Matematiksel Görevlerde Bilişsel Talep ve Semiyotik Temsiller: ChatGPT Tabanlı TRSR Analiz Aracının Geliştirilmesi

Abstract

Bu çalışma, Raymond Duval’in Semiyotik Temsil Kayıtları Teorisi çerçevesinde, ortaokul 7. sınıf cebir görevlerinin bilişsel talep düzeylerini sınıflandırmak amacıyla geliştirilen yapay zekâ destekli " TRSR–Cognitive Demand Analyzer " aracının potansiyelini incelemektedir. Nitel açıklayıcı durum çalışması deseninde tasarlanan araştırmada, ChatGPT tabanlı bu aracın performansını değerlendirmek için 7. sınıf matematik ders kitabı "Cebirsel İfadeler" ünitesinden seçilen görevler kullanılmıştır. ChatGPT’nin sınıflandırmaları ile 7. sınıf öğrencisinin aynı görevleri çözerken yaşadığı bilişsel süreçler karşılaştırılarak, yapay zekâ analizinin öğrencinin gerçek bilişsel deneyimleriyle ne ölçüde örtüştüğü değerlendirilmiştir. Veriler; uzman değerlendirmeleri, ChatGPT sınıflandırmaları ve bir öğrencinin "sesli düşünme" (think-aloud) protokolü aracılığıyla toplanarak karşılaştırmalı analize tabi tutulmuştur. Bulgular, ChatGPT’nin semiyotik temsil süreçlerini (işlem ve dönüşüm) yüksek tutarlılıkla tanımlayabildiğini; ancak dönüşüm ağırlıklı karmaşık görevlerde modelin sunduğu gerekçeleri ayrıntılı ve sistematik bir biçimde yapılandırmakta zorlandığını göstermektedir. Öğrencinin bilişsel talep algısının başlangıçta görevlerin özelliklerine (görsel ya da işlemsel oluşu) dayandığı ancak çözüm süreci ilerledikçe bu algının yeniden yapılandığı görülmüştür. Çalışma sonucunda geliştirilen TRSR–Cognitive Demand Analyzer aracının, bilişsel talep ve semiyotik temsil süreçlerinin analizinde dikkate değer bir potansiyel sergilediği ve yapay zekânın matematiksel görevlerin tasarımı ile analizinde etkili bir destekleyici araç olarak kullanılabileceği görülmüştür.

Keywords

• Bilişsel Talep
• Cebir Öğretimi
• Semiyotik Temsil Kayıtları Teorisi
• ChatGPT

Cognitive Demand and Semiotic Representations in Mathematical Tasks: Development of a ChatGPT-Based TRSR Analysis Tool

Abstract

This study examines the potential of an artificial intelligence–supported tool, the TRSR–Cognitive Demand Analyzer, developed to classify the cognitive demand levels of Grade 7 middle school algebra tasks within Raymond Duval's Theory of Semiotic Representation Registers. Designed as a qualitative explanatory case study, the research employed tasks selected from the "Algebraic Expressions" unit of a Grade 7 mathematics textbook to evaluate the performance of this ChatGPT-based tool. The classifications produced by ChatGPT were compared with the cognitive processes experienced by a Grade 7 student while solving the same tasks to assess the extent to which AI-based analyses correspond to students' actual cognitive experiences. Data were collected through expert evaluations, ChatGPT classifications, and a student's think-aloud protocol, and were subjected to comparative analysis. The findings indicate that ChatGPT identified semiotic representation processes (treatments and conversions) with high consistency; however, the model struggled to structure detailed, systematic justifications for complex tasks involving conversion processes. The student's perception of cognitive demand was initially shaped by task characteristics (visual or procedural), but this perception was reconstructed as the solution process progressed. The results suggest that the TRSR–Cognitive Demand Analyzer demonstrates considerable potential for analyzing cognitive demand and semiotic representation processes, and that artificial intelligence can function as an effective supportive tool in the design and analysis of mathematical tasks.

Keywords

• Cognitive Demand
• Algebra Instruction
• ChatGPT
• theory of semiotic representation records

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