SavedAdd your journal

Journals / Disiplinlerarası Eğitim Araştırmaları Dergisi / 2026 / Cilt: 10 Sayı: 24

Proof Schemes Used and Owned by Artificial Intelligence Chatbots

Yapay Zeka Sohbet Robotları Tarafından Kullanılan ve Sahip Olunan İspat Şemaları

Fikret Cihan(KIRKLARELİ ÜNİVERSİTESİ)0000-0001-8783-4136
Pages
245–263
Publication Date
2026-08-28
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

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.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:People possess proof schemes.
📊
Key Findings & Data:Harel and Sowder’s (1998) proof schemes are used for the codes.
💡
Conclusion & Impact: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.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Yapay zekâ · matematik eğitiminde yapay zekâ · sohbet robotları

Abstract

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.

Özet

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.

🔖

Cite This Article

Cihan, F. (2026). Proof Schemes Used and Owned by Artificial Intelligence Chatbots. Disiplinlerarası Eğitim Araştırmaları Dergisi, Cilt: 10 Sayı: 24, 245–263. https://doi.org/10.57135/jier.1894348

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (58)

  1. Adams, S. S., Arel, I., Bach, J., Coop, R., Furlan, R., Goertzel, B., Hall, J. S., Samsonovich, A., Scheutz, M., Schlesinger, M., Shapiro, S. C., & Sowa, J. F. (2012). Mapping the landscape of human‐level artificial general intelligence. AI Magazine, 33(1), 25-41. https://doi.org/10.1609/aimag.v33i1.2322
  2. Amir, F., & Amir, M. F. (2021). Action proof: Analyzing elementary school students informal proving stages through counter-examples. International Journal of Elementary Education, 5(3), 401-408. https://doi.org/10.23887/ijee.v5i3.35089
  3. Anthropic. (2025, July 4). Claude (Claude Sonnet 4) [AI assistant]. https://claude.ai
  4. Awang, L. A., Yusop, F. D., & Danaee, M. (2025). Current practices and future direction of artificial intelligence in mathematics education: A systematic review. International Electronic Journal of Mathematics Education, 20(2), em0823. https://doi.org/10.29333/iejme/16006
  5. Baytak, A. (2023). The acceptance and diffusion of generative artificial intelligence in education: A literature review. Current Perspectives in Educational Research, 6(1), 7-18. https://doi.org/10.46303/cuper.2023.2
  6. Baytak, A. (2024). The content analysis of the lesson plans created by ChatGPT and Google Gemini. Research in Social Sciences and Technology, 9(1), 329-350. https://doi.org/10.46303/ressat.2024.19
  7. Calonge, D. S., Smail, L., & Kamalov, F. (2023). Enough of the chit-chat: A comparative analysis of four AI chatbots for calculus and statistics. Journal of Applied Learning and Teaching, 6(2), 346-357. https://doi.org/10.37074/jalt.2023.6.2.22
  8. Castelvecchi, D. (2023). How will AI change mathematics? Rise of chatbots highlights discussion. Nature, 615(7950), 15-16. https://doi.org/10.1038/d41586-023-00487-2
  9. Chen, L., Zaharia, M., & Zou, J. (2024). How is ChatGPT’s behavior changing over time? Harvard Data Science Review, 6(2). https://doi.org/10.1162/99608f92.5317da47
  10. Chen, X., Xie, H., Zou, D., & Hwang, G.-J. (2020). Application and theory gaps during the rise of artificial intelligence in education. Computers and Education: Artificial Intelligence, 1, 100002. https://doi.org/10.1016/j.caeai.2020.100002
  11. Cihan, F., & Akkoç, H. (2023). An intervention study for improving pre-service mathematics teachers’ proof schemes. Mathematics Teaching-Research Journal, 15(2), 56-80. https://eric.ed.gov/?id=EJ1394137
  12. Dao, X., & Le, N. (2023). Investigating the effectiveness of ChatGPT in mathematical reasoning and problem solving: Evidence from the Vietnamese National High School graduation examination. arXiv preprint arXiv:2306.06331. https://doi.org/10.48550/arxiv.2306.06331
  13. Dasari, D., Hendriyanto, A., Sahara, S., Suryadi, D., Muhaimin, L. H., Chao, T., & Fitriana, L. (2024). ChatGPT in didactical tetrahedron, does it make an exception? A case study in mathematics teaching and learning. Frontiers in Education, 8, 1295413. https://doi.org/10.3389/feduc.2023.1295413
  14. Ellis, A. E., Lockwood, E., Williams, C. C. W., Dogan, M. F., & Knuth, E. (2012). Middle school students’ example use in conjecture exploration and justification. In L. R. Van Zoest, J. J. Lo, & J. L. Kratky (Eds.), Proceedings of the 34th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 135-142). Kalamazoo, MI: Western Michigan University.
  15. Ergene, O., & Çaylan-Ergene, B. (2025). AI ChatBots’ solutions to mathematical problems in interactive e-textbooks: Affordances and constraints from the eyes of students and teachers. Education and Information Technologies, 30(1), 509-545. https://doi.org/10.1007/s10639-024-13121-z
  16. Getenet, S. (2024). Pre-service teachers and ChatGPT in multistrategy problem-solving: Implications for mathematics teaching in primary schools. International Electronic Journal of Mathematics Education, 19(1), em0766. https://doi.org/10.29333/iejme/14141
  17. Goertzel, B. (2014). Artificial general intelligence: Concept, state of the art, and future prospects. Journal of Artificial General Intelligence, 5(1), 1-48. https://doi.org/10.2478/jagi-2014-0001
  18. Google. (2025a). What Gemini is. https://gemini.google/overview/?hl=tr
  19. Google. (2025b, July 4). Gemini (Gemini 2.5 Flash) [AI assistant]. https://gemini.google.com/app
  20. Guba, E. G., & Lincoln, Y. S. (1981). Effective evaluation: Improving the usefulness of evaluation results through responsive and naturalistic approaches. Jossey-Bass.
  21. Harel, G. (2007). Students’ proof schemes revisited. In P. Boero (Ed.), Theorems in school: From history, epistemology and cognition to classroom practice (pp. 65-78). Sense Publishers.
  22. Harel, G., & Sowder, L. (1998). Students’ proof schemes: Results from exploratory studies. In A. H. Schoenfeld, J. Kaput, & E. Dubinsky (Eds.), Research in collegiate mathematics education III (pp. 234–283). American Mathematical Society.
  23. Harel, G., & Sowder, L. (2007). Toward comprehensive perspectives on the learning and teaching of proof. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 805-842). Information Age Publishing.
  24. Hwang, G.-J., Xie, H., Wah, B. W., & Gašević, D. (2020). Vision, challenges, roles and research issues of artificial intelligence in education. Computers and Education: Artificial Intelligence, 1, 100001. https://doi.org/10.1016/j.caeai.2020.100001
  25. Ilieva, R., Anguelov, K., & Nikolov, Y. (2019). Mathematical algorithms for artificial intelligence. Proceedings of the 45th International Conference on Application of Mathematics in Engineering and Economics (Amee’19), 2172, 110015. https://doi.org/10.1063/1.5133618
  26. Kang, Y. (2024). A study on the didactical application of ChatGPT for mathematical word problem solving. Communications of Mathematical Education, 38(1), 49-67. https://doi.org/10.7468/JKSMEE.2024.38.1.49
  27. Korkmaz-Güler, N., Dertli, Z. G., Boran, E., & Yıldız, B. (2024). An artificial intelligence application in mathematics education: Evaluating ChatGPT’s academic achievement in a mathematics exam. Pedagogical Research, 9(2), em0188. https://doi.org/10.29333/pr/14145
  28. Lee, D., & Yeo, S. (2022). Developing an AI-based chatbot for practicing responsive teaching in mathematics. Computers & Education, 191, 104646. https://doi.org/10.1016/j.compedu.2022.104646
  29. Li, P. H., Lee, H. Y., Cheng, Y. P., Starčič, A. I., & Huang, Y. M. (2023). Solving the self-regulated learning problem: Exploring the performance of ChatGPT in mathematics. In Y. M. Huang & T. Rocha (Eds.), Innovative technologies and learning: Lecture notes in computer science (pp. 77-86). Springer. https://doi.org/10.1007/978-3-031-40113-8_8
  30. Luzano, J. F. P. (2024a). Reshaping mathematics instruction via impact of AI chatbots on secondary education pre-service teachers. International Journal of Studies in Education and Science (IJSES), 5(3), 233-245. https://doi.org/10.46328/ijses.97
  31. Luzano, J. F. P. (2024b). Pedagogical influence of an AI Chatbot Gemini in mathematics education. International Journal of Academic Pedagogical Research (IJAPR), 8(4), 107-112. http://ijeais.org/wp-content/uploads/2024/4/abs/IJAPR240419.html
  32. Mavrych, V., Ganguly, P., & Bolgova, O. (2025). Using large language models (ChatGPT, Copilot, PaLM, Bard, and Gemini) in gross anatomy course: Comparative analysis. Clinical Anatomy, 38(2), 200-210. https://doi.org/10.1002/ca.24244
  33. McLean, S., Read, G. J. M., Thompson, J., Baber, C., Stanton, N. A., & Salmon, P. M. (2021). The risks associated with artificial general intelligence: A systematic review. Journal of Experimental & Theoretical Artificial Intelligence, 35(5), 649-663. https://doi.org/10.1080/0952813x.2021.1964003
  34. Memiş, Y. (2025). Examining the potential and pitfalls of AI in problem solving. Journal of Pedagogical Research, 9(2), 177-190. https://doi.org/10.33902/JPR.202532099 Microsoft. (2025, July 4). Copilot [AI assistant]. https://www.microsoft.com/copilot
  35. Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook (2nd ed.). Sage Publications, Inc.
  36. Mistral AI. (2024, July 4). Le Chat (Mistral Medium 2) [AI assistant]. https://mistral.ai
  37. Muhsen, D. K., Sadiq, A. T. (2025). Understanding artificial general intelligence: Defining characteristics and benchmarks. Journal of Artificial Intelligence and Control Systems, 1(1), 16-29. https://doi.org/10.66967/jaics.2025.v1i103
  38. OpenAI. (2024). Hello gpt-4o. https://openai.com/index/hello-gpt-4o/⁠
  39. OpenAI. (2025a). Introducing ChatGPT. https://openai.com/index/chatgpt/
  40. OpenAI. (2025b, July 4). ChatGPT (GPT-4o) [AI assistant]. https://chat.openai.com/
  41. Opesemowo, O. A. G., & Ndlovu, M. (2024). Artificial intelligence in mathematics education: The good, the bad, and the ugly. Journal of Pedagogical Research, 8(3), 333-346. https://doi.org/10.33902/jpr.202426428
  42. Ouyang, F., & Jiao, P. (2021). Artificial intelligence in education: The three paradigms. Computers and Education: Artificial Intelligence, 2, 100020. https://doi.org/10.1016/j.caeai.2021.100020
  43. Pala, C. A., Lagrimas, D., & Nobis, M. L. (2025). Exploration of chatbots in mathematics education for innovative learning process. Asian Journal of Advanced Research and Reports, 19(5), 178-194. https://doi.org/10.9734/ajarr/2025/v19i51010
  44. Pelton, T., & Francis-Pelton, L. (2023). Adapting ChatGPT to support teacher education in mathematics. In E. Langran, P. Christensen & J. Sanson (Eds.), Proceedings of Society for Information Technology & Teacher Education International Conference (pp. 1662-1670). New Orleans, LA, United States: Association for the Advancement of Computing in Education (AACE). https://www.learntechlib.org/primary/p/222047/
  45. Perplexity AI. (2025, July 4). Perplexity [AI assistant]. https://www.perplexity.ai/
  46. Rahman, M. M., & Watanobe, Y. (2023). ChatGPT for education and research: Opportunities, threats, and strategies. Applied Sciences, 13(9), 5783. https://doi.org/10.3390/app13095783
  47. Sánchez-Ruiz, L. M., Moll-López, S., Núñez-Pérez, A., Moraño-Fernández, J. A., & Vega-Fleitas, E. (2023). ChatGPT challenges blended learning methodologies in engineering education: A case study in mathematics. Applied Sciences, 13(10), 6039. https://doi.org/10.3390/app13106039
  48. Shakarian, P., Koyyalamudi, A., Ngu, N., & Mareedu, L. (2023). An independent evaluation of ChatGPT on mathematical word problems (MWP). arXiv preprint arXiv:2302.13814v2. https://doi.org/10.48550/arXiv.2302.13814
  49. Stake, R. E. (2006). Multiple case study analysis. The Guilford Press.
  50. Sowder, L., & Harel, G. (1998). Types of students’ justifications. The Mathematics Teacher, 91(8), 670-675. https://doi.org/10.5951/MT.91.8.0670
  51. Thomas, L. D. W., Romasanta, A. K. G., & Pujol Priego, L. (2026). Jagged competencies: Measuring the reliability of generative AI in academic research. Journal of Business Research, 203, 115804. https://doi.org/10.1016/j.jbusres.2025.115804
  52. Turing, A. M. (1950). Computing machinery and intelligence. Mind, 59, 433-460. http://dx.doi.org/10.1093/mind/LIX.236.433
  53. Wardat, Y., Tashtoush, M. A., AlAli, R., & Jarrah, A. M. (2023). ChatGPT: A revolutionary tool for teaching and learning mathematics. Eurasia Journal of Mathematics, Science and Technology Education, 19(7), em2286. https://doi.org/10.29333/ejmste/13272
  54. Wei, X. (2024). Evaluating ChatGPT-4 and ChatGPT-4o: Performance insights from NAEP mathematics problem solving. Frontiers in Education, 9, 1452570. https://doi.org/10.3389/feduc.2024.1452570
  55. xAI. (2025, July 4). Grok (Grok 3) [AI assistant]. https://x.ai/grok
  56. Yin, R. K. (2018). Case study research and applications: Design and methods (6th ed.). Sage Publications, Inc.
  57. Zhang, K., & Aslan, A. B. (2021). AI technologies for education: Recent research & future directions. Computers and Education: Artificial Intelligence, 2, 100025. https://doi.org/10.1016/j.caeai.2021.100025
  58. Zhuo, J., Zhang, S., Fang, X., Duan, H., Lin, D., & Chen, K. (2024, November). ProSA: Assessing and understanding the prompt sensitivity of LLMs. In C. Christodoulopoulos, T. Chakraborty, C. Rose, & V. Peng (Eds.), Findings of the Association for Computational Linguistics: EMNLP 2024 (pp. 9610-9631). Association for Computational Linguistics. https://doi.org/10.18653/v1/2024.findings-emnlp.108 Zupic, I. (2026). A human-centered workflow for using large language models in content analysis. arXiv preprint arXiv:2603.19271v1. https://doi.org/10.48550/arXiv.2603.19271