Yapay Zeka Sohbet Robotları Tarafından Kullanılan ve Sahip Olunan İspat Şemaları

Öz

İnsanlar ispat şemalarına sahiptir. Bu şemalar, ispat sürecinin, yani ikna sürecinin bilişsel özelliklerini ortaya koymaktadır. İnsan zekasını taklit eden yapay zekanın (YZ) bilişsel özelliklerinin incelenmesi, acilen ele alınması gereken bir konudur. Bu araştırma, YZ sohbet robotlarının (ChatGPT, Claude, Copilot, Gemini, Grok, Le Chat ve Perplexity) kullandığı ve sahip olduğu ispat şemalarını belirlemeyi amaçlamaktadır. İlk amaç, YZ sohbet robotlarının ilkokul, ortaokul, lise ve üniversite öğrencilerini bazı matematiksel formüllerin doğruluğuna ikna etmek için kullandıkları ispat şemalarını belirlemektir. İkinci amaç ise, YZ sohbet robotlarının bu formüllerin doğruluğuna kendilerini nasıl ikna ettiklerini, yani sahip oldukları ispat şemalarını belirlemektir. Bunun için, ardışık sayılarla ilgili iki benzer matematiksel formül kullanılmıştır. İki benzer formülün kullanılmasının nedeni, YZ sohbet robotlarının iç tutarlılığını incelemektir. Veriler, YZ sohbet robotlarına girilen komutların sonuçlarından elde edilmiştir. Bu veriler, betimsel analiz ile analiz edilmiştir. Kodlar için Harel ve Sowder’ın (1998) ispat şemaları kullanılmıştır. Araştırma sonuçlarına göre, bir öğretim aracı olarak YZ sohbet robotları, tüm eğitim seviyelerindeki öğrencilerin bilişsel düzeylerine uygun ispat şemalarını kullanabilmektedir. Bir yapay zekâ olarak sohbet robotları analitik ispat şemalarına sahiptir. Ancak ilginç bir şekilde, bazı sohbet robotları algısal ispat şemalarına da sahiptir. Ayrıca, sohbet robotları iç tutarlılığa da sahiptir. Bu sonuçlar, “matematik eğitiminde yapay zekâ” ve “yapay zekânın matematiksel gelişimi” için bir mihenk taşı niteliğindedir ve gelecekteki çalışmalara rehberlik etmesi umulmaktadır.

Anahtar Kelimeler

• Yapay zekâ
• matematik eğitiminde yapay zekâ
• sohbet robotları
• yapay zekanın matematiksel gelişimi
• ispat şemaları

Proof Schemes Used and Owned by Artificial Intelligence Chatbots

Öz

People possess proof schemes. These schemes reveal the cognitive characteristics of the proof process, that is, the persuasion process. Investigating the cognitive features of artificial intelligence (AI) that imitate human intelligence is an issue that needs to be addressed urgently. This research aims to identify the proof schemes used and owned by AI chatbots (AICs) (ChatGPT, Claude, Copilot, Gemini, Grok, Le Chat, and Perplexity). The first aim is to identify the proof schemes that AICs use to convince elementary, middle school, high school, and university students of the truth of some mathematical formulas. The second aim is to identify how AICs convince themselves of the truth of these formulas, that is, the proof schemes they own. For this, two similar mathematical formulas related to consecutive numbers were used. The reason for using two similar formulas is to investigate the internal consistency of AICs. The data was obtained from the results of prompts entered into AICs. This data was analyzed using descriptive analysis. Harel and Sowder’s (1998) proof schemes are used for the codes. According to the results of the research, as a teaching tool, chatbots are able to use proof schemes appropriate to the cognitive levels of students at all educational levels. As an AI, chatbots have analytical proof schemes. But interestingly, some chatbots also have perceptual proof schemes. Also, chatbots have internal consistency. These results are a cornerstone for “AI in mathematics education” and “mathematical development of AI” and are hoped to guide future studies.

Anahtar Kelimeler

• AI
• AI in mathematics education
• chatbots
• mathematical development of AI
• proof schemes

Kaynakça

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