Supporting Argumentation on the Mathematical Connections Between the Graphs of f and f' by Rational Questioning

Abstract

The aim of this study is to investigate how teachers’ rational questioning during argumentation influences students’ reasoning about the mathematical connections between the graphs of f and f'. The study was conducted with 13 senior students in a mathematics education program at a university in Türkiye. Students were requested to individually work on a task involving the graph of f' and subsequently asked to derive the graph of f, followed by argumentation on their individual works. The teacher engaged in argumentation by asking rational questions, encouraging the students to behave rationally, and monitoring their performance within the context of rationality. The structure of argumentation was analyzed using Toulmin’s model, the teacher’s questioning by the Teacher Rational Questioning Framework, and students’ behaviors using Habermas’ Construct of Rationality. Through the teacher’s rational questioning, it was observed that students were able to reason more rationally in constructing mathematical connections between the graphs of f and f'. The teacher’s rational manner during argumentation directed students towards rational questioning of each other, supporting them to perform more rationally. The findings suggest that designing learning environments supported by rational questioning could foster a culture of rational behavior in mathematics classrooms.

Keywords

• Argumentation
• Mathematical reasoning
• Rationality theory
• Rational questioning

f ve f' Grafikleri Arasındaki Matematiksel Bağlantılar Üzerine Argümantasyonun Akılcı Sorgulama ile Desteklenmesi

Abstract

Bu çalışmanın amacı, öğretmenin argümantasyon sürecini akılcı sorgulama destekli yürütmesinin öğrencilerin f ile f' grafikleri arasındaki matematiksel bağlantılar üzerine akıl yürütmesini nasıl etkilediğini araştırmaktır. Çalışma, Türkiye’de bir üniversitede matematik eğitimi programında son sınıfta öğrenim görmekte olan 13 öğretmen adayı ile yürütülmüştür. Öğrencilerden f' grafiğinin sunulduğu ve buradan f grafiğinin oluşturulmasının istendiği bir görev üzerinde bireysel çalışmaları ve ardından bireysel çalışma ürünleri üzerine tartışmaları istenmiştir. Dersi veren öğretim elemanı, argümantasyona akılcı sorgulama yaparak dahil olmuş ve öğrencilere akıl yürütme sürecindeki performanslarını akılcılık bağlamında denetleyici ve akılcı davranmaya teşvik edici sorular sormuştur. Argümantasyonun yapısı Toulmin modeli, öğretmenin öğrencileri sorgulaması süreci Öğretmenin Akılcı Sorgulama Çerçevesi ve öğrencilerin öğretmenin soruları karşısındaki söylemleri ve davranışları Habermas Akılcı Davranış Teorisi ile analiz edilmiştir. Öğretmenin akılcı sorgulaması sayesinde öğrencilerin f ve f' grafikleri arasındaki matematiksel bağlantıları kurmada daha akılcı davranabildiği görülmüştür. Öğretmenin akılcı sorgulama davranışı, öğrencileri birbirlerini akılcı sorgulamaya ve akılcı davranma konusunda desteklemeye yöneltmiştir. Elde edilen sonuçlar, öğretmenin matematik sınıflarında akılcı sorgulama destekli öğrenme ortamları oluşturmasının akılcı davranma kültürü oluşturabileceğine işaret etmektedir.

Keywords

• Argümantasyon
• Matematiksel akıl yürütme
• Akılcılık teorisi
• Akılcı sorgulama

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