Model Oluşturma Etkinliklerinde Matematiksel İlişkilendirmelerin Belirlenmesi: Tasarımcı Olarak Matematik Öğretmen Adaylarıyla Bir Durum Çalışması

Öz

Bu araştırmanın amacı, ilköğretim matematik öğretmen adaylarının tasarladıkları model oluşturma etkinliklerinde belirledikleri matematiksel ilişkilendirmeleri incelemektir. Amaçlı örnekleme yöntemine göre seçilen kırk iki lisans öğrencisiyle yürütülen çalışmada nitel araştırma desenlerinden keşfetmeye dayalı durum çalışması kullanılmıştır. Araştırmanın verileri matematik öğretmen adaylarının hazırladıkları matematiksel modelleme problemlerinden ve öğretmen adaylarının problemlerini matematiksel ilişkilendirmeler açısından değerlendirdikleri yazılı ödevlerden toplanmıştır. Çalışmanın veri analizi, ortak yaklaşımları tematik olarak belirlemek ve sınıflandırmak için açık kodlama kullanılarak yapılmıştır. Araştırmanın sonuçları tasarlanan problemlerin çoğunun model oluşturma etkinliklerinin prensipleri ile tutarlı olduğunu göstermiştir. Model oluşturma etkinliklerinin analizinden elde edilen veriler ise dört tür matematiksel ilişkilendirmenin belirlendiğini ortaya çıkarmıştır: (i) gerçek yaşam durumlarıyla ilişkilendirmeler, (ii) matematiksel kavramlar arasındaki ilişkilendirmeler, (iii) farklı temsil biçimleri arasındaki ilişkilendirmeler ve (iv) diğer disiplinlerle ilişkilendirmeler. Modelleme etkinliklerinde belirlenen bu matematiksel ilişkilendirmeler birbirini dışlayan değil aksine birbirini destekleyen ve bazen örtüşen niteliktedir. Matematik öğretmen adaylarının modelleme problemlerindeki matematiksel ilişkilendirmeleri belirlemeleri hem matematiksel ilişkilendirmelere yönelik farkındalıklarını hem de matematiksel modelleme süreci için gerekli olan becerilerin matematiksel ilişkilendirme becerileri ile doğrudan ilişkili olduğuna dair algılarını yansıtmaktadır. Bu nedenle, matematik öğretmen adaylarının matematiksel ilişkilendirmelere ilişkin kapsamlı bir anlayışa sahip olmaları ve bunun modelleme sürecinin temel bir unsuru olduğuna inanmaları matematiksel ilişkilendirmelerin çeşitli boyutlarının ilgili matematik, pedagojik ve müfredat bilgisi ile birlikte model oluşturma etkinliklerine etkili bir şekilde entegre edilebilmesi açısından önemlidir.

Anahtar Kelimeler

• Matematiksel ilişkilendirmeler
• model oluşturma etkinlikleri
• matematiksel modelleme
• matematik öğretmen adayları

Identifying Mathematical Connections in Model-Eliciting Activities: A Case Study with Pre-service Mathematics Teachers as Designers

Abstract

This paper aimed to explore mathematical connections that pre-service elementary mathematics teachers identified in model-eliciting activities that they designed. The study used a qualitative, in-depth exploratory case study approach conducted with a total of 42 undergraduate students selected using a purposive sampling method. Data were collected from mathematical modeling problems prepared by pre-service mathematics teachers and from written assignments in which pre-service teachers evaluated their problems in terms of mathematical connections. Data analysis utilized open coding to identify and label common patterns thematically. Results showed that most of the problems designed were consistent with the principles of the model-eliciting activities. A cross-case analysis of model-eliciting activities revealed that four types of mathematical connections were identified: (i) connections to real-world situations, (ii) connections between mathematical concepts, (iii) connections between different modes of representation, and (iv) connections to other disciplines. The mathematical connections identified in the modeling activities did not seem to be mutually exclusive, but rather supportive and sometimes overlapping. Pre-service mathematics teachers’ identification of mathematical connections in modeling problems reflects both their awareness of mathematical connections and their perception that the skills required for the mathematical modeling process are directly related to mathematical connection skills. Therefore, it is important that pre-service mathematics teachers have a comprehensive understanding of mathematical connections and believe that this is an essential element of the modeling process so that the various dimensions of mathematical connections, along with relevant mathematical, pedagogical, and curricular knowledge, can be effectively integrated into model-eliciting activities.

Keywords

• Mathematical connections
• model-eliciting activities
• mathematical modeling
• pre-service mathematics teachers

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