ERG SES F 07, Parallel Session F 07
Algebra traditionally has been the most difficult area of the mathematics curriculum in terms of teaching and learning it (Kieran, 2007). The problem was the gap between what teachers try to teach versus what students learn (Kieran, 2007). Historically, from Al-Khwarizmi to Vieta and Euler, algebra had been described as a tool for manipulating symbols and solving problems (Kieran, 2007). Over time, it has become recognized that algebra is more than just a tool. In the 1950s research studies related to algebra education were conducted by behaviorist psychology researchers (Kieran, 2007). Therefore, in this period, the researchers particularly focused on strong symbolic orientation, include the simplification of expressions and solving equations, inequalities, and the system of equations. Since their only aim was to have students develop procedural knowledge mechanically, these studies did not yield the expected results. Later, when Piaget constructed cognitive development psychology in the 1960s, mathematics educators were impressed by this approach and incorporated it into their studies (Kieran, 2007). From 1977 until the present day the difficulties and misconceptions in algebraic equation solving (Herscovics and Linchevski, 1994), the variable concept (Usiskin, 1988), unknowns (Stacey and MacGregor, 2000) and the transition from arithmetic to algebra and algebra word problems (Kieran, 2006) have been the most commonly studied areas in algebra education.
Recently, it has been recognized that students need to learn mathematics with understanding by actively building new knowledge from existing knowledge and experience (NCTM 2000), so trend studies now take into consideration this idea and trying to develop algebraic thinking instead symbol manipulation in algebra education. From the mid- 1990s to 2006 the researchers concerned themselves with developing algebraic thinking, especially among elementary school students (Kieran, 2006).
Despite these all efforts, definitions and different perspectives for improving school algebra, research studies in the literature clearly show that a large proportion of students are unsuccessful in learning algebra (Chazan, 1996). Several studies have reported that there have been still many learning difficulties in algebra as mentioned previously. Even though not enough studies have been conducted in Turkey in the field of algebra education, it can nevertheless be said that our learners have the same cognitive difficulties as their counterparts in other countries. They have trouble with the concept of variables (Dede, 2004; Akkaya &Durmuş, 2006; Bekdemir &Işık, 2007) and since they do not construct the variable concept properly they misinterpret the meanings of the letters. Students have also trouble with transition from arithmetic to algebra (Gürbüz & Akkan, 2008), translational skills (Özyildirim, İpek & Akkus, 2009), solving equations (Yenilmez&Avcu, 2009), algebraic expressions and operations (Dede&Peker, 2007) and understanding algebraic word problems (Dede, 2005). Erbaş, Çetinkaya and Ersoy (2009) in their study discovered that the students have difficulties, making common errors and misconceptions, in solving simple linear algebraic equations. Researchers and educators are still trying to find effective ways to teach algebra and help children overcome these common difficulties (Carraher, Schliemann, & Brizuela, 2000). There are research findings indicating that students in grades 6-8 have many misconceptions in algebra. The aim of this study is to reveal these misconceptions.
Akkaya, R., & Durmuş, S. (2006). Misconceptions of elementary school students in grades 6-8 on learning algebra. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 31, 1-12. Bednarz, N., Kieran, C., & Lee, L. (Eds.). (1996). Approaches to algebra: Perspectives for research and teaching. Dordrecht, The Netherlands: Kluwer. Chalouh,L. & Herscovics, N. (1988). Teaching algebraic expressions in a meaningful way. In A.E.Coxford (Ed.), The ideas of algebra, K-12(1988 Yearbook, pp.33-42). Reston, VA: NCTM. Chazan, D. (1996). “Algebra for all students?” The algebra policy debate. Journal of Mathematical Behavior, 15, 455-477. Herscovics, N., Linchevski,L.( 1994).A cognitive gap between arithmetic and algebra. Educational Studies in Mathematics, 27(1), 59-67. Kaput, J. J. (1995). A research base supporting long term algebra reform? In D. T. Owens, M. K. Reed, & G. M. Millsaps (Eds.), Proceedings of the 17 Annual Meeting of PME-NA (Vol. 1, pp. 71-94). Columbus, OH: ERIC Clearinghouse for Science, Mathematics, and Environmental Education. Katz, V. J. (1997). Algebra and its teaching: An historical survey. Journal of Mathematical Behavior, 16(1), 25-38. Kieran, C. (2006). Handbook of research on the psychology of mathematics education past, present and future. In A. Gutierrez & P. Boelo (Eds.), Research On The Learning and Teaching Algebra (pp.11-49). Rotterdam, Netherlands: Sense-Publishers. doi:90-77874-19-4. Kieran, C. (2007). Learning and teaching algebra at the middle school through college levels. In F. Lester (Ed.), Handbook of research on mathematics teaching and learning. Charlotte, NC: Information Age Publishing. National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: Author. Stacey, K. & MacGregor, M. (2000). Learning the algebraic method of solving problems. Journal of Mathematical Behavior, 18 (2), 149-167. Usiskin, Z. (1988). Conceptions of school algebra and uses of variables. In A. Coxford & A. P. Schulte (Eds.), Ideas of algebra, K-12 (1988 Yearbook: 8-19). Reston, VA: NCTM.
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