Representations used by mathematics student teachers in mathematical modeling process

Year 2013, Volume: 4 Issue: 2, - , 26.11.2013

Aytuğ Özaltun , Çağlar Hıdıroğlu , Semiha Kula , Esra Bukova Güzel

Abstract

The purpose of this study is to determine representations used by mathematics student teachers in steps of mathematical modeling process based on their solutions of problems formed in the context of different classification of modeling. The study was conducted with fifteen secondary mathematics student teachers given a Mathematical Modeling course. The participants were separated into five collaboration groups of three students. Data were collected with the detailed written papers given by the groups for the problems and GeoGebra solution files. The groups benefited from verbal, algebraic, figural, tabular and dynamic representations while they were solving the problems. Considering all steps of the process, groups at most used verbal and algebraic representations. While they used only verbal representation in analyzing the problem, they benefited from at most verbal representation and then figural representation in establishing the systematic structure. The most used is algebraic and then verbal representations in the steps of mathematization, meta-mathematization, and mathematical analysis. In the steps of interpretation/evaluation and the model verification, the groups mainly benefited from verbal and then algebraic representations. Further researches towards why representations are preferred in the specific steps of the mathematical modeling process are suggested.

Key Words: Mathematical modeling, modeling problems, mathematics student teachers, representations.

Keywords

Mathematical modeling, modeling problems, mathematics student teachers, representations.

Matematik Öğretmeni Adaylarının Modelleme Sürecinde Kullandıkları Gösterim Şekilleri

Abstract

Bu çalışmanın amacı, matematik öğretmeni adaylarının farklı modelleme türleri bağlamında oluşturulmuş problemlere ilişkin çözümlerinden yola çıkarak matematiksel modelleme sürecinin basamaklarında kullandıkları gösterim şekillerini belirlemektir. Çalışma, Matematiksel Modelleme dersini alan on beş ortaöğretim matematik öğretmen adayıyla gerçekleştirilmiştir. Katılımcılar kendi istekleri doğrultusunda üçer kişilik beş çalışma grubuna ayrılmışlardır. Veriler, grupların altı matematiksel modelleme problemine ilişkin ayrıntılı çözümlerini içeren yazılı yanıt kağıtları ve GeoGebra çözüm dosyaları yardımıyla toplanmıştır. Grupların modelleme problemlerinin çözümünde sözel, cebirsel, şekilsel, grafiksel, tablo ve dinamiksel gösterim şekillerinden yararlandıkları belirlenmiştir. Sürecin tüm basamaklarına göre gruplar en fazla sözel ve cebirsel gösterimleri kullanmışlardır. Problemin analizi basamağında sadece sözel gösterim kullanılırken, sistematik yapıyı kurma basamağında ise en fazla sözel ardından ise şekilsel gösterimden yararlanılmıştır. Matematikselleştirme, üst matematikselleştirme ve matematiksel analiz basamaklarında en çok kullanılan cebirsel ve ardından sözel gösterimler olmuştur. Yorumlama/değerlendirme ve modelin doğrulanması basamaklarında ise gruplar ağırlıklı olarak sözel ve ardından da cebirsel gösterimlerden yararlanmışlardır. Gösterim şekillerinin matematiksel modelleme sürecinin hangi basamaklarında niçin tercih edildiğine yönelik araştırmaların yapılması önerilmektedir.

Anahtar Kelimeler:   Matematiksel modelleme, modelleme problemleri, matematik öğretmeni adayları, gösterim şekilleri.

Keywords

Matematiksel modelleme, modelleme problemleri, matematik öğretmeni adayları, gösterim şekilleri.

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