Doğrusal Fonksiyonun Öğrenilmesine Yönelik Tasarlanan Matematiksel Modelleme Etkinliği Üzerine Çalışan Öğrencilerin Nicel Muhakemeleri

Öğrencilerin nicel muhakeme yoluyla doğrusal fonksiyondaki temel nicelikleri düşünmeleri, yeni nicelikler oluşturmaları ve farklı gösterimler arasında ilişkilendirmeler yapmaları fonksiyonların kavramsal öğrenme süreci için önemlidir. Bu çalışmada doğrusal fonksiyonun öğrenilmesine yönelik tasarlanan bir modelleme etkinliği üzerinde çalışan öğrencilerin nicel muhakemelerini incelemek amaçlanmıştır. Öğretim deneyine dayalı gerçekleştirilen çalışmanın katılımcılarını bir fen lisesinde öğrenim gören on tane 10.sınıf öğrencisi oluşturmaktadır. Öğrenciler verilen etkinlik üzerinde kendi belirledikleri ikişer kişilik gruplar halinde çalışmışlardır. Grupların çözüm kâğıtları ve etkinlik çalışmaları boyunca alınan video kamera kayıtlarının transkriptleri araştırmanın veri kaynaklarını oluşturmuştur. Toplanan veriler öğrencilerin nicel muhakemeleri doğrultusunda devam eden analizler ve geriye dönük analizler olarak iki aşamada analiz edilmiştir. Analizler, öğrencilerin deneyimledikleri ya da anlam yükleyebildikleri bir durum üzerinde çalışırlarken zihinsel olarak daha aktif eylemler sergilediklerini göstermiştir. Etkinliğin yansıtıcı soyutlamayı destekleyecek nicel muhakemeleri göz önüne alarak tasarlanmasının öğrencilerin nicelikleri oluşturmalarını desteklemede önemli bir etken olduğu söylenebilir. Bu bağlamda modelleme etkinliklerinden kavram öğretimi süreçlerinde yararlanılması önerilmektedir.

Students’ Quantitative Reasoning while Engaging in a Mathematical Modeling Task Designed for Learning Linear Function

It is important for students to think the quantities related to the linearfunctions, to construct new quantities and to relate the differentrepresentations of linear functions through quantitative reasoning. Thepurpose of this study is to examine the students’ quantitative reasoningwhile engaging in the mathematical modeling task, which was designed, forlearning the linear function. The participants of the study conducted with ateaching experiment were consisted of ten 10th grade students with threegirls and seven boys. The students engaged in the written task in pairs. Thedata were gathered from each group’s written solutions and thetranscriptions of the camera recordings of the process of enagaging in thetask. The data were analysed by ongoing and retrospective analyses in thedirection of the students' quantitative reasoning. Based on the data analysis,it was seen that students were cognitively more active while they wereworking on a situation which they had experienced or which was meaningfulfor them. It could be said that designing the task by considering thequantitative reasoning to trigger reflective abstraction was important factorfor students to be supported for constructing the quantities. In this context, itis suggested to benefit from mathematical modeling tasks while teaching theconcepts.

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