Training mathematics teachers’ error behavior through ChatGPT-based error situations

Katja Lenz; Julia Sirock

doi:10.29333/iejme/18101

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Katja Lenz ¹ , Julia Sirock ² ^*

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¹ University of Education Schwäbisch Gmünd, Schwäbisch Gmünd, GERMANY² University of Education Heidelberg, Heidelberg, GERMANY^* Corresponding Author

Abstract

This study examines the potential of ChatGPT as a training tool for prospective mathematics teachers, focusing on error behavior and instructional strategies for solving word problems. ChatGPT consistently generated incorrect solutions, mirroring common learner error patterns. Based on the responses of prospective teachers
(N = 26) to these errors, three types of guidance emerged: co-constructive, directive, and non-responsive. These types represent varying instructional strategies guiding learners, as identified in previous research. In addition, participants evaluated the realism and usefulness of ChatGPT-based interactions. While many found the tool valuable for practicing guidance techniques and anticipating learners’ misconceptions, they noted limitations at the same time, including a lack of emotional nuance. Overall, the findings emphasize both the opportunities and limitations of using artificial intelligence-based dialogue systems in teacher education.

Keywords

artificial intelligence in education
ChatGPT
error behavior
teacher-student interaction
teacher education
mathematics education
word problem-solving

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

INT ELECT J MATH ED, Volume 21, Issue 2, May 2026, Article No: em0873

https://doi.org/10.29333/iejme/18101

Publication date: 01 Apr 2026

Online publication date: 13 Mar 2026

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References

Ade-Ojo, G. O., Markowski, M., Essex, R., Stiell, M., & Jameson, J. (2022). A systematic scoping review and textual narrative synthesis of physical and mixed-reality simulation in pre-service teacher training. Journal of Computer Assisted Learning, 38(3), 861-874. https://doi.org/10.1111/jcal.12653
Ammel, R. (2023). Wie gut ist ChatGPT als Mathe-Coach? Teil 1: Textaufgaben [How good is ChatGPT as a math coach? Part 1: Word problems]. Mathegym. https://mathegym.de/blog/wie-gut-ist-chatgpt-als-mathe-coach
Anderson, A., Hamilton, R. J., & Hattie, J. (2004). Classroom climate and motivated behaviour in secondary schools. Learning Environments Research, 7, Article 211e225. https://doi.org/10.1007/s10984-004-3292-9
Arora, S., Narayan, A., Chen, M. F., Orr, L., Guha, N., Bhatia, K., Chami, I., Sala, F., & Ré, C. (2022). Ask me anything: A simple strategy for prompting language models. arXiv. https://doi.org/10.48550/arXiv.2210.02441
Asare, B., Arthur, Y. D., & Boateng, F. O. (2023). Exploring the impact of ChatGPT on mathematics performance: The influential role of student interest. Educational Science and Management, 1(3), 158-168. https://doi.org/10.56578/esm010304
Bastian, A., Kaiser, G., Meyer, D., Schwarz, B., & König, J. (2022). Teacher noticing and its growth toward expertise: An expert-novice comparison with pre-service and in-service secondary mathematics teachers. Educational Studies in Mathematics, 110(2), 205-232. https://doi.org/10.1007/s10649-021-10128-y
Baumert, J., & Kunter, M. (2006). Stichwort: Professionelle Kompetenz von Lehrkräften [Keyword: Professional competence of teachers]. Zeitschrift für Erziehungswissenschaft, 9(4), 469-520. https://doi.org/10.1007/s11618-006-0165-2
Baumert, J., & Kunter, M. (2011). Das Kompetenzmodell von COACTIV [COACTIV’s competency model]. In M. Kunter, J. Baumert, W. Blum, U. Klusmann, S. Krauss, & M. Neubrand (Eds.), Professionelle Kompetenz von Lehrkräften: Ergebnisse des Forschungsprogramms COACTIV (pp. 29-53). Waxmann. https://doi.org/10.1007/s35834-011-0017-x
Baumert, J., Kunter, M., Blum, W., Klusmann, U., Krauss, S., & Neubrand, M. (2011). Professionelle Kompetenz von Lehrkräften, kognitiv aktivierender Unterricht und die mathematische Kompetenz von Schülerinnen und Schülern (COACTIV): Ein Forschungsprogramm [Professional competence of teachers, cognitively activating teaching and the mathematical competence of students (COACTIV): A research program]. In M. Kunter, J. Baumert, W. Blum, U. Klusmann, S. Krauss, & M. Neubrand (Eds.), Professionelle Kompetenz von Lehrkräften: Ergebnisse des Forschungsprogramms COACTIV (pp. 7-25). Waxmann. https://doi.org/10.31244/9783830974338
Berliner, D. C. (1991). Educational psychology and pedagogical expertise: New findings and new opportunities for thinking about training. Educational Psychologist, 26(2), 145-155. https://doi.org/10.1207/s15326985ep2602_6
Besser, M., & Krauss, S. (2009). Zur Professionalität als Expertise [On professionalism as expertise]. In O. Zlatkin-Troitschanskaia (Ed.), Beltz-Bibliothek. Lehrprofessionalität: Bedingungen, Genese, Wirkungen und ihre Messung (pp. 71-82). Beltz.
Blum, W., & Leiss, D. (2005). Modellieren im Unterricht mit der “Tanken”–Aufgabe [Modeling in the classroom using the “refueling” task]. Mathematik Lehren, 128, 18-21.
Bromme, R. (1992). Der Lehrer als Experte: Zur Psychologie des professionellen Wissens [The teacher as expert: On the psychology of professional knowledge]. H. Huber.
Bromme, R. (2008). Kompetenzen, Funktionen und unterrichtliches Handeln von Lehrer/innen [Competencies, functions and teaching practices of teachers]. In B. Rendtorff (Ed.), Schule, Jugend und Gesellschaft (pp. 244-256). Kohlhammer.
Bryden, K. (2023). Math is the worst enemy of ChatGPT. Crast. https://crast.net/265780/math-is-the-worst-enemy-of-chatgpt/
Caylan-Ergene, B., Ergene, O., & Kontorovich, I. (2025). Analysing the validity of ChatGPT’s solutions to statistical problems. In T. Fujita (Ed.), Proceedings of the British Society for Research into Learning Mathematics (pp. 1-6). BSRLM.
Cochran-Smith, M., & Zeichner, K. M. (Eds.). (2005). Studying teacher education: The report of the AERA panel on research and teacher education. American Educational Research Association. https://permalink.obvsg.at/AC08413669
Contel, F., & Cusi, A. (2025). Investigating the role of ChatGPT in supporting metacognitive processes during problem-solving activities. Digital Experiences in Mathematics Education, 11, 167-191. https://doi.org/10.1007/s40751-024-00164-7
Creswell, J. W., & Plano Clark, V. L. (2018). Designing and conducting mixed methods research. SAGE.
Dahal, N. (2024). Exploring capabilities and limitations of generative AI chatbots in solving math algorithm problems. In Proceedings of the 15^th International Congress on Mathematical Education (pp. 1-4). ICME.
Daroczy, G., Wolska, M., Meurers, W. D., & Nuerk, H.-C. (2015). Word problems: A review of linguistic and numerical factors contributing to their difficulty. Frontiers in Psychology, 6. https://doi.org/10.3389/fpsyg.2015.00348
Dilling, F., & Herrmann, M. (2024). Using large language models to support pre-service teachers’ mathematical reasoning, an exploratory study on ChatGPT as an instrument for creating mathematical proofs in geometry. Frontiers in Artificial Intelligence, 7. https://doi.org/10.3389/frai.2024.1460337
Elia, I., van den Heuvel-Panhuizen, M., & Kolovou, A. (2009). Exploring strategy use and strategy flexibility in non-routine problem solving by primary school high achievers in mathematics. ZDM Mathematics Education, 41, 605-618. https://doi.org/10.1007/s11858-009-0184-6
Ergene, O., & Ergene, B. C. (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, 509-545. https://doi.org/10.1007/s10639-024-13121-z
Frieder, S., Berner, J., Petersen, P., & Lukasiewicz, T. (2023a). Large language models for mathematicians. arXiv. https://doi.org/10.48550/arXiv.2312.04556
Frieder, S., Pinchetti, L., Chevalier, A., Griffiths, R.-R., Salvatori, T., Lukasiewicz, T., Petersen, P. C., & Berner, J. (2023b). Mathematical capabilities of ChatGPT. arXiv. https://doi.org/10.48550/arXiv.2301.13867
Gíslason, I. (2023). What can mathematics teacher-students learn from dialogue with AI? In Proceedings of the 13^th Congress of the European Society for Research in Mathematics Education. CERME. https://doi.org/10.13140/RG.2.2.10592.05121
Greefrath, G., Kaiser, G., Blum, W., & Borromeo Ferri, R. (2013). Mathematisches Modellieren–Eine Einführung in theoretische und didaktische Hintergründe [Mathematical modeling–An introduction to theoretical and didactic backgrounds]. In R. Borromeo Ferri, G. Greefrath, & G. Kaiser (Eds.), Realitätsbezüge im Mathematikunterricht. Mathematisches Modellieren für Schule und Hochschule: Theoretische und didaktische Hintergründe (pp. 11-37). Springer. https://doi.org/10.1007/978-3-658-01580-0_1
Hattie, J. A. C., & Donoghue, G. M. (2016). Learning strategies: A synthesis and conceptual model. npj Science of Learning, 1, Article 16013. https://doi.org/10.1038/npjscilearn.2016.13
Hattie, J., & Timperley, H. (2007). The power of feedback. Review of Educational Research, 77(1), 81-112. https://doi.org/10.3102/003465430298487
Hegarty, M., Mayer, R. E., & Monk, C. A. (1995). Comprehension of arithmetic word problems: A comparison of successful and unsuccessful problem solvers. Journal of Educational Psychology, 87(1), 18-32. https://doi.org/10.1037/0022-0663.87.1.18
Heimbeck, D., Frese, M., Sonnentag, S., & Keith, N. (2003). Integrating errors into the training process: The function of error management instructions and the role of goal orientation. Personnel Psychology, 56, 362-366. https://doi.org/10.1111/j.1744-6570.2003.tb00153.x
Heinze, A. (2004). Zum Umgang mit Fehlern im Unterrichtsgespräch der Sekundarstufe I. Theoretische Grundlegung, Methode und Ergebnisse einer Videostudie [Dealing with errors in classroom discussions in lower secondary school: Theoretical foundations, methodology, and results of a video study]. Journal für Mathematik-Didaktik, 25(3/4), 221-244. https://doi.org/10.1007/BF03339324
Helfrich-Schkarbanenko, A. (2023). Mathematik und ChatGPT: Ein Rendezvous am Fuße der technologischen Singularität [Mathematics and ChatGPT: A rendezvous at the foot of the technological singularity]. Springer. https://doi.org/10.1007/978-3-662-68209-8
Hembree, R. (1992). Experiments and relational studies in problem solving: A meta-analysis. Journal for Research in Mathematics Education, 23(3), 242-273. https://doi.org/10.2307/749120
Heung, Y. M. E., & Chiu, T. K. F. (2025). How ChatGPT impacts student engagement: A systematic review and meta-analysis study. Computers & Education: Artificial Intelligence, 8, Article 100361. https://doi.org/10.1016/j.caeai.2025.100361
Hiebert, J., Gallimore, R., Garnier, H., Givvin Bogard, K., Hollingsworth, H., Jacobs, J., et al. (2003). Teaching mathematics in seven countries: Results from the TIMSS 1999 video study. U.S. Department of Education, Washington, DC: National Center for Education Statistics.
Huget, J., & Buchholtz, N. (2024). ChatGPT als Reflexionsinstrument zur Förderung von Unterrichtsplanungskompetenzen von Lehramtsstudierenden [ChatGPT as a reflection tool to promote lesson planning skills in student teachers]. In P. Ebers, F. Rösken, B. Barzel, A. Büchter, F. Schacht, & P. Scherer (Eds.), Beiträge zum Mathematikunterricht 2024. 57. Jahrestagung der Gesellschaft für Didaktik der Mathematik (pp. 925-932). WTM. https://doi.org/10.37626/GA9783959872782.0
IBM Corp. (2022). IBM SPSS statistics for windows (version 29). IBM Corp. https://www.ibm.com/products/spss-statistics
Kadel, J., Buschmann, C., Haas, S., Meßner, M. T., & Adl-Amini, K. (2023). Planspiele und simulative Methoden in der Lehrkräftebildung–Ein Literaturüberblick [Simulation games and simulation methods in teacher education–A literature review]. Zeitschrift Für Hochschulentwicklung, 18, 19-39. https://doi.org/10.21240/zfhe/SH-PS/02
Kennedy, M. M., Soyeon, A., & Jinyoung, C. (2008). The value added by teacher education. In M. Cochran-Smith (Ed.), Handbook of research on teacher education: Enduring questions in changing contexts (pp. 1247-1271). Routledge. https://doi.org/10.4324/9780203938690-134
Koehler, M., & Mishra, P. (2009). What is technological pedagogical content knowledge (TPACK)? Contemporary Issues in Technology and Teacher Education, 9(1), 60-70.
Kortenkamp, U., & Dohrmann, C. (2023). Pre-service teacher training with AI: Using ChatGPT discussions to practice teacher-student discourse. In M. Ayalon, B. Koichu, R. Leikin, L. Rubel, & M. Tabach (Eds.), Proceedings of the 46^th Conference of the International Group for the Psychology of Mathematics Education.
Kuckartz, U., & Rädiker, S. (2022). Methoden, Praxis, Computerunterstützung [Methods, practice, computer support]. Beltz Juventa.
Kunter, M., Kleickmann, T., Klusmann, U., & Richter, D. (2011). Die Entwicklung professioneller Kompetenz von Lehrkräften [The development of professional competence of teachers]. In M. Kunter, J. Baumert, W. Blum, U. Klusmann, S. Krauss, & M. Neubrand (Eds.), Professionelle Kompetenz von Lehrkräften: Ergebnisse des Forschungsprogramms COACTIV (pp. 55-68). Waxmann. https://doi.org/10.31244/9783830974338
Leiner, D. J. (2019). SoSci survey (version 3.1.06). soSci. www.soscisurvey.de
Leiss, D., Schukajlow, S., Blum, W., Messner, R., & Pekrun, R. (2010). The role of the situation model in mathematical modelling, task analyses, student competencies, and teacher interventions. Journal für Mathematik-Didaktik, 31(1), 119-141. https://doi.org/10.1007/s13138-010-0006-y
Lenz, K. (2024). Einstellungen von angehenden Grundschullehrkräften zum Einsatz digitaler Werkzeuge im Mathematikunterricht [Attitudes of prospective primary school teachers towards the use of digital tools in mathematics lessons]. In P. Ebers, F. Rösken, B. Barzel, A. Büchter, F. Schacht, & P. Scherer (Eds.), Beiträge zum Mathematikunterricht 2024. 57. Jahrestagung der Gesellschaft für Didaktik der Mathematik (pp. 393-396). WTM. https://doi.org/10.37626/GA9783959872782.0
MAXQDA. (2025). MAXQDA software für qualitative Datenanalyse, 1989-2025 [MAXQDA software for qualitative data analysis, 1989-2025]. MAXQDA. https://www.maxqda.com/
Mercer, N., & Littleton, K. (2007). Dialogue and the development of children’s thinking: A sociocultural approach. Routledge. https://doi.org/10.4324/9780203946657
Meyer, L., Seidel, T., & Prenzel, M. (2006). Wenn Lernsituationen zu Leistungssituationen werden: Untersuchung zur Fehlerkultur in einer Videostudie [When learning situations become performance situations: An investigation into the culture of error in a video study]. Schweizerische Zeitschrift für Bildungswissenschaften, 28, 21-41. https://doi.org/10.24452/sjer.28.1.4717
Oser, F., & Spychiger, M. (2005). Lernen ist schmerzhaft: Zur Theorie des negativen Wissens und zur Praxis der Fehlerkultur [Learning is painful: On the theory of negative knowledge and the practice of a culture of error]. Beltz.
Pantziara, M., Gagatsis, A., & Elia, I. (2009). Using diagrams as tools for the solution of non-routine mathematical problems. Educational Studies in Mathematics, 72(1), 39-60. https://doi.org/10.1007/s10649-009-9181-5
Pólya, G. (2010). Schule des Denkens: Vom Lösen mathematischer Probleme. Sammlung Dalp [School of thinking: On solving mathematical problems. Dalp collection]. Francke.
Riese, J., & Reinhold, P. (2012). Die professionelle Kompetenz angehender Physiklehrkräfte in verschiedenen Ausbildungsformen [The professional competence of prospective physics teachers in various forms of education]. Zeitschrift für Erziehungswissenschaft, 15(1), 111-143.https://doi.org/10.1007/s11618-012-0259-y
Santagata, R. (2005). Practices and beliefs in mistake-handling activities. A video study of Italian and U.S. mathematics lessons. Teaching and Teacher Education, 21(5), 491-508. https://doi.org/10.1016/j.tate.2005.03.004
Scheunpflug, A., Baumert, J., & Kunter, M. (2006). Schwerpunkt: Professionelle Kompetenz von Lehrkräften [Focus: Professional competence of teachers]. Zeitschrift für Erziehungswissenschaft, 9, 465-468. https://doi.org/10.1007/s11618-006-0164-3
Schorcht, S., Baumanns, L., Buchholtz, N., Huget, J., Peters, F., & Pohl, M. (2023). Ask smart to get smart: Mathematische Ausgaben generativer KI-Sprachmodelle verbessern durch gezieltes prompt engineering [Ask smart to get smart: Improving the mathematical output of generative AI language models through targeted prompt engineering]. Mitteilungen Der Gesellschaft Für Didaktik Der Mathematik, 115, 12-23.
Schreiber, C. (2010). Semiotische Prozess-Karten–Chatbasierte Inskriptionen in mathematischen Problemlöseprozessen [Semiotic process maps–Chat-based inscriptions in mathematical problem-solving processes]. Waxmann.
Shulman, L. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14. https://doi.org/10.3102/0013189X015002004
Şimşek, N. (2025). Integration of ChatGPT in mathematical story-focused 5E lesson planning: Teachers and pre-service teachers’ interactions with ChatGPT. Education and Information Technologies, 30(8), 11391-11462. https://doi.org/10.1007/s10639-024-13258-x
Spannagel, C. (2023). Hat ChatGPT eine Zukunft in der Mathematik [Does ChatGPT have a future in mathematics]? Mitteilungen Der Deutschen Mathematiker-Vereinigung, 31(3), 168-172. https://doi.org/10.1515/dmvm-2023-0055
Stahnke, R., & Blömeke, S. (2021). Novice and expert teachers’ situation-specific skills regarding classroom management: What do they perceive, interpret and suggest? Teaching and Teacher Education, 98, Article 103243. https://doi.org/10.1016/j.tate.2020.103243
Steuer, G. (2014). Fehlerklima in der Klasse: Zum Umgang mit Fehlern im Mathematikunterricht [The climate surrounding mistakes in the classroom: How to deal with errors in mathematics lessons]. Springer. https://doi.org/10.1007/978-3-658-05293-5
Steuer, G., Rosentritt-Brunn, G., & Dresel, M. (2013). Dealing with errors in mathematics classrooms. Structure and relevance of perceived error climate. Contemporary Educational Psychology, 38(3), 196-210. https://doi.org/10.1016/j.cedpsych.2013.03.002
Sturm, N. (2018). Problemhaltige Textaufgaben lösen: Einfluss eines Repräsentationstrainings auf den Lösungsprozess von Drittklässlern [Solving problematic word problems: The influence of representation training on the problem-solving process of third graders]. Spektrum Akademischer Verlag. https://doi.org/10.1007/978-3-658-21398-5
Taber, K. S. (2018). The use of Cronbach’s alpha when developing and reporting research instruments in science education. Research in Science Education, 48(6), 1273-1296. https://doi.org/10.1007/s11165-016-9602-2
Terhart, E. (2001). Lehrerberuf und Lehrerbildung: Forschungsbefunde, Problemanalysen, Reformkonzepte. Beltz Pädagogik [The teaching profession and teacher education: Research findings, problem analyses, reform concepts. Beltz pedagogy]. Beltz.
Terhart, E. (2008). Die Lehrerbildung [Teacher training]. In K. S. Cortina (Ed.), Das Bildungswesen in der Bundesrepublik Deutschland: Strukturen und Entwicklungen im Überblick (pp. 745-772). Rowohlt-Taschenbuch-Verlag.
Thurm, D., Klinger, M., Barzel, B., & Rögler, P. (2017). Überzeugungen zum Technologieeinsatz im Mathematikunterricht: Entwicklung eines Messinstruments für Lehramtsstudierende und Lehrkräfte [Beliefs about the use of technology in mathematics education: Development of a measurement instrument for student teachers and teachers]. Mathematica Didactica, 40(1), 19-36. https://doi.org/10.18716/ojs/md/2017.1230
Tulis, M. (2013). Error management behavior in classrooms: Teachers’ responses to student mistakes. Teaching and Teacher Education, 33, 56-68. https://doi.org/10.1016/j.tate.2013.02.003
Venkatesh, V., Morris, M. G., Davis, G. B., & Davis, F. D. (2003). User acceptance of information technology: Toward a unified view. MIS Quarterly, 27(3), 425-478. https://doi.org/10.2307/30036540
Verschaffel, L., Schukajlow, S., Star, J., & van Dooren, W. (2020). Word problems in mathematics education: A survey. ZDM Mathematics Education, 52, 1-16. https://doi.org/10.1007/s11858-020-01130-4
Vicente, S., Verschaffel, L., Sánchez, R., et al. (2022). Arithmetic word problem solving. Analysis of Singaporean and Spanish textbooks. Educational Studies in Mathematics, 111, 375-397. https://doi.org/10.1007/s10649-022-10169-x
Xuan-Quy, D., & Ngoc-Bich, L. (2023). Investigating the effectiveness of ChatGPT in mathematical reasoning and problem solving: Evidence from the Vietnamese national high school graduation examination. ArXiv. Vorab-Onlinepublikation. https://doi.org/10.48550/arXiv.2306.06331
Yanar, A. N., & Ergene, Ö. (2025). Integrating artificial intelligence in education: How pre-service mathematics teachers use ChatGPT for 5E lesson plan design. Journal of Pedagogical Research, 9(2), 158-176. https://doi.org/10.33902/JPR.202533163

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APA

Lenz, K., & Sirock, J. (2026). Training mathematics teachers’ error behavior through ChatGPT-based error situations. International Electronic Journal of Mathematics Education, 21(2), em0873. https://doi.org/10.29333/iejme/18101

Vancouver

Lenz K, Sirock J. Training mathematics teachers’ error behavior through ChatGPT-based error situations. INT ELECT J MATH ED. 2026;21(2):em0873. https://doi.org/10.29333/iejme/18101

AMA

Lenz K, Sirock J. Training mathematics teachers’ error behavior through ChatGPT-based error situations. INT ELECT J MATH ED. 2026;21(2), em0873. https://doi.org/10.29333/iejme/18101

Chicago

Lenz, Katja, and Julia Sirock. "Training mathematics teachers’ error behavior through ChatGPT-based error situations". International Electronic Journal of Mathematics Education 2026 21 no. 2 (2026): em0873. https://doi.org/10.29333/iejme/18101

Harvard

Lenz, K., and Sirock, J. (2026). Training mathematics teachers’ error behavior through ChatGPT-based error situations. International Electronic Journal of Mathematics Education, 21(2), em0873. https://doi.org/10.29333/iejme/18101

MLA

Lenz, Katja et al. "Training mathematics teachers’ error behavior through ChatGPT-based error situations". International Electronic Journal of Mathematics Education, vol. 21, no. 2, 2026, em0873. https://doi.org/10.29333/iejme/18101