İlkokul Öğrencilerinin Sayıların Denk Gösterimlerine Dair Kavrayışları ve Esnek Hesaplama Becerileri

Abstract

Bu araştırmada ilkokul dördüncü sınıf öğrencilerinin sayıların denk gösterimlerine dair kavrayışlarının ve esnek hesaplama becerilerinin incelenmesi amaçlanmıştır. Betimsel tarama modelinin kullanıldığı bu araştırmanın örneklemini uygun örnekleme yöntemine göre belirlenen 157 ilkokul dördüncü sınıf öğrencisi oluşturmaktadır. Araştırma verileri onluk taban bilmeceleri ve esnek hesaplama soruları aracılığıyla toplanmıştır. Onluk taban bilmeceleri, öğrencilerin, sayıların denk gösterimlerini kavrama, alışılmışın dışında gruplama yapabilme, sayıyı yeniden adlandırma gibi becerilerini ölçmeye yönelik sorulardan oluşmaktadır. Öğrencilerin esnek hesaplama becerileri ise iki ve üç basamaklı sayılarla toplama/çıkarma işlemlerini içeren dört soru ile incelenmiştir. Onluk taban bilmecelerinde çocukların sorulara verdikleri yanıtlar doğru/yanlış olarak kodlanmış ve betimsel istatistik değerleri (frekans ve yüzde değerleri) hesaplanmıştır. Öğrencilerin esnek hesaplama becerilerini incelemek amacıyla ise kullandıkları stratejiler incelenmiştir. Öğrencilerin sayıların denk gösterimlerine dair kavrayışlarının esnek hesaplama becerilerine göre nasıl farklılaştığını incelemek için Kruskal Wallis testi yapılmıştır. Analiz sonuçları, öğrencilerin onluk taban bilmecelerinden aldıkları puanların, esnek hesaplama becerilerine göre farklılaştığını göstermektedir. Buna göre, basamak değeri bilgisini kavramsallaştırabilen öğrenciler aynı zamanda esnek hesaplamalar yapabilmektedir. Bunun aksine basamak değerini, sayılara ilişkin çoklu temsilleri ve denk gösterimleri yeterince anlamlandıramayan öğrencilerin ise işlemsel bilgiye bağlılığı bir kez daha kanıtlanmıştır. Basamak değeri kavramının öğretiminde gruplama, yeniden adlandırma, yeniden gruplandırma, farklı temsillere yer verme gibi süreçlere yer verilmesi önerilmektedir.

Keywords

• Esnek hesaplama
• basamak değeri
• denk gösterim
• sayı duyusu.

Primary School Students’ Understanding of Equivalent Representations of Numbers and Flexible Calculation Skills

Abstract

This study aimed to examine fourth grade primary school students' understanding of equivalent representations of numbers and their flexible calculation skills. The sample of this research, in which the descriptive survey model was used, consists of 157 fourth grade primary school students determined according to the convenient sampling method. Research data was collected through base ten riddles and flexible calculation questions. Base-ten riddles consist of questions aimed at measuring students' skills such as comprehending equivalent representations of numbers, making unusual groupings, and renaming numbers. Students' flexible calculation skills were examined with four questions involving addition/subtraction operations with two- and three-digit numbers. The answers given by the children to the base ten riddles were coded as correct/incorrect and descriptive statistics values (frequency and percentage values) were calculated. In order to examine students' flexible calculation skills, the strategies they used were examined. The Kruskal Wallis test was conducted to examine how students' understanding of equivalent representations of numbers differed according to their flexible calculation skills. The analysis results show that the scores students received from base ten riddles differ according to their flexible calculation skills. Accordingly, students who can conceptualize place value information can also make flexible calculations. On the contrary, students who cannot adequately understand place value, multiple representations of numbers and equivalent representations have once again proven their dependence on procedural knowledge. It is recommended to include processes such as grouping, renaming, regrouping, and including different representations in teaching the concept of place value.

Keywords

• Flexible calculation
• place value
• equivalent representation
• number sense

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