ChatGPT's Knowledge in Mathematics Teaching: An Example of Rational Numbers
DOI:
https://doi.org/10.47750/pegegog.15.02.07Keywords:
mathematical concepts, ChatGPT, pedagogical content knowledge (PCK)Abstract
This research examines ChatGPT's content knowledge (mathematics) and pedagogical content knowledge on the concept of rational numbers. The study was conducted using a case study model within the framework of qualitative research methods. Data were collected by posing open-ended questions to ChatGPT-4 and ChatGPT-4.0 versions, based on the new curriculum objectives set by the Ministry of National Education of Türkiye in 2024. The findings indicate that ChatGPT may be adequate for teaching rational numbers in line with the knowledge required in middle school courses; however, certain limitations in its pedagogical content knowledge were identified. Specifically, it was observed that ChatGPT's pedagogical responses were limited in concepts such as representing rational numbers on the number line and converting them to decimal forms. The research emphasizes that while ChatGPT may not replace teachers, it could play a supportive role in teaching processes, and its integration into education should be carefully considered.
Downloads
References
Baidoo-Anu, D., & Ansah, L. O. (2023). Education in the era of generative artificial intelligence (AI): Understanding the potential benefits of ChatGPT in promoting teaching and learning. Journal of AI, 7(1), 52-62.
Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389-407. https://doi.org/10.1177/0022487108324554
Bang, Y., Cahyawijaya, S., Lee, N., Dai, W., Su, D., Wilie, B., Lovenia, H., Ji, Z., Yu, T., Chung, W., Do, Q. V., Xu, Y., & Fung, P. (2023). A multitask, multilingual, multimodal evaluation of ChatGPT on reasoning, hallucination, and interactivity. arXiv. https://doi.org/10.18653/v1/2023.ijcnlp-main.45
Brown, T., Mann, B., Ryder, N., Subbiah, M., Kaplan, J. D., Dhariwal, P., Neelakantan, A., Shyam, P., Sastry, G., Askell, A., Agarwal, S., Herbert-Voss, A., Krueger, G., Henighan, T., Child, R., Ramesh, A., Ziegler, D. M., Wu, J., Winter, C.,… Amodei, D. (2020). Language models are few-shot learners. Advances in Neural Information Processing Systems, 33, 1877–1901.
Chen, J. J. & Lin, J. C. (2024). Artificial intelligence as a double-edged sword: Wielding the POWER principles to maximize its positive effects and minimize its negative effects. Contemporary Issues in Early Childhood, 25(1), 146-153. https://doi.org/10.1177/14639491231169813
Chen, L., Chen, P., & Lin, Z. (2020). Artificial intelligence in education: A review. Ieee Access, 8,75264–75278. https://doi.org/10.1109/ACCESS.2020.2988510
Cooper, G. (2023). Examining science education in ChatGPT: An exploratory study of generative artificial intelligence. Journal of Science Education and Technology, 32(3), 444-452. https://doi.org/10.1007/s10956-023-10039-y
Cotton, D., Cotton, P., & Shipway, J. (2023). Chatting and cheating. Ensuring academic integrity in the era of ChatGPT. Innovations in Education and Teaching International, 61(2), 228-239. https://doi.org/10.1080/14703297.2023.2190148
Creswell, J. W. (2013). Qualitative inquiry and research design: Choosing among five approaches (3rd ed.). Sage Publications.
Çevikbaş, M., & Argün, Z. (2017). Geleceğin Matematik Öğretmenlerinin Rasyonel ve İrrasyonel Sayı Kavramları Konusundaki Bilgileri (Knowledge of future mathematics teachers on concepts of rational and irrational numbers). Uludağ University Faculty of Education Journal, 30(2), 551-581. https://doi.org/10.19171/uefad.368968
Dempere, J., Modugu, K., Hesham, A., & Ramasamy, L. K. (2023). The impact of ChatGPT on higher education. Frontiers in Education, 8, 1206936. https://doi.org/10.3389/FEDUC.2023.1206936
Dumlu, B. Ö., Gezer, E., & Yıldız, B. (2024). Eşitsizlik Konusunda ChatGPT ile Hazırlanan Ders Planlarının İncelenmesi (Examination of lesson plans on inequalities prepared with ChatGPT). Turkish Journal of Educational Sciences, 22(1), 337-358. https://doi.org/10.37217/tebd.1338959
Ellis, A. R., & Slade, E. (2023). A new era of learning: considerations for ChatGPT as a tool to enhance statistics and data science education. Journal of Statistics and Data Science Education, 31(2), 128-133. https://doi.org/10.1080/26939169.2023.2223609
Fırat, M. (2023). How ChatGPT can transform autodidactic experiences and open education? OSF Preprints, 1–5. https://doi.org/10.31219/osf.io/9ge8m
Fraenkel, J. R., & Wallen, N. E. (2006). How to design and evaluate research in education (6th ed.). McGraw-Hill.
Frieder, S., Pinchettil, L., Griffiths, R., Salvatori, T., Lukasiewicz, T., Petersen, P., Chevalier, A., & Berner, J. (2023). Mathematical capabilities of ChatGPT. arXiv. https://doi.org/10.48550/arXiv.2301.13867
Gouia-Zarrad, R., & Gunn, C. (2024). Enhancing students’ learning experience in mathematics class through ChatGPT. International Electronic Journal of Mathematics Education, 19(3), em0781. https://doi.org/10.29333/iejme/14614
Grossman, P. L. (1990). The making of a teacher: Teacher knowledge and teacher education. New York: Teachers College Press.
Guo, B., Zhang, X., Wang, Z., Jiang, M., Nie, J., Ding, Y., Yue, J., & Wu, Y. (2023). How close is ChatGPT to human experts? Comparison corpus, evaluation, and detection. arXiv. https://doi.org/10.48550/arXiv.2301.07597
Hill, H. C., Schilling, S. G., & Ball, D. L. (2004). Developing measures of teachers’ mathematics knowledge for teaching. The Elementary School Journal, 105(1), 11-30. https://doi.org/10.1086/428763
Hwang, G. J., & Tu, Y. F. (2021). Roles and research trends of artificial intelligence in mathematics education: A bibliometric mapping analysis and systematic review. Mathematics, 9(6), 584. https://doi.org/10.3390/math9060584
Korkmaz Guler, N., Dertli, Z. G., Boran, E., & Yildiz, B. (2024). An artificial intelligence application in mathematics education: Evaluating ChatGPT’s academic achievement in a mathematics exam. Pedagogical Research, 9(2), https://doi.org/10.29333/pr/14145
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. International Conference on Innovative Technologies and Learning.
Lincoln, Y. S., & Guba, E. G. (1985). Naturalistic inquiry. Sage Publications.
Loos, E., Gröpler, J., & Goudeau, M. L. S. (2023). Using ChatGPT in education: human reflection on ChatGPT’s self-reflection. Societies, 13(8), 196. https://doi.org/10.3390/soc13080196
MEB. (2024). Mathematics Course Curriculum. Retrieved from http://mufredat.meb.gov.tr/.
Merriam, S. B. (2009). Qualitative research: A guide to design and implementation: Revised and expanded from qualitative research and case study applications in education. Jossey-Bass.
Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook (2nd ed.). Thousand Oaks: Sage
NCTM. (2000). Principles and standards for school mathematics. National Council of Teachers of Mathematics.
NCTM. (2014). Principles to actions: Ensuring mathematical success for all. National Council of Teachers of Mathematics.
OpenAI. (2022). Introducing ChatGPT. Retrieved from https://openai.com
OpenAI. (2024). Introducing ChatGPT-4.0. Retrieved from https://openai.com
Pedro, F., Subosa, M., Rivas, A., & Valverde, P. (2019). Artificial intelligence in education: Challenges and opportunities for sustainable development. Retrieved from https://unesdoc.unesco.org/ark:/48223/pf0000366994
Plevris, V., Papazafeiropoulos, G., & Jiménez Rios, A. (2023). Chatbots put to the test in math and logic problems: a comparison and assessment of ChatGPT-3.5, ChatGPT-4, and Google bard. AI, 4(4), 949-969.
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
Rudolph, J., Tan, S., & Tan, S. (2023). ChatGPT: Bullshit spewer or the end of traditional assessments in higher education? Journal of Applied Learning & Teaching, 6(1), 1–20. https://doi.org/10.37074/jalt.2023.6.1.9
Schwab, J. J. (1983). The practical 4: Something for curriculum professors to do. Curriculum inquiry, 13(3), 239-265.
Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14.
Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1-22.
Susnjak, T. (2022). ChatGPT: The end of online exam integrity? arXiv pre-print arXiv:2212.09292.
Taani, O., & Alabidi, S. (2024). ChatGPT in education: benefits and challenges of ChatGPT for mathematics and science teaching practices. International Journal of Mathematical Education in Science and Technology, 1–30. https://doi.org/10.1080/0020739X.2024.2357341
Tapan-Broutin, M. S. (2023). Examination of questions asked by pre-service mathematics teachers in their initial experiences with ChatGPT. Journal of Uludag University Faculty of Education, 36(2), 707-732. https://doi.org/10.19171/uefad.1299680
Timms, M. J. (2016). Letting artificial intelligence in education out of the box: educational cobots and smart classrooms. International Journal of Artificial Intelligence in Education, 26, 701-712. https://doi.org/10.1007/s40593-016-0095-y
Urhan, S., Gençaslan, O., & Dost, Ş. (2024). An argumentation experience regarding concepts of calculus with ChatGPT. Interactive Learning Environments, https://doi.org/10.1080/10494820.2024.2308093
Van Driel, J. H., Verloop, N., & de Vos, W. (1998). Developing science teachers’ pedagogical content knowledge. Journal of Research in Science Teaching, 35(6), 673-695.
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
Yıldırım, A., & Şimşek, H. (1999). Sosyal bilimlerde nitel araştırma yöntemleri (Qualitative research methods in social sciences). Seçkin Publications.
Yin, R. K. (2018). Case study research and applications: Design and methods (6th ed.). Sage Publications.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Pegem Journal of Education and Instruction
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
NonCommercial — You may not use the material for commercial purposes.
No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
