\begin{thebibliography}{22}
\providecommand{\natexlab}[1]{#1}

\bibitem[{Cobbe et~al.(2021)Cobbe, Kosaraju, Bavarian, Chen, Jun, Kaiser, Plappert, Tworek, Hilton, Nakano, Hesse, and Schulman}]{cobbe2021gsm8k}
Karl Cobbe, Vineet Kosaraju, Mohammad Bavarian, Mark Chen, Heewoo Jun, Lukasz Kaiser, Matthias Plappert, Jerry Tworek, Jacob Hilton, Reiichiro Nakano, Christopher Hesse, and John Schulman. 2021.
\newblock Training verifiers to solve math word problems.
\newblock \emph{arXiv preprint arXiv:2110.14168}.

\bibitem[{Daheim et~al.(2024)Daheim, Macina, Kapur, Gurevych, and Sachan}]{daheim-etal-2024-stepwise}
Nico Daheim, Jakub Macina, Manu Kapur, Iryna Gurevych, and Mrinmaya Sachan. 2024.
\newblock \href {https://doi.org/10.18653/v1/2024.emnlp-main.478} {Stepwise verification and remediation of student reasoning errors with large language model tutors}.
\newblock In \emph{Proceedings of the 2024 Conference on Empirical Methods in Natural Language Processing}, pages 8386--8411, Miami, Florida, USA. Association for Computational Linguistics.

\bibitem[{Demszky et~al.(2021)Demszky, Liu, Mancenido, Cohen, Hill, Jurafsky, and Hashimoto}]{demszky-etal-2021-measuring}
Dorottya Demszky, Jing Liu, Zid Mancenido, Julie Cohen, Heather Hill, Dan Jurafsky, and Tatsunori Hashimoto. 2021.
\newblock \href {https://doi.org/10.18653/v1/2021.acl-long.130} {Measuring conversational uptake: A case study on student-teacher interactions}.
\newblock In \emph{Proceedings of the 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing (Volume 1: Long Papers)}, pages 1638--1653, Online. Association for Computational Linguistics.

\bibitem[{Dettmers et~al.(2023)Dettmers, Pagnoni, Holtzman, and Zettlemoyer}]{dettmers2023qlora}
Tim Dettmers, Artidoro Pagnoni, Ari Holtzman, and Luke Zettlemoyer. 2023.
\newblock Qlora: Efficient finetuning of quantized llms.
\newblock \emph{Advances in neural information processing systems}, 36:10088--10115.

\bibitem[{Hendrycks et~al.(2021{\natexlab{a}})Hendrycks, Burns, Basart, Zou, Mazeika, Song, and Steinhardt}]{hendrycks2021mmlu}
Dan Hendrycks, Collin Burns, Steven Basart, Andy Zou, Mantas Mazeika, Dawn Song, and Jacob Steinhardt. 2021{\natexlab{a}}.
\newblock \href {https://arxiv.org/abs/2009.03300} {Measuring massive multitask language understanding}.
\newblock In \emph{International Conference on Learning Representations ({ICLR})}.

\bibitem[{Hendrycks et~al.(2021{\natexlab{b}})Hendrycks, Burns, Kadavath, Arora, Basart, Tang, Song, and Steinhardt}]{hendrycks2021math}
Dan Hendrycks, Collin Burns, Saurav Kadavath, Akul Arora, Steven Basart, Eric Tang, Dawn Song, and Jacob Steinhardt. 2021{\natexlab{b}}.
\newblock \href {https://arxiv.org/abs/2103.03874} {Measuring mathematical problem solving with the {MATH} dataset}.
\newblock In \emph{Advances in Neural Information Processing Systems (NeurIPS) Datasets and Benchmarks Track}.

\bibitem[{Hu et~al.(2021)Hu, Shen, Wallis, Allen-Zhu, Li, Wang, and Chen}]{hu2021lora}
Edward~J. Hu, Yelong Shen, Phillip Wallis, Zeyuan Allen-Zhu, Yuanzhi Li, Weizhu Wang, and Zichao Chen. 2021.
\newblock \href {https://arxiv.org/abs/2106.09685} {Lora: Low-rank adaptation of large language models}.
\newblock \emph{arXiv preprint arXiv:2106.09685}.

\bibitem[{Jiang et~al.(2023)Jiang, Sablayrolles, Mensch, Bamford, Chaplot, de~las Casas, Bressand, Lengyel, Lample, Saulnier, Renard-Lavaud, Lachaux, Stock, Le~Scao, Lavril, Wang, Lacroix, and El~Sayed}]{jiang2023mistral7b}
Albert~Q. Jiang, Alexandre Sablayrolles, Arthur Mensch, Chris Bamford, Devendra~Singh Chaplot, Diego de~las Casas, Florian Bressand, Gianna Lengyel, Guillaume Lample, Lucile Saulnier, L\'{e}lio Renard-Lavaud, Marie-Anne Lachaux, Pierre Stock, Teven Le~Scao, Thibaut Lavril, Thomas Wang, Timoth\'{e}e Lacroix, and William El~Sayed. 2023.
\newblock {Mistral 7B}.
\newblock \emph{arXiv preprint arXiv:2310.06825}.

\bibitem[{Kochmar et~al.(2025)Kochmar, Maurya, Petukhova, Srivatsa, Tack, and Vasselli}]{kochmar2025findings}
Ekaterina Kochmar, Kaushal~Kumar Maurya, Kseniia Petukhova, KV~Aditya Srivatsa, Ana{\"i}s Tack, and Justin Vasselli. 2025.
\newblock Findings of the {BEA} 2025 shared task on pedagogical ability assessment of {AI}-powered tutors.
\newblock In \emph{Proceedings of the 20th Workshop on Innovative Use of NLP for Building Educational Applications}.

\bibitem[{Lakshminarayanan et~al.(2017)Lakshminarayanan, Pritzel, and Blundell}]{lakshminarayanan2017deep}
Balaji Lakshminarayanan, Alexander Pritzel, and Charles Blundell. 2017.
\newblock Simple and scalable predictive uncertainty estimation using deep ensembles.
\newblock In \emph{Advances in Neural Information Processing Systems 30 (NeurIPS 2017)}, pages 6402--6413.

\bibitem[{Macina et~al.(2023)Macina, Daheim, Chowdhury, Sinha, Kapur, Gurevych, and Sachan}]{macina-etal-2023-mathdial}
Jakub Macina, Nico Daheim, Sankalan Chowdhury, Tanmay Sinha, Manu Kapur, Iryna Gurevych, and Mrinmaya Sachan. 2023.
\newblock \href {https://doi.org/10.18653/v1/2023.findings-emnlp.372} {{M}ath{D}ial: A dialogue tutoring dataset with rich pedagogical properties grounded in math reasoning problems}.
\newblock In \emph{Findings of the Association for Computational Linguistics: EMNLP 2023}, pages 5602--5621, Singapore. Association for Computational Linguistics.

\bibitem[{Maurya et~al.(2025)Maurya, Srivatsa, Petukhova, and Kochmar}]{maurya-etal-2025-unifying}
Kaushal~Kumar Maurya, Kv~Aditya Srivatsa, Kseniia Petukhova, and Ekaterina Kochmar. 2025.
\newblock \href {https://aclanthology.org/2025.naacl-long.57/} {Unifying {AI} tutor evaluation: An evaluation taxonomy for pedagogical ability assessment of {LLM}-powered {AI} tutors}.
\newblock In \emph{Proceedings of the 2025 Conference of the Nations of the Americas Chapter of the Association for Computational Linguistics: Human Language Technologies (Volume 1: Long Papers)}, pages 1234--1251, Albuquerque, New Mexico. Association for Computational Linguistics.

\bibitem[{{Mistral AI Team}(2024)}]{mistral2024mathstral}
{Mistral AI Team}. 2024.
\newblock Mathstral~7b~v0.1: A math reasoning and scientific discovery model.
\newblock \url{https://mistral.ai/news/mathstral}.

\bibitem[{Nye et~al.(2014)Nye, Graesser, and Hu}]{nye-etal-2014-autotutor}
Benjamin~D. Nye, Arthur~C. Graesser, and Xiangen Hu. 2014.
\newblock \href {https://doi.org/10.1007/s40593-014-0029-5} {Autotutor and family: A review of 17 years of natural language tutoring}.
\newblock \emph{International Journal of Artificial Intelligence in Education}, 24(4):427--469.

\bibitem[{{OpenAI}(2022)}]{openai2022chatgpt}
{OpenAI}. 2022.
\newblock Chatgpt: Optimizing language models for dialogue.
\newblock \url{https://openai.com/blog/chatgpt}.

\bibitem[{{OpenAI}(2023)}]{openai2023gpt4}
{OpenAI}. 2023.
\newblock {GPT-4} technical report.
\newblock \emph{arXiv preprint arXiv:2303.08774}.

\bibitem[{Tack and Piech(2022)}]{tack-piech-2022-teacher}
Ana{\"i}s Tack and Chris Piech. 2022.
\newblock \href {https://doi.org/10.5281/zenodo.6853187} {The {AI} teacher test: Measuring the pedagogical ability of blender and {GPT-3} in educational dialogues}.
\newblock In \emph{Proceedings of the 15th International Conference on Educational Data Mining}, pages 522--529, Durham, United Kingdom. International Educational Data Mining Society.

\bibitem[{Touvron et~al.(2023{\natexlab{a}})Touvron, Lavril, Izacard, Martinet, Lachaux, Lacroix, Rozi\`ere, Goyal, Hambro, Azhar, Rodriguez, Joulin, Grave, and Lample}]{touvron2023llama}
Hugo Touvron, Thibaut Lavril, Gautier Izacard, Xavier Martinet, Marie-Anne Lachaux, Timoth\'{e}e Lacroix, Baptiste Rozi\`ere, Naman Goyal, Eric Hambro, Faisal Azhar, Aurelien Rodriguez, Armand Joulin, Edouard Grave, and Guillaume Lample. 2023{\natexlab{a}}.
\newblock {LLaMA}: Open and efficient foundation language models.
\newblock \emph{arXiv preprint arXiv:2302.13971}.

\bibitem[{Touvron et~al.(2023{\natexlab{b}})}]{touvron2023llama2}
Hugo Touvron and 1 others. 2023{\natexlab{b}}.
\newblock {Llama 2}: Open foundation and fine-tuned chat models.
\newblock \emph{arXiv preprint arXiv:2307.09288}.

\bibitem[{Wang et~al.(2024)Wang, Zhang, Robinson, Loeb, and Demszky}]{wang-etal-2024-bridging}
Rose Wang, Qingyang Zhang, Carly Robinson, Susanna Loeb, and Dorottya Demszky. 2024.
\newblock \href {https://doi.org/10.18653/v1/2024.naacl-long.120} {Bridging the novice-expert gap via models of decision-making: A case study on remediating math mistakes}.
\newblock In \emph{Proceedings of the 2024 Conference of the North American Chapter of the Association for Computational Linguistics}, pages 2174--2199, Mexico City, Mexico. Association for Computational Linguistics.

\bibitem[{Xu et~al.(2023)Xu, Xie, Qin, Tao, and Wang}]{xu2023parameterefficient}
Lingling Xu, Haoran Xie, Si-Zhao~Joe Qin, Xiaohui Tao, and Fu~Lee Wang. 2023.
\newblock Parameter-efficient fine-tuning methods for pretrained language models: A critical review and assessment.
\newblock \emph{arXiv preprint arXiv:2312.12148}.

\bibitem[{Zhou et~al.(2023)Zhou, Cai, Ye, Zhan, and Liu}]{zhou2023revisiting}
Da-Wei Zhou, Zi-Wen Cai, Han-Jia Ye, De-Chuan Zhan, and Ziwei Liu. 2023.
\newblock Revisiting class-incremental learning with pre-trained models: Generalizability and adaptivity are all you need.
\newblock \emph{arXiv preprint arXiv:2303.07338}.

\end{thebibliography}
