2-193.
  • Das, K. (2020). A study on misconception of using brackets in arithmetic expression. Shanlax International Journal of Education, 8(4), 76-80.
  • Davidenko, S. (1997). Building the concept of function from students' everyday activities. The Mathematics Teacher, 90(2), 144-149.
  • Draper, C., & Lott, J. W. (2020). Addressing early algebra misconceptions and misinformation in classrooms. Wisconsin Teacher of mathematics, 1, 32-35.
  • Erbaş, A. K., Cetinkaya, B., & Ersoy, Y. (2009). Student difficulties and misconceptions in solving simple linear equations, Education and Science, 34(152), 44-59.
  • Gall, M. Gall., & Borg, W. (2007). Educational research: An introduction (8th ed.). New York: Pearson.
  • Gomes, J. C., & Jaques, P. A. (2020). A data-driven approach for the identification of misconceptions in step-based tutoring systems. Anais do XXXI Simpósio Brasileiro de Informática na Educação, 1122-1131.
  • Grouws, D. A. (Ed.). (1992). Handbook of research on mathematics teaching and learning. New York, USA: Macmillan.
  • Gürel, Z. Ç. & Okur, M. (2017). The Misconceptions of $7^{th} and $8^{th} Graders on the Equality and Equation Topics. Cumhuriyet International Journal of Education, 6(4), 479-507.
  • Hall, R. D. (2002). An analysis of errors made in the solution of simple linear equations. Philosophy of mathematics education journal, 15(1), 1-67.
  • Herscovics, N. & Linchevski, L. (1994). Cognitive gap between arithmetic and algebra. Educational Studies in Mathematics, 27(1), 59-78.
  • Kaput, J. (1999). Teaching and learning a new algebra. In E. Fennema and T. Romberg (Eds.), Mathematics Classrooms that Promote Understanding (pp. 133–155). NJ: Lawrence Erlbaum Associates, Inc., Publishers.
  • Kieran, C. (1984). A comparison between novice and more-expert algebra students on tasks dealing with the equivalence of equations. In Proceedings of the sixth annual meeting of PME-NA (pp. 83-91).
  • Kieran, C. (1992). The learning and teaching of school algebra. In D. Grouws (Ed). Handbook of research on mathematics teaching and learning. (pp. 390-419). New York: Macmillan.
  • Larino, L. B. (2018). An Analysis of Errors Made by Grade 7 Students in Solving Simple Linear Equations in One Variable. International Journal of Scientific & Engineering Research, 9(12), 764-769.
  • Matz, M. (1982): Towards a process model for school algebra errors. In D. Sleeman & J. S. Brown (Eds.), Intelligent tutoring systems (pp. 25–50). New York: Academic Press.
  • MoNE. (2018). Mathematics curriculum (Primary and Secondary School 1, 2, 3, 4, 5, 6, 7 and .grades)]. Ministry of Education (MoNE), Board of Education, Ankara, Turkey.
  • National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: Author.
  • Oktaç, A. (2010). Birinci dereceden tek bilinmeyenli denklemler ile ilgili kavram yanılgıları. In E. Bingölbali & M. F. Özmantar (Eds) Matematiksel zorluklar ve çözüm önerileri [Mathematical difficulties and solution suggestions] (2nd Edition, pp. 241-262). Ankara: Pegem Academy Publications
  • Perso, T. (1992). Making the most of errors. Australian Mathematics Teacher, 48(2), 12-14.
  • Pomerantsev, L., & Korosteleva, O. (2003). Do prospective elementary and middle school teachers understand the structure of algebraic expressions. Issues in the Undergraduate Mathematics Preparation of School Teachers: The Journal, 1(08), 1-10.
  • Rosnick, P., & Clement, J. (1980). Learning without understanding: The effect of tutoring strategies on algebra misconceptions. The Journal of mathematical behavior, 3(1), 3– 27.
  • Şandır, H., Ubuz, B., & Argün, Z. (2007). 9 th grade students’ difficulties in arithmatic operations, ordering numbers, solving equations and inequalities. Hacettepe University Journal of Education, 32(32), 274-281.
  • Sarımanoğlu, N. U. (2019). The investigation of middle school students’ misconceptions about Algebra. Studies in Educational Research and Development, 3(1), 1-22.
  • Seeley, C., & Schielack, J. F. (2007). A look at the development of algebraic thinking in curriculum focal points. Mathematics Teaching in the Middle School, 13(5), 266-269.
  • Şimşek, B., & Soylu, Y. (2018). Examination of the reasons for these mistakes made by elementary school $7^{th} grade students in relation to algebraic expressions. Journal of International Social Research, 11(59), 830-848.
  • Stacey K., & Macgregor M. (2001). Curriculum reform and approaches to algebra. In Sutherland R., Rojano T., Bell A., Lins R. (Eds.). Perspectives on School Algebra (pp. 141-153). Dordrecht: Springer.
  • Sutherland, R., & Rojano, T. (1993). A spreadsheet approach to solving algebra problems. The Journal of Mathematical Behavior, 12(4), 353–383.
  • Tavşan, S. (2020). Examination of Sixth Grade Students' Ability to Convert Algebraic Expressions into Verbal Expressions. Ondokuz Mayıs University Journal of Education Faculty, 39(3), 275-288.
  • Tooher, H., & Johnson, P. (2020). The role of analogies and anchors in addressing students’ misconceptions with algebraic equation. Issues in Educational Research, 30(2), 756- 781.
  • Umanah, E. (2020). Assessing student understanding while solving linear equations using flowcharts and algebraic methods (Electronic Theses). Retrieved from https://scholarworks.lib.csusb.edu/etd/1088 at 07.01.2021.
  • Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2019). Elementary and middle school mathematics: Teaching developmentally (10th ed). Upper Saddle River, NJ: Pearson.
  • Vlassis, J. (2001). Solving equations with negatives or crossing the formalizing gap, In. M. Heuvel-Panhuizen (Ed.) Proceedings of the 25th Conference of the International Group for the Psychology of Mathematics Education, 4, 375-382.
  • Vlassis, J. (2004). Making sense of the minus sign or becoming flexible in ‘negativity’. Learning and instruction, 14(5), 469-484.
  • Yasseen, A. R., Yew, W. T., & Meng, C. C. (2020). Misconceptions in school algebra. International Journal of Academic Research in Business and Social Sciences, 10(5), 803-812.

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