Ortaokul Matematik Öğretmen Adaylarının Belirli İntegral ve Belirsiz İntegral Tanımlamaları

Öz

Araştırmacılar analizin matematik, matematik eğitimi ve diğer disiplinlerdeki önemini ve bu dersin temel kavramlarından biri olan integrale ilişkin öğrencilerin kavramsal anlamalarının geliştirilmesi gerektiğini vurgulamaktadır. Bu nedenle, bu çalışmanın amacı, ortaokul matematik öğretmen adaylarının belirli integrali ve belirsiz integrali nasıl tanımladıklarını ve ayrıca belirli integral ve belirsiz integral arasındaki ilişkiyi ne derece ifade edebildiklerini araştırmaktır. Bu amaçla, 173 ortaokul matematik öğretmen adayından üç soruyu cevaplamaları istenmiştir. Elde edilen bulgulara göre, ortaokul matematik öğretmen adayları hem belirli hem de belirsiz integrali tanımlarken benzer kavramlara değinmektedir. Bu kavramlar sınır, notasyon, matematiksel formül, örnek verme, alan, hacim, ters türev, hesaplama süreci, sonucun yapısı (sayı, fonksiyon, cebirsel ifade veya bilinmeyen) ve c sabiti olarak sınıflandırılmıştır. Ayrıca her bir integral türü için en çok bahsedilen kavramın sınır olduğu görülmüştür. Ancak, katılımcıların azınlığının cevaplarında belirli integral ve belirsiz integral arasındaki ilişkiye dair ifadeler bulunmuştur.

Anahtar Kelimeler

• Belirli integral
• Belirsiz integral
• Analiz Ortaokul matematik öğretmeni adayı

Pre-service Middle School Mathematics Teachers’ Descriptions of Definite Integral and Indefinite Integral

Öz

The importance of calculus in mathematics, mathematics education, and other disciplines and the necessity of developing students’ conceptual understanding regarding integral, which is one of the major concepts in calculus course, are among the issues emphasized by researchers. Thus, the purposes of this study were to examine how pre-service middle school mathematics teachers describe definite integral and indefinite integral and also to what extent they can see the relation between definite integral and indefinite integral. For these purposes, 173 pre-service middle school mathematics teachers were asked to answer three questions. According to the findings, the concepts pre-service middle school mathematics teachers mentioned while describing both definite and indefinite integral are similar which are bound, notation, mathematical formula, example, area, volume, antiderivative, calculation process, the form of result (number, function, algebraic expression or unknown), and the constant c. It was also seen that mostly mentioned concept is bound for each type of integral. However, the minority of them presented evidence regarding the relation between definite integral and indefinite integral in their responses.

Anahtar Kelimeler

• Definite integral
• Indefinite integral
• Calculus
• Pre-service middle school mathematics teachers

Kaynakça

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