İlköğretim Matematik Öğretmen Adaylarının Değişim Oranı ile İlgili Düşünme Biçimlerinin Bir Modelleme Etkinliği Bağlamında İncelenmesi

Year 2017, Volume: 8 Issue: 1, 188 - 217, 05.04.2017

Mahmut Kertil Ayhan Kürşat Erbaş Bülent Çetinkaya

https://doi.org/10.16949/turkbilmat.304212

Abstract

Öğretmen adaylarının matematiksel modelleme konusunda mesleki bilgi ve
becerilerini geliştirmeyi hedefleyen geniş kapsamlı bir çalışmanın parçası
olarak, bu çalışmada nüfus artışını konu alan bir modelleme etkinliği
bağlamında ilköğretim matematik öğretmen adaylarının “değişim oranı” kavramı
üzerine düşünme biçimleri incelenmektedir. Çalışmanın katılımcılarını bir
devlet üniversitesinin ilköğretim matematik öğretmenliği bölümünde son sınıfa
devam eden 9 öğretmen adayı oluşturmaktadır. Bir matematiksel modelleme dersi
kapsamında yapılan çalışmanın veri kaynaklarını; grup çalışmalarından derlenen
yazılı raporlar ve çalışma kâğıtları, etkinlik sonrası düşünce raporları ve
araştırmacı alan notları oluşturmaktadır. Bulgulara göre, çalışmanın
katılımcıları “zamana bağlı nüfus artış oranı (hızı)” ifadesini yüzdelik ve eğim olmak üzere iki farklı şekilde yorumlamıştır. Öğretmen
adaylarının yüzdelik yorumları daha
yoğun olmakla birlikte modelleme etkinliği bağlamında nüfus verilerindeki yıl
aralıklarının eşit verilmemesi bazı katılımcıları eğim yorumuna yönlendirmiştir. Ortaya çıkan bu iki farklı düşünme
şekli, öğretmen adaylarının yüzdelik ve eğim yorumu arasındaki farkı ve bu
ikisi arasındaki matematiksel ilişkiyi yorumlamada zorlandıklarını
göstermektedir. Ayrıca “rate of change” kavramının Türkçe ifadesi ile ilgili
problemli bir durum da gözlemlenmiştir. Çalışmanın sonuçları, öğretmen
adaylarının konu ile ilgili zorluklarının muhtemel kaynağı olan birimli oran ve birimsiz oran kavramları arasındaki fark dikkate alınarak
tartışılmıştır.  

Keywords

Değişim oranı, birimli oran, birimsiz oran, yüzde, matematiksel modelleme, matematik öğretmen eğitimi

Pre-service Elementary Mathematics Teachers’ Ways of Thinking about Rate of Change in the Context of a Modeling Activity

Abstract

As a part of a larger study
aiming at developing pre-service teachers’ pedagogical knowledge about
mathematical modeling, this study investigates pre-service elementary
mathematics teachers’ ways of thinking regarding rate of change in the context
of a modeling task on population growth. The participants of the study were 9
prospective middle school mathematics teachers in their senior year attending a
public university. The study was conducted as a part of an undergraduate course
on mathematical modeling for prospective teachers. Data were collected through
the prospective teachers’ written group work and reports regarding their
solution to the modeling activity, individual reflection papers, and
researchers’ field-notes. The results showed that participants demonstrated two
different ways of thinking about the expression “rate of change in population
with respect to time”: (i) percentage of change in population, and (ii) per
year change in population (slope). Even though “percentage” interpretation was
dominant, some of the participants were directed to “per year change in
population” interpretation as the year intervals in the problem context were
not given with equal intervals. The results revealed about prospective
teachers’ difficulties in conceiving the difference and the mathematical
relationship between “percentage” and “slope” interpretations. The results also
revealed about the problematic aspect of expressing the term/concept “rate of
change” in Turkish. As possible sources of these difficulties, the results are
discussed in light of the distinction between rate and ratio.

Keywords

Rate of change, rate, ratio, percentage, mathematical modeling, mathematics teacher education

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