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

Abstract

It is important for students to think the quantities related to the linear functions, to construct new quantities and to relate the different representations of linear functions through quantitative reasoning. The purpose of this study is to examine the students’ quantitative reasoning while engaging in the mathematical modeling task, which was designed, for learning the linear function. The participants of the study conducted with a teaching experiment were consisted of ten 10th grade students with three girls and seven boys. The students engaged in the written task in pairs which they decided to work together themselves. The data were each group’s written solutions and the transcriptions of the camera recordings of the process of working on the task. The collected data were analysed in two stages as ongoing analyses and retrospective analyses in the direction of the students' quantitative reasoning. Based on the data analysis, it was seen that students were cognitively more active while they were working on a situation which they had experienced or which was meaningful for them. It could be said that designing the task by considering the students’ quantitative reasoning triggering reflective abstraction was important factor in supporting the students to construct the quantities. In this context, it is suggested to use from mathematical modeling tasks during the teaching concept.

Keywords

• Linear Function,Mathematical Modeling,Quantitative Reasoning,Teaching Experiment

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

Abstract

Öğrencilerin nicel muhakeme yoluyla doğrusal fonksiyondaki temel çoklukları düşünmeleri, yeni çokluklar oluşturmaları ve farklı gösterimler arasında ilişkilendirmeler yapmaları kavramsal öğrenme için önemlidir. Bu çalışmada doğrusal fonksiyonun öğrenilmesine yönelik tasarlanan modelleme etkinliği üzerinde çalışan öğrencilerin nicel muhakemelerini incelemek amaçlanmıştır. Öğretim deneyine dayalı gerçekleştirilen çalışmanın katılımcılarını bir fen lisesindeki üçü kız, yedisi erkek on tane 10.sınıf öğrencisi oluşturmaktadır. Öğrenciler yazılı olarak verilen etkinlik üzerinde kendi belirledikleri ikişer kişilik gruplar halinde çalışmışlardır. Grupların çözüm kağıtları ve etkinlik çalışmaları boyunca alınan video kamera kayıtlarının transkriptleri araştırmanın verilerini 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 çoklukları oluşturmalarını desteklemede önemli bir etken olduğu söylenebilir. Bu bağlamda modelleme etkinliklerinden kavram öğretimi süreçlerinde yararlanılması önerilmektedir.

Keywords

• Doğrusal Fonksiyon,Matematiksel Modelleme,Nicel Muhakeme,Öğretim Deneyi

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