Covariational Reasoning of Prospective Mathematics Teachers: How Do Dynamic Animations Affect?

Year 2020, Volume: 11 Issue: 2, 312 - 342, 31.08.2020

Mahmut Kertil

https://doi.org/10.16949/turkbilmat.652481

Abstract

Covariational reasoning is about the ability of coordinating the variation in two simultaneously and dynamically changing quantities and being able to see these quantities at the same time by forming a multiplicative unit. Covariational reasoning ability has been considered as necessary and foundational to the understanding of many mathematical concepts ranging from elementary to tertiary levels. In this study, covariational reasoning abilities of prospective elementary school mathematics teachers and the effects of dynamic animations created in computer-based environments on these abilities have been investigated. Case study was used as a research design one of which is a qualitative research methodology. The participants of the study were 19 prospective elementary school mathematics teachers attending to an elective Computer-Assisted Mathematics Education course and four of them were selected for semi-structured interviews. The results showed the weakness in prospective elementary school mathematics teachers’ covariational reasoning abilities and the potential of dynamic animations in supporting covariational reasoning. The animations in dynamic computer environments seem to have minimal effect on paper and pencil solutions in general. However, these animations, if they were used with their data collection and graph drawing properties, affected prospective teachers ways of reasoning in two ways: (i) forcing them to revise and rethink about the current ways of reasoning used during paper and pencil solutions, and (ii) lowering the cognitive load or removing the necessity of deep thinking on the situation. For the first case, the activities supported with the dynamic animations play a supportive role in developing covariational reasoning. For the second case, the dynamic animations did not contribute to prospective teachers’ covariational reasoning, rather they just played a mediating tool role that helps them to find a result.

Keywords

Change, rate of change, covariation, covariational reasoning, quantitative reasoning

Matematik Öğretmen Adaylarının Kovaryasyonel Düşünme Becerileri: Dinamik Animasyonlar Nasıl Etkiliyor?

Abstract

Kovaryasyonel düşünme eş zamanlı ve dinamik olarak değişen iki niceliğin birlikte değişimini düşünerek koordine edebilme ve değişimler arasındaki ilişkiyi bir bütün olarak yorumlayabilme becerisidir. Kovaryasyonel düşünme becerisi oran-orantı, türev ve integral gibi ilköğretim ve daha ileri düzeyde birçok matematiksel kavramın anlaşılmasında önemlidir. Bu çalışmada, ilköğretim matematik öğretmen adaylarının kovaryasyonel düşünme becerileri ve bilgisayar destekli ortamlarında oluşturulan dinamik animasyonların bu becerileri nasıl etkilediği incelenmiştir. Nitel araştırma yöntemlerinden özel durum çalışması kullanılmıştır. Çalışmanın katılımcıları, Bilgisayar Destekli Matematik Öğretimi dersine kayıtlı son sınıf 19 ilköğretim matematik öğretmen adayı olup dört öğretmen adayı ile yarı-yapılandırılmış görüşmeler yapılmıştır. Elde edilen bulgular öğretmen adaylarının kovaryasyonel düşünme becerilerinin yeterli düzeyde olmadığını ve dinamik geometri yazılımları ile elde edilen animasyonların kovaryasyonel düşünme becerisine katkı sağlayabileceğini göstermektedir. Sadece dinamik animasyon oluşturmanın ve onu izlemenin öğretmen adaylarının kâğıt-kalem çözümlerine etkisi çok azdır. Fakat animasyonlar, dinamik geometri programının veri alma ve grafik çizdirme özellikleri ile birlikte kullanıldığında, öğretmen adaylarının kovaryasyonel düşünme becerilerini iki şekilde etkilemiştir: (i) statik (kâğıt-kalem) bağlamlardaki düşünme biçimlerinden farklı sonuçlar vererek tekrar düşünmeye sevk etme veya (ii) zihinsel iş yükünü alarak durum üzerinde derin düşünme gereksinimini ortadan kaldırma. Birinci durumda dinamik animasyonlar öğretmen adayları için kovaryasyonel düşünmeyi destekleyici bir unsur olurken ikinci durumda ise çözüme odaklı ve durum üzerinde derinlemesine düşünme ihtiyacını ortadan kaldıran bir araç rolünü almıştır.

Keywords

Değişim, değişim oranı, kovaryasyon, kovaryasyonel düşünme, niceliksel düşünme

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