Altıncı Sınıf Öğrencilerinin Cebirsel İfadeleri Sözel İfadelere Dönüştürebilme Becerilerinin İncelenmesi

Özet: Bu çalışmanın amacı, altıncı sınıf öğrencilerinin cebirsel ifadelerden sözel ifadelere geçebilme becerilerini incelemek ve bu temsil biçimleri arasındaki geçiş durumlarını ortaya koymaktır. Bu nedenle, araştırmada, nitel araştırma modellerinden biri olan durum çalışması kullanılmıştır. Araştırmanın çalışma grubu, kolay ulaşılabilir örnekleme yöntemi ile seçilen ve 2018-2019 eğitim-öğretim yılı bahar döneminde Trabzon’da bulunan bir köy okulunda altıncı sınıfta öğrenim görmekte olan 19 öğrencidir (8 erkek, 11 kız). Veri toplama aracı olarak, uzman görüşleri doğrultusunda araştırmacı tarafından hazırlanan ve toplam yedi cebirsel ifadeden oluşan açık uçlu bir test kullanılmıştır. Öğrencilerin bu testte yer alan sorulara verdikleri cevaplar “Boş cevap: 0 puan; Sadece değişkeni tanımlama: 1 puan; Sadece katsayıyı veya değişkeni kullanma-hatalı kurgulama: 2 puan; Katsayı ve değişkeni kullanma-hatalı kurgulama: 3 puan; Katsayı ve değişkeni kullanma-doğru kurgulama: 4 puan” olmak üzere araştırmacı tarafından geliştirilen beş dereceli rubrik kullanılarak puanlanmıştır. Araştırma sonucunda, öğrencilerin çoğunluğunun cebirsel ifadelerdeki değişkenleri doğru bir şekilde tanımladığı, katsayıları doğru bir şekilde ele aldığı ve bunun sonucunda, verilen cebirsel ifadeleri uygun sözel ifadelere dönüştürmede başarılı oldukları görülmüştür. Ayrıca, bazı öğrencilerin cebirsel ifadedeki değişkeni doğru tanımladığı halde sözel ifadesini yazarken değişkeni değil “bir” sayısını kullandığı, bir kısım öğrencinin ise sözel ifade yazarken parantezi ve işlemlerin sırasını dikkate almadığı tespit edilmiştir. Ek olarak, bazı öğrencilerin yazdıkları sözel ifadelerde cebirsel ifadeleri sonucu bir sayıya eşit olacak şekilde ele aldıkları belirlenmiştir.

Examination of Sixth Grade Students' Ability to Convert Algebraic Expressions into Verbal Expressions

Algebra is built on the concept of a variable; on the other hand, variables are defined with letters such as "a, b, x, y, …" (Yenilmez and Teke, 2008). Wheatley (1995) likens the variables used in algebra to pronouns in a sentence. In other words, he states that just like pronouns can be used instead of individuals in a sentence, variables can be used instead of numbers in algebra (as cited in Dede, 2004). Variables are the basis for the transition from arithmetic to algebra (Arcavi and Schoenfeld, 1988). Soylu (2008) explains that the full understanding of the concept of variable is a necessity for learning algebra and advanced mathematics. When the literature was examined, it was seen that many studies are dealing with various topics and reaching different results in the context of algebra. Some of these found that students or prospective teachers at different grade levels had difficulties in understanding and interpreting the basic concepts and letters in algebraic expressions (Kieran, 1992; Knuth, Alibali, McNeil, Weinberg and Stephens, 2005; Küchemann, 1978; MacGregor and Stacey, 1997; Rosnick, 1999; Sitrova, 2017; Soylu, 2006; Ünlü and Sarpkaya-Aktaş, 2017) while others concluded that they had challenges in the transition process from algebraic representation to different types of representation (Akgün, 2009; Yılmaz, 2011). Furthermore, studies demonstrated that students did not take into account the order of operations in algebraic expressions (Akkan, Çakıroğlu, and Güven, 2009; Akkaya and Durmuş, 2006; Booth, 1988; Perso, 1992). It was observed that the studies reached mostly focused on determining the meanings that students attributed to the concept of variable. As a result of considering these studies, it is thought that there is a lack in the literature in the context of examining students' transition conditions between different forms of representation. Lesh, Post, and Behr (1987) express that students' situation in this context is an indicator of understanding mathematics and emphasize the importance of multiple representation approach in understanding mathematics. Similarly, Even (1998) states that expressing the same situation with different representation forms has benefits such as being flexible during the transition from one representation to another, developing better conceptual understanding, deepening understanding, and contributing to problem-solving skills. Besides, it is stated that making connections by transforming between different forms of representation is one of the skills that students should have in the "Principles and Standards for School Mathematics" report prepared in 2000 by the National Council of Teachers of Mathematics (NCTM). When the mathematics curriculum is examined, it is seen that the sixth grade is the transition stage from arithmetic to algebra (Ministry of Education [ME], 2018). It is thought significant that students studying at this level can better construct basic concepts and make the transition between the forms of representation appropriately to their level in order to be successful in future algebra topics. So, it is necessary to determine what meanings they attributed to the algebraic expressions to reveal the current situation of the students studying in the sixth grade, which is considered as the first step of completing the transition to algebra. Thus, students can be assisted by conducting studies to complete them if they have deficiencies and correct them if they have misunderstandings. Starting from this, the aim of this study was to examine of sixth-grade students' ability to convert algebraic expressions into verbal expressions and to reveal the transition conditions between these forms of representation. In this research, an illustrative case study method was used. Participants of the research were selected by the easily accessible sampling method. The study group consisted of 19 (8 boys, 11 girls) sixthgrade students studying at a village school in Trabzon in the spring term of the 2018-2019 academic year. As a data collection tool, an open-ended test consisting of seven items was used, which was developed by the researcher, and aimed to enable students to express algebraic expressions verbally. Students' answers to the questions in this test were scored using a five-degree rubric developed by the researcher in the form of "Empty answer: 0 points; Defining the variable only: 1 point; Using only coefficient or variable-erroneous editing: 2 points; Using coefficient and variable-erroneous editing: 3 points; Using coefficient and variable-correct editing: 4 points". Then, the examples of verbal expression situations where the students, who did not get full scores from the test, used the variable or coefficient in the given algebraic expressions insufficiently or wrongly were illustrated.

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