Gifted Students’ repeating patterning skills and cognitive demand levels

Year 2023, Volume: 6 Issue: 1, 70 - 95, 31.05.2023

Fatma Erdoğan , Neslihan Gül

https://doi.org/10.33400/kuje.1221801

Cited By: 1

Abstract

The ability to generalize, one of the key characters of mathematical giftedness, is related to mathematical patterns. Patterns and especially repeating patterns come to the fore as a context for the development of algebraic and functional thinking at an early age. In addition, determining the cognitive effort that students put forward in the process of working with repeating patterns is important for the development of patterning skills. In line with what has been stated, the aim of this study was to explore the repeating patterning skills of gifted students and their cognitive demand levels. In the study, case study design was used. Participants are five fifth grade students who were diagnosed as gifted through diagnostic tests. The data were collected with the "Repeating Number Pattern Task Form" consisting of open-ended problems. The data collection method is task-based interview. The data were analyzed by thematic analysis method. According to the findings, all students correctly determined the immediate, near, far term, and rule of the repeating number pattern task. According to the results of the study, students used “recursive”, “counting”, “division with remainder”, and “counting up/down from a multiple” strategies to find the immediate, near, and far term. All students explained the relationship in the arrangement of the numbers in the pattern by determining the unit of repeat. The results of the study show that students exhibit cognitive demand at the level of “procedures without connections” and “procedures with connections” to find the immediate and near term of the pattern task. In addition, students exhibited cognitive demand at the level of “procedures with connections” to find the far term and rule of the pattern.

Keywords

özel yeteneklilik, matematiksel özel yeteneklilik, örüntüler, bilişsel istem, matematik eğitimi

Özel yetenekli öğrencilerin tekrarlanan örüntü becerileri ve bilişsel istem düzeyleri

Abstract

Matematiksel özel yetenekliliğin kilit karakterlerinden biri olan genelleme becerisi, matematiksel örüntülerle ilişkilidir. Erken yaşlarda cebirsel ve fonksiyonel düşünmenin gelişimi için bir bağlam olarak örüntüler ve özellikle tekrarlanan örüntüler öne çıkmaktadır. Ayrıca, öğrencilerin tekrarlanan örüntülerle çalışma süreçlerinde ortaya koydukları bilişsel çabanın belirlenmesi, örüntü becerisinin gelişimi açısından önemlidir. Belirtilenler doğrultusunda, bu çalışmanın amacı, özel yetenekli öğrencilerin tekrarlanan örüntü becerilerini ve tekrarlanan örüntülerle çalışma sürecinde ortaya koydukları bilişsel istem düzeylerini keşfetmektir. Çalışmada, durum çalışması deseni kullanılmıştır. Katılımcılar, beşinci sınıf düzeyinde öğrenim gören, tanılama testleri aracılığıyla özel yetenekli tanısı konulan beş öğrencidir. Veriler, açık uçlu problemlerden oluşan “Tekrarlanan Sayı Örüntüsü Görev Formu”yla toplanmıştır. Veri toplama yöntemi, görev temelli görüşmedir. Veriler tematik analiz yöntemiyle çözümlenmiştir. Bulgulara göre, tüm öğrenciler, tekrarlanan sayı örüntüsü görevinin yakın, orta, uzak terimine ve kuralına doğru bir şekilde ulaşmıştır. Çalışma sonuçlarına göre, özel yetenekli öğrenciler tekrarlanan sayı örüntüsü görevinin yakın, orta ve uzak terimini bulmak için “yinelemeli”, “sayma”, “bölümden kalanı sayma” ve “çarpım üzerine sayma” stratejilerini kullanmışlardır. Örüntüde yer alan rakamların dizilişindeki ilişkiyi tüm öğrenciler tekrar birimini belirleyerek açıklamıştır. Çalışma sonuçları, özel yetenekli öğrencilerin örüntü görevinin yakın ve orta uzaklıktaki terimini bulmak için “bağlantısız işlemler” ve “bağlantılı işlemler” düzeyinde bilişsel istem sergilediklerini göstermiştir. Ayrıca, öğrenciler örüntünün uzak terimini ve kuralını bulmak için “bağlantılı işlemler” düzeyinde bilişsel istem sergilemişlerdir.

Keywords

özel yeteneklilik, matematiksel özel yeteneklilik, örüntüler, bilişsel istem, matematik eğitimi

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