Middle School Pre-Service Mathematics Teachers’ Sense Making of Numbers and Operations Through Representations

Öz

In this study, it is aimed to examine the meanings that middle school pre-service mathematics teachers attribute to numbers and operations while developing their own number systems through a model eliciting activity. For this purpose, pre-service teachers were asked to work on a model eliciting activity in small groups within the scope of a teacher education course. In this activity, preservice teachers are expected to develop a representation system for natural numbers, integers, addition and subtraction operations. The data of the research consists of representations and explanations in the number systems developed by eight groups of pre-service teachers (34 pre-service teachers in total). The data were analyzed by content analysis. As a result of the research, it was seen that pre-service teachers attribute different meanings to numbers and operations in the notations they use in the number systems they have developed. Pre-service teachers exhibited their conceptual understanding by constructing meanings such as cardinality and part-whole relation for numbers and operations in these representations. However, they could not develop their representations for integers and addition-subtraction operations to support the conceptual meaning. These results reveal that pre-service teachers especially have conceptual deficiencies towards negative integers and tend to do algorithm-based addition and subtraction.

Anahtar Kelimeler

• mathematical symbols
• meanings of numbers
• meanings of operations
• cardinality
• part-whole relations
• pre-service teacher education

İlköğretim Matematik Öğretmen Adaylarının Sayıları ve İşlemleri Gösterimler Yoluyla Anlamlandırması

Öz

Bu çalışmada ilköğretim matematik öğretmen adaylarının bir modelleme etkinliği aracılığıyla kendi sayı sistemlerini geliştirirken sayılara ve işlemlere yükledikleri anlamları incelemek amaçlanmıştır. Bu amaçla bir ders kapsamında öğretmen adaylarından grup çalışmasıyla bir modelleme etkinliği üzerinde çalışmaları istenmiştir. Bu modelleme etkinliğinde öğretmen adaylarından doğal sayılar, tam sayılar, toplama ve çıkarma işlemleri için bir temsil sistemi geliştirmeleri beklenmektedir. Araştırmanın verilerini, sekiz grup matematik öğretmen adayı (toplam 34 öğretmen adayı) tarafından geliştirilen sayı sistemlerindeki gösterimler ve açıklamalar oluşturmaktadır. Veriler içerik analizi ile çözümlenmiştir. Araştırmanın sonucunda öğretmen adaylarının geliştirdikleri sayı sistemlerinde kullandıkları gösterimlerde sayılara ve işlemlere farklı anlamlar yükledikleri görülmüştür. Öğretmen adayları bu gösterimlerde sayılar ve işlemler için kardinalite ve parça-bütün ilişkisi gibi anlamlar oluşturarak kavramsal anlamalarını ortaya koymuşlardır. Ancak tam sayılar ve toplama-çıkarma işlemleri için gösterimlerini kavramsal anlamı destekleyecek şekilde geliştirememişlerdir. Bu sonuçlar öğretmen adaylarının özellikle negatif tam sayılara yönelik kavramsal eksikliklerini ve algoritmaya dayalı toplama ve çıkarma işlemi yapma eğiliminde olduklarını ortaya koymaktadır.

Anahtar Kelimeler

• matematiksel semboller
• sayıların anlamları
• işlemlerin anlamları
• kardinalite
• parça-bütün ilişkisi
• öğretmen adayları

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