Original article | Turkish Journal of Teacher Education 2018, Vol. 7(1) 1-16
Demet Baran Bulut, Berna Aygun, Ali Sabri İpek
pp. 1 - 16 | Manu. Number: MANU-1811-16-0002
Published online: June 30, 2018 | Number of Views: 246 | Number of Download: 795
The aim of the present study is to enable primary and secondary students (in grades 3, 4 and 5) how to understand the equal sign. The participants of the study were comprised of a total of 245 students selected from two different cities in the East Black Sea region in Turkey. Of the 245 students, who were selected on a voluntary basis, 78, 72, and 95 students were from grades 3, 4 and 5, respectively. The 17-item data collection tool employed in the study was designed by the researchers by making use of the tests developed by Saenz-Ludlow and Walgamuth (1998), Witherspoon (1999), Knuth et al. (2005). The study employed a qualitative research design in which data analysis was based on the method of content analysis in which frequency and percentage analysis techniques were utilized. The findings indicated that students focused more on the operational meaning of the equal sign rather than its relational meaning. Furthermore, it has been found that students are more successful in symbolic representation than other representations. In addition, it was found that students had misconceptions regarding the equal sign. Thus, it is believed that by establishing learning environments in which the equal sign can be used to solve equations presented in problems and multiple representations, the misconceptions that students possess can be minimized.
Keywords: Equal sign, operational meaning , relational meaning, representations
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Alexandrou-Leonidou, V. and Philippou, G. (2007). Elementary school students’ understanding and use of the equal sign. In: Pitta-Pantazi, D. and Philippou, G. (Eds.): CERME–5 Proceedings. Larnaca, Cyprus, 825-834.
Alibali, M. W., Knuth, E. J., Hattıkudur, S., Mcneil, N.M. & Stephens, A.C. (2007). A longitudinal look at middle-school students’ understanding of the equal sign and equivalent equations. Mathematical Thinking and Learning, 9, 221-247.
Arzarello, F., Bazzini, L., & Chiappini, G. (1993). Cognitive processes in algebraic thinking: Towards a theoretical framework. In I. Hirabayashi, N. Nohda, K. Shigematsu, and F. L. Lin (Eds.), Proceedings of 17th International Conference on 37 the Psychology of Mathematics Education, (vol.1, pp. 138-145). Tokio (Japan).
Behr, M., Erlwanger, S. & Nichols, E. (1980), ‘How children view the equals sign?’. Mathematics Teaching, 92, 13-15.
Boulton-Lewis, G., Cooper, T. J., Atweh, B., Pillay, H., & Wills, L. (1998). Arithmetic, pre-algebra and algebra: A model of transition. In C. Kanes, M. Goos, & E. Warren (Eds.), Teaching mathematics in new times (Proceedings of the 21st annual conference of the Mathematics Research Group of Australasia) (pp. 114- 120). Gold Coast: MERGA.
Büyüköztürk, Ş., Kılıç Çakmak, E., Akgün, Ö. E., Karadeniz, Ş., Demirel, F. (2013). Bilimsel Araştırma Yöntemleri. Ankara: Pegem Akademi Yayıncılık.
Cajori, F. (1993). A history of mathematical notations. New York: Dover Publications.
Carpenter, T. P. & Levi, L. (2000). Developing conceptions of algebraic reasoning in the primary grades. National Center for Improving Student Learning and Achievement in Mathematics and Science: University of Wisconsin-Madison.
Carpenter, T.P., Levi, L. & Farnsworth, V. (2000). Building a foundation for learning algebra in the elementary grades. National Center for Improving Student Learning and Achievement in Mathematics and Science: University of Wisconsin-Madison.
Carpenter, T. P., Franke, M. L., & Levi, L. (2003). Thinking mathematically: integrating arithmetic and algebra in elementary school. Portsmouth: Heinemann.
Cooper, T.J. & Baturo, A. R. (1992). Algebra in the primary school: Extending arithmetic, in A. R. Baturo and T. J. Cooper (eds.), New Directions in algebra education, Centre for Mathematics and Science Education, Brisbane, Australia.
Doğan-Temur, Ö. ve Sancak, G. (2012). Dördüncü sınıf öğrencilerinin eşit işaretini nasıl algıladıklarının incelenmesi. Milli Eğitim Dergisi, 194, 240-252.
Driscoll, M. (1999). Fostering Algebraic Thinking: A Guide for Teachers, Grades 6-10. Heinemann, 361 Hanover Street, Portsmouth, NH 03801-3912.
Falkner, K.P., Levi, L. & Carpenter, T.P. (1999). Children’s understanding of equality: A foundation for algebra. Teaching Children Mathematics, 6 (4), 232-6
Goldin, G. A., & Janvier, C. (1998). Representations and the psychology of mathematics education. Journal of Mathematical Behavior, 17(1), 1–4
Güleryüz, H. (2001). En Son Değişikliklerle İlköğretim Okulu Programı. Ankara: Pegem A Yayıncılık.
Hersovics, N. ve Linchevski, L. (1994). A Cognative gap between arithmetic and algebra. Educational Studies in Mathematics, 27(1), 59‐78.
Janvier, C. (1987). Representation system and mathematics. In C. Janvier (Ed.), Problems of Representations in the Learning and Teaching of Mathematics, New Jersey: Lawrence Erlbaum Associates.
Kieran, C. (1981). Concepts associated with the equality symbol. Educational Studies in Mathematics, 12(3), 317-326.
Kieran, C., (1992). The Learning and Teaching of School Slgebra. In D.A. Grouws (Eds.). Handbook of Research on Mathematics Teaching and Learning, 390-419. New York: Macmillan.
Kieran C. (2004), The Equation / Inequality Connection in Constructing Meaning for Inequality Situations, Psychology of Mathematics Education, Vol.1, pp: 143-147
Knuth, E. J., Alibali, M. W., McNeil, N. M., Weinberg, A., & Stephens, A. S. (2005). Middle School Students’ Understanding of Core Algebraic Concepts: Equality & Variable. International Reviews on Mathematical Education, 37, 68-76.
Knuth, E., J., Stephens, A. C., McNeil, N., M. ve Alibali, M., W., (2006). Does Understanding the Equal Sign Matter? Evidence from Solving Equations. Journal for Research in Mathematics Education, 37, 297-312.
Knuth, E., J., Alibali, M., W., Hattikudur, S., McNeil, N., M. ve Stephens, A., C., (2008). The Importance of Equal Sign Understanding in the Middle Grades. Mathematics Teaching in the Middle School, 13, 514-519.
Linchevski, L. (1995). Algebra with numbers and arithmetic with letters: A definition of pre-algebra. The Journal of Mathematical Behavior, 14(1), 113-120.
Lesh, R., Post, T., & Behr, M. (1987). Representations and translations among representations in mathematics learning and problem solving. In C. Janvier (Ed.), Problems of Representation in the Teaching and Learning of Mathematics, New Jersey: Lawrence Erlbaum Associates.
Miles, M. B., & Huberman, A. M. (1994). An Expanded Sourcebook Qualitative Data Analysis. United States of America: Sage Publications.
Milli Eğitim Bakanlığı [MEB], (2013). Ortaokul Matematik Dersi (5, 6, 7 ve 8. Sınıflar) Öğretim Programı. Ankara: MEB Basımevi.
Milli Eğitim Bakanlığı [MEB], (2015). İlkokul Matematik Dersi (1, 2, 3 ve 4. Sınıflar) Öğretim Programı. Ankara: MEB Basımevi.
Molina, M. & Ambrose, R. (2008). From an Operational to Relational Conception of Equal Sign. Thirds Graders’ Developing Algebraic Thinking. Focus on Learning Problems in Mathematics, 30(1), 61-80.
National Council of Teachers of Mathematics (NCTM) (2000). Principles and standards for school mathematics. Reston, VA: Author.
Saenz-Ludlow, A. & Walgamuth, C. (1998). Third Graders’ Interpretations of Equality and Equal Symbol. Educational Studies in Mathematics, 35(2), 153-187.
Stallings, L. (2000). A Brief History of Algebraic Notation. School, Science and Mathematics, 100(5), 230.
Usiskin, Z. (1998). Conceptions of school algebra and uses of variables. In A. F. Coxford, (Ed). The Ideas of Algebra, K–12 (pp. 8–19). Reston, VA: The National Council of Teachers of Mathematics.
Van Amerom, B. A. (2002). Reinvention of early algebra: Developmental research on the transition from arithmetic to algebra. Unpublished doctoral dissertation, University of Utrecht, The Netherlands.
Verschaffel, L., & De Corte, E. (1996). Number and arithmetic. In International handbook of mathematics education (pp. 99-137). Springer, Dordrecht.
Witherspoon, M. L. (1999). ‘And the answer is … symbolic literacy (accurate interpretation of mathematical or numerical symbols!)’. Teaching Children Mathematics, 5(7), 396-399.
Yaman, H., Toluk, Z. & Olkun, S. (2003). İlköğretim öğrencileri eşit işaretini nasıl algılamaktadır?. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi 24, 142-151.
Yavuz, B. (2010). İlköğretim öğrencilerinin eşit ve eşitsizlik işaretleri hakkındaki düşünceleri ve arasındaki ilişki. (Yayımlanmamış yüksek lisans tezi). Abant İzzet Baysal Üniversitesi/Sosyal Bilimler Enstitüsü, Bolu.
Yavuzsoy-Köse, N. ve Tanışlı, D. (2011). İlköğretim matematik ders kitaplarında eşit işareti ve ilişkisel düşünme. Necatibey Eğitim Fakültesi Elektronik Fen ve Matematik Eğitimi Dergisi (EFMED). 5 (2), 251-277.
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