İlköğretim öğrencilerinde muhakeme etme ve ispatlama düşüncesinin gelişimi
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Date
2007-10-22
Authors
Arslan, Çiğdem
Journal Title
Journal ISSN
Volume Title
Publisher
Uludağ Üniversitesi
Abstract
Bu araştırma ilköğretim 6, 7 ve 8. sınıf öğrencilerinin muhakeme etme ve ispatlama düşüncesinin gelişiminin incelenmesi amacıyla hazırlanmıştır. İspatlama düşüncesinin gelişiminin incelenmesi amacıyla hazırlanmıştır. İspatlama düşüncesinin gelişimi matematik içinde önemeli bir konudur. Öyle ki matematiğin örüntüleri bulma ve ispatlama çalışması olarak bile nitelendirildiği olur. Matematiğin ispatlamayla ilgili iki aşamalı yöntemi bulunmaktadır. İlki bir özellik yada ilişkiyi bulma veya ortaya çıkarma çabasını; ikincisi ise bulunan ilişkisinin ispatlanma sürecini içermektedir. İspatlama süreci genellemelerin üretilmesinde izlenen yoldur. Araştırma Bursa ili merkez ilçelerinde bulunan ve rastgele seçilen yedi ilköğretim okulunda okuyan 679 öğrenci ile 2005-2006 öğretim yılının ikinci yarıyılında gerçekleştirilmiştir. Tarama modelinde düzenlenen çalışmanın öğrencilerin zihinsel gelişim basamaklarına uygun düşen ispat düzeylerinin belirlenmesi kısmı nicel, yargılarının arkasında yatan sebeplerin incelenmesi kısmı nitel olarak yapılmıştır. Beş sorudan oluşan veri toplama aracı araştırmanın nicel boyutunu gerçekleştirmek için öğrencilere kendi sınıflarında uygulanmış, nitel boyutunu gerçekleştirmek için seçilen 36 öğrenci ile özel görüşmeler yapılmıştır. Öğrencilerin tüm düşüncelerini açıklamalarına yetecek süre verilmiştir. Veri analizi sonucunda, ilköğretim 6, 7 ve 8. sınıf öğrencilerinin muhakeme etme düzeylerinin literatürce desteklenen ortalama verilere göre düşük olduğu ve bu süreçte kullanılması beklenen stratejilerden yeterli düzeyde kullanamadıkları verilen ifadenin doğruluğunu göstermede tercih ettikleri ispat türünün sınıf seviyesi ile birlikte belli oranda değiştiği (görsel ve örnekte doğrulamadan cebirsel ispatı yönelme) görülmüştür. Özellikle 8. sınıf öğrencileri ile 6 ve 7. sınıf öğrencilerinin cebirsel ispatı tercih etme düzeyleri arasında anlamlı farklılık bulunmuştur.
This study was aimed to investigate sixth, seventh and eighth grade students' development of reasoning and proof ideas. Development of proof idea is such an important subject in mathematics that sometimes mathematics is described as study of finding patterns and proving. In mathematics, there is a method on proving with two stages. The first one includes effort to find or reveal a characteristic or a pattern; the second one includes process of proving of relationship that have been found. Proving process is the way which is followed to produce generalizations. The study were carried out in 2005-2006 school year with 679 students from seven different primary schools that were randomly selected in Bursa. The current research has two sections. The first part has quantitative data which measured the levels of proof of the participants according to cognitive development levels. The second part which has qualitative data that has analyzed the reasons of the students decisions. The data source which is consisted of five questions was given to the participants in their regular lesson hour for the quantitative part of research; private interviews were made with 36 students for the qualitative section of this research. During interviews, sufficient time was given to each participant in order to explain their reasonmg. As results of data analyses, according to average data supported by literature it was observed that 6th, 7th and 8th grade students have a low level of reasoning, they couldn't utilize expected strategies at an enough level and kind of proof which they have preferred to show correctness of given expression have changed in proportion of grade level (from visual and empirical to algebraic). It was found that there was a significant difference between eighth graders and the other students.
This study was aimed to investigate sixth, seventh and eighth grade students' development of reasoning and proof ideas. Development of proof idea is such an important subject in mathematics that sometimes mathematics is described as study of finding patterns and proving. In mathematics, there is a method on proving with two stages. The first one includes effort to find or reveal a characteristic or a pattern; the second one includes process of proving of relationship that have been found. Proving process is the way which is followed to produce generalizations. The study were carried out in 2005-2006 school year with 679 students from seven different primary schools that were randomly selected in Bursa. The current research has two sections. The first part has quantitative data which measured the levels of proof of the participants according to cognitive development levels. The second part which has qualitative data that has analyzed the reasons of the students decisions. The data source which is consisted of five questions was given to the participants in their regular lesson hour for the quantitative part of research; private interviews were made with 36 students for the qualitative section of this research. During interviews, sufficient time was given to each participant in order to explain their reasonmg. As results of data analyses, according to average data supported by literature it was observed that 6th, 7th and 8th grade students have a low level of reasoning, they couldn't utilize expected strategies at an enough level and kind of proof which they have preferred to show correctness of given expression have changed in proportion of grade level (from visual and empirical to algebraic). It was found that there was a significant difference between eighth graders and the other students.
Description
Keywords
Matematiksel muhakeme, İspat, Doğrulama, Genelleme, Mathematical reasoning, Proof, Justification, Generalization
Citation
Arslan, Ç. (2007). İlköğretim öğrencilerinde muhakeme etme ve ispatlama düşüncesinin gelişimi. Yayınlanmamış doktora tezi. Uludağ Üniversitesi Sosyal Bilimler Enstitüsü.