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

Year 2019, Volume: 10 Issue: 1, 157 - 194, 10.04.2019

Aytuğ Özaltun Çelik , Esra Bukova Güzel

https://doi.org/10.16949/turkbilmat.446403

Abstract

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

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

Abstract

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.

Keywords

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

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