İkinci Dereceden Fonksiyonların Öğrenilmesi Sürecinde Öğrencilerin Nicel Muhakemelerini Tetikleyen Bir Öğretim Dizisi

Bu çalışmanın amacı ikinci dereceden fonksiyonların öğrenilmesi sürecinde nicel muhakemeyi tetikleyen bir öğretim dizisi tasarlamaktır. Çalışma, döngüsel bir süreç olan tasarım tabanlı araştırma modeline dayandırılmıştır. Tasarı, uygulama ve analiz olacak şekilde üç aşamada gerçekleştirilen tasarım tabanlı araştırmanın uygulama aşaması iki ardıl döngüyü kapsamıştır. İlk döngü, öğretim dizisinin bir sınıf ortamındaki farklı öğrencilerin öğrenmelerini destekleyip desteklemediğini değerlendirmek amacıyla on öğrenci ile, ikinci döngü ise iki onuncu sınıf öğrencisi ile gerçekleştirilmiştir. Çalışmadaki veri toplama araçları öğretim deneyleri boyunca alınan video kamera kayıtları, araştırmacı gözlem notları, öğrencilerle yapılan klinik mülakatlar ve öğrencilerin yansıtıcı günlükleridir. Çalışmanın veri analiz sürecinde veri toplama süreci ile eş zamanlı bir şekilde sürekli karşılaştırmalı olarak devam eden analizler ve birinci ve ikinci döngülerin sonunda öğrencilerin nicel muhakemeleri bağlamında geriye dönük analizler yapılmıştır. Öğretim dizisindeki gerçek yaşam bağlamlı etkinlikler dinamik durumları içerdiği için öğrencilerin fonksiyonel ilişkileri anlamlandırmalarına ve fonksiyonun eş zamanlı değişim fikrini oluşturmalarına imkan vermiştir. Matematik öğretmenlerinin öğrencilerin ikinci dereceden fonksiyonları öğrenmelerini desteklemek amacıyla öğretim dizisini kendi sınıf ortamlarına uygun şekilde revize ederek kullanmaları önerilmektedir.

Anahtar Kelimeler:

İkinci dereceden fonksiyon, mantıksal-matematiksel öğrenme etkinliği, matematiksel modelleme, nicel muhakeme, öğretim dizisi

An Instructional Sequence Triggering Students’ Quantitative Reasoning during Learning of Quadratic Functions

The purpose of this study is to design an instructional sequence triggering students’ quantitative reasoning in the process of learning quadratic functions. The study was conducted as a design-based research, following a cyclical process. The study consisted of three phases of the design, implementation, and analysis phases and the implementation phase consisted of two consecutive cycles. While the first cycle was carried out to evaluate the success of the instructional sequence in supporting student learning in a class with ten 10th students, the second cycle was carried out with two 10th grade students. The video recordings taken during the teaching experiments, the researchers’ observation notes, the clinical interviews, and the students’ reflective journals constituted the data sources of the study. In the data analysis process of the study, the constant comparison method simultaneously conducted with the data collection process was used and also a retrospective analysis of the teaching experiments data was conducted after completing the cycles. Because the tasks were grounded in real-life contexts involving dynamic situations, they contributed to the students’ understanding of functional relations and helped them construct the idea of covarying change in the functions. It is suggested that mathematics teachers revise and use the instructional sequence according to their own classroom context with the aim of supporting their students’ understanding of quadratic functions.

Keywords:

logico-mathematical activity, mathematical modeling, quantitative reasoning, Quadratic function, instructional sequence,

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