The National Council of Teachers of Mathematics (NCTM, 2024) calls for mathematics teachers to actively engage with artificial intelligence (AI) development and application in teaching and stresses the need for continuous adaptation to technological advancements to better prepare students for a future intertwined with AI. ChatGPT is an advanced AI chatbot developed by OpenAI. It is designed to understand and generate human-like text based on the input it receives (OpenAI, 2022). For education purposes, ChatGPT can perform a wide range of tasks in teaching and learning by utilizing deep learning algorithms trained on large data sets. For example, ChatGPT has the potential to provide guidance in problem-solving, generate course materials, and facilitate personalized learning experiences that are tailored to a particular audience or level of expertise (Lo, 2023). However, ChatGPT’s performance in mathematics is unsatisfactory compared to other subjects. Concerns have been raised about including inconsistency in solving mathematical problems (Korkmaz Guler et al., 2024), difficulties with mathematical word problems (Shakarian et al., 2023), providing incorrect reasoning (Urhan et al., 2024), and a failure to address misconceptions (Wardat et al., 2023). In addition, the findings from these studies emphasize the essential role of teachers in guiding students to foster positive students’ perceptions of ChatGPT (Zhuang & Zhang, 2024), critically assess ChatGPT-generated output, facilitate the co-creation of shared knowledge, and link prior knowledge with new insights.
The Standards for Preparing Teachers of Mathematics (AMTE, 2017) emphasized the importance of teacher education programs incorporating practice-based experiences for prospective mathematics teachers. To maximize the power of ChatGPT in a mathematics classroom, teachers must possess some professional and technical understanding of the tool, such as its capabilities and limitations, and appropriately integrate ChatGPT into instructions alongside other teaching strategies. Without proper training, teachers may struggle to leverage the benefits of ChatGPT in the classroom. Therefore, it is critical for mathematics teacher preparation programs to provide opportunities for prospective mathematics teachers to develop the necessary knowledge and skills to utilize ChatGPT effectively for instructional purposes.
ChatGPT-4 includes the customized GPT function to allow users to tailor the AI's responses to specific needs or tasks, enabling personalized interactions and more targeted information retrieval or task execution (OpenAI, 2023). In this paper, we illustrate the application of the customized GPT to simulate potential student responses in a mathematics task, enabling prospective secondary mathematics teachers (PSMTs) to interact with these simulated responses to practice their teacher questioning skills.
Background
The method course is a required course designed to equip PSMTs with the teaching skills to teach mathematics at the middle school and high school levels. Typically, PSMTs enroll in this course prior to Phase II of their student teaching experiences. A cohort of six PSMTs participated in this study, and only two of them had taught a formal math class. One of the primary objectives of the course is to support PSMTs in developing questions that they can ask when they teach ratio concepts in the future. These questions should be able to assess and advance student thinking and better prepare PSMTs to support students in making progress toward the mathematical goals of the lesson (Smith et al., 2017). The “Orange Juice Problem” (OJP, derived from Shell Center for Mathematics Education) was introduced to PSMTs to identify possible misconceptions from students and develop questions that assess and advance students’ thinking accordingly. However, the OJP activity only offered written responses from students, which is more typical when assessing homework assignments. It can be challenging for PSMTs to fully grasp students’ thinking process based solely on their written solutions. In addition, without follow-up interactions with students, it is hard for PSMTs to assess the effectiveness of their questions in achieving the learning objectives.
Use Custom GPT for OJP
In late 2023, OpenAI (2023) released a new feature on the ChatGPT 4.0 platform to allow subscribers to create customized versions of ChatGPT for a specific purpose. Users simply need to follow ChatGPT's guidance to explain their demands with text-based input to create a custom GPT. A published custom GPT can be shared within the GPT community for other uses to access. In the previous OJP activities, many PSMTs reported it was challenging to identify a starting point for accessing the student thinking process through questioning due to their limited teaching experiences. Recognizing this challenge, we saw the potential to create a custom GPT that simulates student-teacher interactions within the OJP context to help PSMTs practice their questioning skills.
After several rounds of testing with custom GPT, we developed a Student GPT that could simulate a middle school student who struggles with mathematics. We provided Student GPT with three categories of common misconceptions and limited the situation to the OJP context. Below is a summary of inputs based on our interactions with custom GPT during the creation process of Student GPT.
As a middle school student character struggling with mathematics, this GPT embodies the common misunderstandings middle schoolers face with ratio concepts, proportional relationships, and mathematical errors. It focuses on three areas of confusion: 1. Mixing up additive and multiplicative relationships. 2. Not understanding how changes in one quantity affect another. 3. Relying solely on one method to solve ratios and proportions. This GPT aims to help educators recognize and address these learning challenges by presenting questions and answers that showcase these misconceptions. It simulates the perspective of a student who is curious but often confuses basic mathematical concepts.
The Student GPT allows PSMTs to role-play as teachers, to interact with a simulated middle school student, and to practice their questioning skills in a dynamic environment similar to an actual classroom, which is challenging to achieve in a traditional method course. In addition, it provides customized experiences for each PSMT in the method course to practice their teacher questioning skills based on their prior knowledge and teaching experiences. In the method course, PSMTs first worked in pairs to create assessing and advancing questions respectively, based on four provided student solutions (Smith et al., 2017). Then, PSMTs were guided to work individually to interact with the Student GPT. Based on the responses of the Student GPT, PSMTs needed to ask follow-up teacher questions to guide the Student GPT in working toward the correct answer to the problem. Figure 1 shows the part of the chat history between PSMTs and the Student GPT.
Figure 1
Chat History Between PSMTs and the Student GPT. 
Note. Anonymous represents two different PSMTs.
Incorporating AI into the Mathematics Teacher Preparation Programs
As AMTE (2017) recommended, mathematics teacher preparation programs should offer ongoing feedback to prospective teachers in assessing their mathematics teaching practice. According to our observation and PSMTs’ feedback, the Student GPT was useful in demonstrating a mathematics student’s thinking process and integrating possible mathematics misconceptions within its responses. For PSMTs with limited teaching experiences, the Student GPT provided ongoing real-time text-based communications that enabled them to have simulated interactions with a “real” middle school student. This allowed PSMTs to practice responding to common student misconceptions and refine their questioning techniques in a safe, controlled environment. The immediate feedback and follow-up questions generated by Student GPT allowed PSMTs to check the effects of their questions and adjust the questioning techniques accordingly.
However, we also noticed that Student GPT requires further improvement and refinement for enhanced performance. For example, PSMTs in the method course reported that Student GPT often generated lengthy and wordy responses, unlike those of a middle schooler. On one hand, this might be due to the nature of the English language and the need for related training data for the model. On the other hand, the lengthy responses could have resulted from PSMTs' ineffective questions. For example, one PSMT conducted four rounds of interactions with Student GPT to guide it in finding the common denominator but still failed. In addition, it would be beneficial if the current version of Student GPT could encompass a broader range of mathematics problems across different grade levels and content areas. Despite their limitations, AI tools such as the Student GPT offer valuable opportunities for mathematics teacher preparation programs to explore their impact on teaching and learning, helping PSMTs to engage in authentic teaching simulations, develop their pedagogical content knowledge, and reflect on strategies for addressing student misconceptions in mathematics. (AMTE 2017; NCTM, 2024).
References
Association of Mathematics Teacher Educators. (2017). Standards for Preparing Teachers of Mathematics. Available online at: https://amte.net/standards
Bill, V., & Smith, M. S. (2008). Characteristics of Assessing and Advancing Questions. University of Pittsburgh: Institute for Learning.
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National Council of Teachers of Mathematics (2024). Artificial Intelligence and Mathematics Teaching.https://www.nctm.org/uploadedFiles/Standards_and_Positions/Position_Stat...
OpenAI. (2022). Introducing ChatGPT. https://openai.com/blog/chatgpt
OpenAI. (2023). ChatGPT: Optimizing language models for dialogue. OpenAI. https://openai.com/blog/chatgpt/
Orange Juice Problem Activity. Shell Centre for Mathematical Education. (n.d.). https://www.mathshell.org/
Shakarian, P., Koyyalamudi, A., Ngu, N., & Mareedu, L. (2023). An Independent Evaluation of ChatGPT on Mathematical Word Problems (MWP). arXiv preprint arXiv:2302.13814. https://doi.org/https://doi.org/10.48550/arXiv.2302.13814
Smith, M. S., Steele, M. D., & Raith, M. L. (2017). Taking action: Implementing effective mathematics teaching practices in grades 6-8. National Council of Teachers of Mathematics Reston, VA.
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