7th Grade Students’ Mathematical Solution Strategies before Algebra Instruction: Equality and Equations Topic

Yıl 2024, Cilt: 12 Sayı: 2, 262 - 285, 24.12.2024

Şeyma Duman , Seçil Yemen Karpuzcu

https://doi.org/10.52826/mcbuefd.1445987

Öz

Understanding students’ arithmetic knowledge, algebraic thinking, informal reasoning and difficulties in solving equations is essential to articulate the development of algebra learning-teaching process. In algebra, one of the important steps for learning-teaching equality and equations is to determine the current situation of the students. This study aimed to reveal and explain the informal mathematical solution strategies of seventh-grade students before teaching the subject of equality and equations. This study was a case study with the participants of 94 seventh-grade students in a middle school in the 2022-2023 academic year. The data collection tool was an open-ended test, which was piloted and had content validity, consisting of nine questions. Data obtained from students’ written statements in the test were coded and analyzed. In the findings, we saw that students could not yet distinguish between equations and algebraic expressions. The students attempted to find the “unknown” mostly with arithmetic and semantic methods in their informal solutions. The students’ mistakes in the solutions showed that they had arithmetic-based deficiencies. As a result, before teaching equations, the relational meaning of equality can be mentioned informally in classrooms. Moreover, students can be supported to develop relational skills through particular activities during the arithmetic period.

Anahtar Kelimeler

algebra, equation, middle school mathematics, case study

7. Sınıf Öğrencilerinin Cebir Öğretimi Öncesi Matematiksel Çözüm Stratejileri: Eşitlik ve Denklem Konusu

Öz

Öğrencilerin aritmetik bilgilerini, cebirsel düşünmelerini, denklem çözümlerindeki informel akıl yürütmelerini ve karşılaştıkları zorlukları anlamak, onların cebir öğrenme-öğretme süreçlerinin gelişimini açıklamak için önemlidir. Cebirde eşitlik ve denklem öğrenme-öğretme için önemli bir adım öğrencilerin mevcut durumlarının belirlenmesidir. Bu çalışmanın amacı, eşitlik ve denklemler konusu öğretilmeden önce yedinci sınıf öğrencilerinin informel matematiksel çözüm stratejilerini ortaya çıkarmak ve açıklamaktır. Bu çalışma, 2022-2023 eğitim-öğretim yılında bir ortaokulda öğrenim gören 94 yedinci sınıf öğrencisinin katılımıyla gerçekleştirilen bir durum çalışmasıdır. Veri toplama aracı, pilot uygulaması yapılan ve kapsam geçerliliği sağlanmış, dokuz sorudan oluşan açık uçlu bir testtir. Öğrencilerin testteki çözümlerine ilişkin yazılı ifadelerinden elde edilen veriler kodlanarak analiz edilmiştir. Bulgularda, öğrencilerin denklemler ve cebirsel ifadeler arasındaki farkı henüz ayırt edemedikleri görülmüştür. Öğrenciler informel çözümlerinde çoğunlukla aritmetik ve semantik yöntemlerle “bilinmeyeni” bulmaya çalışmışlardır. Öğrencilerin çözümlerdeki hataları aritmetik temelli eksikliklerinin olduğunu göstermektedir. Sonuç olarak, denklemler konusu öğretilmeden önce sınıflarda informel olarak eşitliğin ilişkisel anlamından bahsedilebilir. Ayrıca, aritmetik dönemde öğrenme aşamasında çeşitli etkinliklerle öğrencilerin ilişkisel becerileri kazanmaları desteklenebilir.

Anahtar Kelimeler

cebir, denklem, ortaokul matematiği, durum çalışması

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