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Exploring the Integration of Artificial Intelligence in Math Education: Preservice Teachers' Experiences and Reflections on Problem-Posing Activities with ChatGPT

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Title: Exploring the Integration of Artificial Intelligence in Math Education: Preservice Teachers' Experiences and Reflections on Problem-Posing Activities with ChatGPT
Language: English
Authors: Young Rae Kim (ORCID 0000-0001-9518-0021), Mi Sun Park (ORCID 0000-0002-7564-9133), Eunmi Joung
Source: School Science and Mathematics. 2026 126(1):9-23.
Availability: Wiley. Available from: John Wiley & Sons, Inc. 111 River Street, Hoboken, NJ 07030. Tel: 800-835-6770; e-mail: cs-journals@wiley.com; Web site: https://www.wiley.com/en-us
Peer Reviewed: Y
Page Count: 15
Publication Date: 2026
Document Type: Journal Articles
Reports - Research
Education Level: Higher Education
Postsecondary Education
Descriptors: Artificial Intelligence, Technology Uses in Education, Technology Integration, Mathematics Education, Preservice Teacher Education, Preservice Teachers, Reflective Teaching, Problem Solving, Error Patterns, Error Correction, Recognition (Psychology), Metacognition
DOI: 10.1111/ssm.18336
ISSN: 0036-6803
1949-8594
Abstract: This study addresses the need for research that incorporates educational perspectives and theories to understand the impact of Artificial Intelligence (AI) on learning and teaching. Utilizing AI-integrated mathematical problem-posing (AIM) activities and the AI-powered scaffolding (AIS) strategy, the research investigated preservice teachers' (PTs') experiences with AI and their capacity for error recognition and correction in problems posed by ChatGPT. The findings reveal that while the PTs excelled at verifying error-free problems, they struggled significantly with identifying and correcting errors, indicating a gap in their instructional preparedness. The study demonstrates that AIM activities are effective tools for assessing and developing PTs' error recognition and correction skills. Additionally, AIM activities support the transfer of mathematical knowledge to pedagogical and instructional practices, contributing to PTs' growth as adaptable educators. The research highlights the need to integrate AI-based activities into PT training to build robust mathematical knowledge and teaching skills. Focusing on learning, pedagogy, and the human aspects of technology use, AIM activities and the AIS strategy enable PTs to engage critically with AI outputs and enhance their metacognitive skills. These insights emphasize the importance of incorporating AI-integrated methods into teacher preparation programs to better equip future educators for an AI-driven educational landscape.
Abstractor: As Provided
Entry Date: 2026
Accession Number: EJ1495622
Database: ERIC
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  Value: <anid>AN0191298893;ssm01feb.26;2026Feb04.04:59;v2.2.500</anid> <title id="AN0191298893-1">Exploring the integration of artificial intelligence in math education: Preservice Teachers' experiences and reflections on problem‐posing activities with ChatGPT </title> <sbt id="AN0191298893-2">INTRODUCTION</sbt> <p>This study addresses the need for research that incorporates educational perspectives and theories to understand the impact of Artificial Intelligence (AI) on learning and teaching. Utilizing AI‐integrated mathematical problem‐posing (AIM) activities and the AI‐powered scaffolding (AIS) strategy, the research investigated preservice teachers' (PTs') experiences with AI and their capacity for error recognition and correction in problems posed by ChatGPT. The findings reveal that while the PTs excelled at verifying error‐free problems, they struggled significantly with identifying and correcting errors, indicating a gap in their instructional preparedness. The study demonstrates that AIM activities are effective tools for assessing and developing PTs' error recognition and correction skills. Additionally, AIM activities support the transfer of mathematical knowledge to pedagogical and instructional practices, contributing to PTs' growth as adaptable educators. The research highlights the need to integrate AI‐based activities into PT training to build robust mathematical knowledge and teaching skills. Focusing on learning, pedagogy, and the human aspects of technology use, AIM activities and the AIS strategy enable PTs to engage critically with AI outputs and enhance their metacognitive skills. These insights emphasize the importance of incorporating AI‐integrated methods into teacher preparation programs to better equip future educators for an AI‐driven educational landscape.</p> <p>The recent position statement by the National Council of Teachers of Mathematics (NCTM, [<reflink idref="bib26" id="ref1">26</reflink>]) underscores that artificial intelligence (AI)‐based technological tools complement rather than replace mathematics teachers, emphasizing the continued importance of teachers possessing robust mathematics knowledge and effective teaching skills to leverage AI effectively. It also emphasizes the importance of students maintaining a critical perspective on AI‐powered findings due to the limitations of current generative AI technologies, such as ChatGPT and Copilot, which may produce errors and hallucinations—false or fabricated information, particularly regarding the potential biases ingrained in datasets used for training. Consequently, AI‐based technological tools have a positive impact on bringing about "evolutionary‐not revolutionary‐change" in mathematics instruction by encouraging teachers to develop assessments and instructional methods that integrate this critical mindset (NCTM, [<reflink idref="bib26" id="ref2">26</reflink>], p. 2). Recognizing this, teacher preparation programs need to provide multiple opportunities for preservice teachers (PTs) to engage in evaluating the use of AI‐based technological tools in mathematics education to best prepare their students for an AI‐powered future.</p> <p>Problem posing has been steadily recognized in mathematics education as a powerful means to promote students' mathematical abilities, including conceptual understanding, creativity, problem‐solving skills, mathematical dispositions, and achievements in mathematics (e.g., Lee, [<reflink idref="bib21" id="ref3">21</reflink>]; Silver, [<reflink idref="bib34" id="ref4">34</reflink>]). However, problem posing can be acknowledged as a challenging and novel task, distinct from problem‐solving. Therefore, providing scaffolds to students (Wang et al., [<reflink idref="bib39" id="ref5">39</reflink>]) is crucial, which includes strategies such as interaction scaffolding, which involves peers or teachers (e.g., Bonotto, [<reflink idref="bib3" id="ref6">3</reflink>]; Walkington & Hayata, [<reflink idref="bib38" id="ref7">38</reflink>]). We expect that an AI‐powered scaffolding (AIS) strategy for supporting problem posing—providing students with scaffolds by integrating AI‐based technological tools into problem‐posing activities—could have a positive impact on the effectiveness of problem posing in mathematics education.</p> <p>Addressing the need for PTs to engage in evaluating the use of AI‐based technological tools and to provide their future students with meaningful scaffolding for mathematics learning, this study investigated the experiences of PTs in AI‐integrated mathematical problem‐posing (AIM) activities using ChatGPT. In particular, we were interested in examining the extent to which these AI‐integrated activities might facilitate the transfer of knowledge from mathematics content knowledge to mathematics pedagogical and instructional practice knowledge. This approach also provides mathematics educators and teacher educators with valuable insights into how to integrate AI to enhance mathematics teaching and learning. This study is guided by the following research questions:</p> <p></p> <ulist> <item> To what extent do PTs verify the correctness of problems posed by ChatGPT in AIM activities?</item> <p></p> <item> What are their experiences using ChatGPT as an instructional tool within the AIM activities and the AIS strategy for supporting problem posing in teaching and learning mathematics?</item> </ulist> <hd id="AN0191298893-3">LITERATURE REVIEW</hd> <p></p> <hd id="AN0191298893-4">AI in mathematics teaching and learning</hd> <p>AI applications in education are gaining popularity and becoming an important part of mathematics education, just as other technologies are essential for effective teaching and learning of mathematics (e.g., NCTM, [<reflink idref="bib26" id="ref8">26</reflink>]). Research shows that AI has been used in various ways in mathematics education and can provide resources for students to improve mathematics learning by fostering conceptual understanding, boosting student achievement, enhancing creative thinking skills, and developing problem‐solving abilities through tailored learning experiences, precise feedback, and greater engagement (Hwang, [<reflink idref="bib12" id="ref9">12</reflink>]; Mohamed et al., [<reflink idref="bib25" id="ref10">25</reflink>]). In addition, AI applications have significant potential to support educators and administrators by creating intelligent student support systems and adaptive and personalized learning environments, managing large student populations, reducing administrative burdens, and allowing teachers to focus more on empathic human teaching (Zawacki‐Richter et al., [<reflink idref="bib42" id="ref11">42</reflink>]).</p> <p>For example, Wardat et al. ([<reflink idref="bib40" id="ref12">40</reflink>]) explore ChatGPT for teaching mathematics, finding it beneficial for instant feedback but raising accuracy concerns. AI enhances students' procedural knowledge with step‐by‐step problems and systematic tasks, while multimedia explanations and interactive abilities improve conceptual understanding (Jančařík et al., [<reflink idref="bib14" id="ref13">14</reflink>]; Mohamed et al., [<reflink idref="bib25" id="ref14">25</reflink>]). Mohamed et al.'s ([<reflink idref="bib25" id="ref15">25</reflink>]) systematic review of studies published between 2017 and 2021 shows AI's positive impact on mathematics education, making learning more exciting, creative, and effective through various approaches, including intelligent tutoring, integrated systems, machine learning models, comprehensive approaches, and robotics, which is the most used.</p> <p>Despite its potential, AI's integration into education faces various implementation challenges. While AI can handle complex tasks beyond human capability, it generates concerns about potentially replacing human roles (Mohamed et al., [<reflink idref="bib25" id="ref16">25</reflink>]), contributing to the public perception of AI risks (Neri & Cozman, [<reflink idref="bib27" id="ref17">27</reflink>]), which often include worries about machines taking over human roles. Research highlights ethical concerns and the need for critical reflection on AI's pedagogical and ethical implications. Issues like educational surveillance and privacy are often overlooked (e.g., Mohamed et al., [<reflink idref="bib25" id="ref18">25</reflink>]; Zawacki‐Richter et al., [<reflink idref="bib42" id="ref19">42</reflink>]). For example, Zawacki‐Richter et al. ([<reflink idref="bib42" id="ref20">42</reflink>]) highlight concerns about China's AI classroom face recognition systems that monitor student participation and expressions, raising concerns about educational surveillance. Research also concludes that comprehensive AI approaches, despite their effective impact on mathematics learning and teaching, raise serious issues of privacy and data protection due to the vast amounts of data, including confidential information about students and faculty, that they require (Mohamed et al., [<reflink idref="bib25" id="ref21">25</reflink>]; Zawacki‐Richter et al., [<reflink idref="bib42" id="ref22">42</reflink>]). Additionally, AI's integration into education and its implementation continue to pose difficulties for academics and practitioners due to limited connections with theoretical pedagogical views and the complexity of replicating human intelligence in educational systems, with many studies focusing on data analysis and model development rather than advancing pedagogical and psychological theories. Therefore, research studies highlight the necessity for further research that incorporates educational perspectives and theories to comprehend the impact of AI on learning and teaching (Bartolomé et al., [<reflink idref="bib1" id="ref23">1</reflink>]; Mohamed et al., [<reflink idref="bib25" id="ref24">25</reflink>]; Zawacki‐Richter et al., [<reflink idref="bib42" id="ref25">42</reflink>]).</p> <p>Educators now recognize AI's benefits, requiring comprehensive training for effective curriculum integration (Wardat et al., [<reflink idref="bib40" id="ref26">40</reflink>]). Cope et al. ([<reflink idref="bib7" id="ref27">7</reflink>]) stress that AI will never replace educators, a view supported by the recent NCTM ([<reflink idref="bib26" id="ref28">26</reflink>]) position statement, which asserts that AI‐based tools "do not replace the need to teach math or problem solving" (p. 2). The statement also emphasizes the need for teachers to develop strong mathematics knowledge and effective teaching skills essential for utilizing AI effectively. It is vital to adopt an ethics of care prioritizing learning, pedagogy, and the human aspects of technology use, and to remember that AI systems require human oversight and can make errors (Prinsloo, [<reflink idref="bib29" id="ref29">29</reflink>]; Zawacki‐Richter et al., [<reflink idref="bib42" id="ref30">42</reflink>]). Educators should stress the importance of maintaining a critical perspective on AI outputs, as current generative AI technologies such as ChatGPT and Copilot can produce errors, hallucinations, and reflect biases from training datasets. As a result, AI‐based tools can foster evolutionary change in mathematics education by encouraging teachers to develop instructional and assessment methods for students to incorporate a critical mindset (NCTM, [<reflink idref="bib26" id="ref31">26</reflink>]). Recently, the U.S. Department of Education's ([<reflink idref="bib37" id="ref32">37</reflink>]) guidelines present five key recommendations—education values, evidence‐based impact, equity, safety, and transparency—that should guide the development of safe, effective, and equitable AI tools for education, while aligning with federal policies for responsible AI use.</p> <p>In this study, we examined AIM activities—a novel, pedagogically meaningful way of integrating current generative AI technologies, such as ChatGPT and Copilot, into a well‐researched instructional strategy, namely mathematical problem posing—rather than just focusing on the technology itself and relying solely on data and algorithms for educational guidance, as cautioned by Selwyn ([<reflink idref="bib31" id="ref33">31</reflink>]). AIM activities are expected to be used as instructional and assessment methods that integrate critical thinking skills essential for effective mathematics learning and teaching. This approach allows for the use of AI in an educationally valuable way, prioritizing learning, pedagogy, and the human aspects of AI use within regular classroom activities. The following section will articulate the potential effectiveness of AIM activities utilizing the AIS strategy with reference to educational perspectives and the underlying theories.</p> <hd id="AN0191298893-5">Problem posing in mathematics teaching and learning</hd> <p>Problem posing has increasingly been highlighted alongside problem‐solving as a mutually supportive skill in mathematics education (e.g., Cankoy & Özder, [<reflink idref="bib5" id="ref34">5</reflink>]; Gonzales, [<reflink idref="bib10" id="ref35">10</reflink>]). Engaging in problem‐posing activities enhances students' mathematical attitudes and achievement, much like problem‐solving activities (Wang et al., [<reflink idref="bib39" id="ref36">39</reflink>]). This study adopts Silver's ([<reflink idref="bib33" id="ref37">33</reflink>]) definition of problem posing—"both the generation of new problems and the reformulation of given problems," occurring "before, during, or after the solution of a problem" (p. 19)—as it is a prominent and widely referenced definition (Baumanns & Rott, [<reflink idref="bib2" id="ref38">2</reflink>]) that also aligns with the study's purposes. Thus, the AIM activities used in this study involve an entire process of posing problems and consecutive problem‐solving.</p> <p>Problem posing, often discussed alongside problem‐solving, offers distinct advantages in mathematics education. Research shows it enhances students' conceptual understanding more than problem‐solving and involves a lower cognitive load, facilitating learning with reduced cognitive burden (Retnowati et al., [<reflink idref="bib30" id="ref39">30</reflink>]; Sweller et al., [<reflink idref="bib35" id="ref40">35</reflink>]). Additionally, problem posing better prepares students for learning from subsequent instruction for knowledge transfer (Kapur, [<reflink idref="bib15" id="ref41">15</reflink>]) and improves their ability to comprehend, communicate, and connect mathematical concepts (Dickerson, [<reflink idref="bib9" id="ref42">9</reflink>]). The effects of problem posing may stem from its ability to enhance metacognitive skills by encouraging self‐monitoring and self‐regulation, which helps students pose problems correctly (Brown & Walter, [<reflink idref="bib4" id="ref43">4</reflink>]). It may also improve conceptual understanding by linking real‐world scenarios to mathematical concepts within problems (Brown & Walter, [<reflink idref="bib4" id="ref44">4</reflink>]; Chang et al., [<reflink idref="bib6" id="ref45">6</reflink>]). This process can help students organize their thoughts and connect to mathematical concepts, deepening conceptual understanding (Baumanns & Rott, [<reflink idref="bib2" id="ref46">2</reflink>]; Chang et al., [<reflink idref="bib6" id="ref47">6</reflink>]). It also enables mathematics educators to use problem posing as a formative assessment tool to measure students' conceptual progress (e.g., Silver, [<reflink idref="bib34" id="ref48">34</reflink>]; Wang et al., [<reflink idref="bib39" id="ref49">39</reflink>]).</p> <p>Despite its effectiveness, problem posing has received relatively less attention in mathematics education practice and research compared to problem‐solving. This may be because problem posing is seen as a challenging and novel task, distinct from problem‐solving (e.g., Bonotto, [<reflink idref="bib3" id="ref50">3</reflink>]; Wang et al., [<reflink idref="bib39" id="ref51">39</reflink>]). Research highlights several areas needing further exploration: the relationship between problem posing and mathematical content knowledge, the impact of educational technology, and scaffolding strategies to improve its effectiveness, especially in higher education, with more quantitative research in teaching, teacher education, and educational technology (Lee, [<reflink idref="bib21" id="ref52">21</reflink>]; Wang et al., [<reflink idref="bib39" id="ref53">39</reflink>]). Lee ([<reflink idref="bib21" id="ref54">21</reflink>]) also recommends further research on how students pose problems when given an answer (e.g., posing a problem where the answer is 2/3) or calculation (e.g., posing a problem that could be solved through the computation of 1/2 + 2/3).</p> <hd id="AN0191298893-6">AIS strategy for supporting mathematical problem posing</hd> <p>Addressing the need for further research on the topics mentioned above, this study examined the integration of AI‐based technological tools that provide students with scaffolding in traditional mathematical problem‐posing activities conducted in regular classrooms. This strategy prioritizes learning, pedagogy, and the human aspects of AI use, rather than focusing solely on the AI application itself. It also incorporates educational perspectives and theories to understand the impact of AI on learning and teaching mathematics, as articulated below.</p> <hd id="AN0191298893-7">Scaffolding strategy to improve the effectiveness of mathematical problem posing</hd> <p>Due to the perceived complexity and novelty of problem posing, providing scaffolds to students is crucial (Wang et al., [<reflink idref="bib39" id="ref55">39</reflink>]). Strategies such as interaction scaffolding, involving peers (e.g., Bonotto, [<reflink idref="bib3" id="ref56">3</reflink>]; Kontorovich et al., [<reflink idref="bib20" id="ref57">20</reflink>]) or teachers (Kitchings, [<reflink idref="bib19" id="ref58">19</reflink>]), are representative examples. This study proposes that an AIS strategy for supporting mathematical problem posing, which is a previously unexplored scaffolding strategy in the existing literature, could be key to enhancing the effectiveness of problem posing for learning and teaching mathematics. We expect that such an AIS strategy could improve effectiveness by reducing students' cognitive burden when creating real‐world problem scenarios with AI assistance, making problem posing a more engaging activity, and facilitating learning through connections between mathematics, real‐world situations, and social activities (Sweller et al., [<reflink idref="bib35" id="ref59">35</reflink>]).</p> <hd id="AN0191298893-8">Leveraging AI limitations to foster metacognitive engagement</hd> <p>This study leverages the limitations of current generative AI tools like ChatGPT and Copilot—specifically, their tendency to produce errors and hallucinations—to engage students in metacognitive activities. Kim et al. ([<reflink idref="bib18" id="ref60">18</reflink>]) identified three metacognitive triggers at multiple levels—individual, social, and environmental: individual self‐reflection, social interactions with peers or teachers, and learning environments such as classroom activities and technology use. This theoretical model distinguishes cognitive activities ("thinking with" cognitive components) from metacognitive activities ("thinking about" cognitive components) (e.g., Lesh et al., [<reflink idref="bib22" id="ref61">22</reflink>]). We expect that AIM activities could catalyze students' metacognitive activities at the environmental level by encouraging critical evaluation of AI outputs, which often include errors and hallucinations. This will prompt consistent self‐monitoring and self‐regulation of their cognitive processes during problem posing, ultimately empowering their learning and deepening their conceptual understanding.</p> <hd id="AN0191298893-9">Theoretical frameworks for teacher preparation</hd> <p>This study is grounded in the intersection of two theoretical frameworks: Professional Noticing and Technological Pedagogical Content Knowledge (TPACK). The framework of Professional Noticing (Jacobs et al., [<reflink idref="bib13" id="ref62">13</reflink>]) emphasizes teachers' development of a set of three interrelated skills: attending to student strategies, interpreting student understanding, and deciding how to respond pedagogically. This framework is especially pertinent for examining PTs' ability to recognize and respond to errors in AIM activities, which mirrors the process of identifying and addressing student misconceptions. TPACK, developed by Mishra and Koehler ([<reflink idref="bib24" id="ref63">24</reflink>]), extends Shulman's ([<reflink idref="bib32" id="ref64">32</reflink>]) concept of Pedagogical Content Knowledge (PCK)—the blending of Content Knowledge (CK) and Pedagogical Knowledge (PK), which is defined as teachers' specialized knowledge to teach content effectively, combining subject expertise with strategies to make it accessible and engaging—to include technology integration. It provides a framework to examine how PTs synthesize their understanding of content (mathematical concepts), pedagogy (teaching strategies), and technology (AI‐based tools). This framework is particularly relevant for exploring PTs' experiences using ChatGPT within the AIM activities and the AIS strategy, and how they transfer and integrate knowledge of mathematics content, pedagogy, and AI‐based technological tools in teaching mathematics.</p> <hd id="AN0191298893-10">METHODOLOGY</hd> <p>A convergent mixed methods design was employed to address the research questions: (a) To what extent do PTs verify the correctness of problems posed by ChatGPT in AIM activities? and (b) What are their experiences using ChatGPT as an instructional tool within the AIM activities and the AIS strategy for supporting problem posing in teaching and learning mathematics? The mixed methods design is appropriate because we conducted the simultaneous collection and analysis of both quantitative metrics of error identification and correction, integrated with qualitative insights into PTs' problem‐solving process after data collection, to ensure a comprehensive, holistic understanding of both broad trends and detailed, context‐rich insights into PTs' experiences (Creswell & Plano Clark, [<reflink idref="bib8" id="ref65">8</reflink>]).</p> <hd id="AN0191298893-11">Participants</hd> <p>Participants in this study were 42 out of 48 PTs (87.5%) enrolled in three different sections of a mathematics methods course (31 PTs in two sections of elementary math methods course and 11 PTs in one section of middle and secondary math methods course) as part of a teacher education program at a university, a Hispanic‐serving institution in the southwestern United States, with about 77% of students identifying as students of color. All participants were juniors or seniors taking the mathematics methods course during the spring of 2024, which was taught by the first author. Prior to the study, which was approved by the University Institutional Review Board, informed consent was obtained from the PTs who voluntarily participated.</p> <hd id="AN0191298893-12">Developing and implementing AIM activities</hd> <p>We developed the AIM activities involving problem posing when given an answer or calculation, as recommended by Lee ([<reflink idref="bib21" id="ref66">21</reflink>]) for further research. The AIM activities included a questionnaire with three different problem‐posing tasks, two of which were required: (a) Task 1 involved a word problem with the answer of 2/3, (b) Task 2 involved a word problem requiring the computation of 1/2 + 2/3, and (c) the third was optional: Task 3 involved a word problem requiring the computation of 2 1/3 + 1/2.</p> <p>In addition to addressing the need for further research on the topics articulated in the prior sections, we developed the AIM activities to serve both instructional and assessment purposes. First, we utilized the free generative AI tool, ChatGPT‐3.5, to provide scaffolding for students to pose problems involving fundamental mathematical concepts, such as rational numbers. This is intended to ensure inclusion and equity in AI by allowing all potential participants, including the PTs in this study, to access ChatGPT‐3.5, even though we recognize that true equity requires more than tool availability. Second, without requesting confidential information, the AIM activities offer scaffolding for traditional mathematical problem‐posing activities that can be conducted in regular classrooms, thereby mitigating data privacy concerns.</p> <p>Third, the AIM activities involve scenarios where the PTs imagined themselves in their mathematics classrooms and instructed their imaginary students to create real‐life mathematical word problems within the provided problem situations. The imaginary students were then asked to solve these problems independently. Subsequently, the PTs were required to grade and analyze student work, correcting errors and addressing any confusion. In reality, during the tasks, the PTs were instructed to pose a word problem and solve it using ChatGPT‐3.5 within the provided problem situations. The PTs then graded and analyzed the outcomes from ChatGPT‐3.5, assuming that the problems and problem‐solving processes posed and solved by ChatGPT‐3.5 respectively represented the outcomes of their imaginary students.</p> <p>As a result, in this study, we utilized the AIM activities as an assessment tool to evaluate the PTs' ability to identify and correct errors that their future students might make in problem posing, as well as to offer meaningful feedback for mathematics learning. This approach not only serves as a methodological tool for examining the extent of PTs' transfer of mathematics content knowledge for teaching but also addresses two instructional purposes: (a) helping PTs recognize the importance of maintaining a critical perspective on AI outputs, which often contain errors, hallucinations, and biases; and (b) emphasizing the continued need for developing strong mathematics knowledge and effective teaching skills essential for utilizing AI effectively.</p> <p>As this study adopts Silver's ([<reflink idref="bib33" id="ref67">33</reflink>]) definition of problem posing, which involves a process occurring before, during, or after the solution of a problem, the AIM activities encompass the entire process of posing problems and consecutive problem‐solving. Figure 1 illustrates a sample AIM activity where students: (a) use ChatGPT‐3.5 to pose a daily life word problem with an answer of 2/3; (b) assess and revise the outcome if needed; (c) solve the revised problem with ChatGPT‐3.5; and (d) evaluate and correct the solution and process as necessary.</p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/SSM/01feb26/ssm18336-fig-0001.jpg?ephost1=dGJyMNXb4kSepq84yOvqOLCmsE6epq5Srqa4SK6WxWXS" alt="ssm18336-fig-0001.jpg" title="1 Sample of an AI‐integrated mathematical problem‐posing activity." /> </p> <p></p> <hd id="AN0191298893-14">Data collection</hd> <p>After exploring methods to teach fractions in Week 10 of the 16‐week session, such as the five interpretations of fractions—Part Whole, Measure, Quotient, Ratio, and Operator—and fraction operations, 42 PTs individually completed the AIM activities as homework: two required activities involved posing daily life word problems with the answer of 2/3 (Task 1) and requiring the computation of 1/2 + 2/3 (Task 2), and one optional activity involved posing a daily life word problem requiring the computation of 2 1/3 + 1/2 (Task 3). The PTs were also asked to provide reflections on their experiences with the use of ChatGPT through the AIM activities and the AIS strategy, which aimed to assist in the teaching and learning of mathematics. Their reflections were prompted by the following questions: (a) How did interacting with ChatGPT influence your understanding of mathematical concepts? and (b) In what ways do you think this technology could be further integrated into your math learning and teaching journey? Of the 42 PTs, 38 completed their reflection journals, while 4 did not. The primary sources of data for this study were the PTs' outcomes on the AIM activities, their reflection journals, and researcher field notes. A total of 109 problems posed by ChatGPT‐3.5 were evaluated by the PTs (42 problems in Task 1, 40 problems in Task 2, and 27 problems in Task 3), as shown in Table 1.</p> <p>1 TABLE Distribution of problems posed by ChatGPT‐3.5 evaluated by the preservice teachers' across tasks.</p> <p> <ephtml> <table><thead valign="bottom"><tr><th align="left">AIM activities</th><th align="left">Number of problems posed by ChatGPT‐3.5</th><th align="left">Total</th></tr><tr><th align="left">Error‐free</th><th align="left">Error‐containing</th></tr><tr><th align="left">Identified as correct</th><th align="left">Identified as incorrect</th><th align="left">Mistakenly identified as correct</th><th align="left">Successfully identified as incorrect</th></tr><tr><th align="left" /><th align="left">Successfully revised</th><th align="left">Failed to revise</th></tr></thead><tbody valign="top"><tr><td align="left">Task 1</td><td align="left">12</td><td align="left">1</td><td align="left">7</td><td align="left">16</td><td align="left">6</td><td align="left">42</td></tr><tr><td align="left">Task 2</td><td align="left">7</td><td align="left">0</td><td align="left">24</td><td align="left">5</td><td align="left">4</td><td align="left">40</td></tr><tr><td align="left">Task 3</td><td align="left">18</td><td align="left">0</td><td align="left">7</td><td align="left">0</td><td align="left">2</td><td align="left">27</td></tr><tr><td align="left">Subtotal</td><td align="left">37</td><td align="left">1</td><td align="left">38</td><td align="left">21</td><td align="left">12</td><td align="left">109</td></tr><tr><td align="left">Total</td><td align="center">38</td><td align="center">71</td><td align="left" /></tr><tr><td align="center">109</td><td align="left" /></tr></tbody></table> </ephtml> </p> <p>1 Abbreviation: AIM, AI‐integrated mathematical problem‐posing.</p> <hd id="AN0191298893-15">Data analysis</hd> <p>By evaluating the PTs' outcomes on the AIM activities, the first two authors independently analyzed whether the PTs identified errors in the problems and problem‐solving processes posed and solved by ChatGPT‐3.5, and whether they corrected those errors. For the quantitative analysis, we assessed the PTs' accuracy in verifying the correctness of problems posed by ChatGPT‐3.5 and calculated the verification rates. We calculated the percentage of correctly identified error‐free or error‐containing problems, the error recognition failure rates, and the error correction failure rates. These metrics addressed the extent of verification and the effectiveness of the PTs in identifying and correcting errors. For the qualitative analysis, the first two authors also independently applied open coding and conducted a thematic analysis to identify common themes within the PTs' journal reflections and gain a detailed understanding of their perceptions and experiences. Figure 2 illustrates the detailed data analysis process with examples of codes and themes.</p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/SSM/01feb26/ssm18336-fig-0002.jpg?ephost1=dGJyMNXb4kSepq84yOvqOLCmsE6epq5Srqa4SK6WxWXS" alt="ssm18336-fig-0002.jpg" title="2 The data analysis process using the convergent mixed methods design. AIM, AI‐integrated mathematical problem‐posing; PT's, preservice teachers'." /> </p> <p></p> <p>These analyses allowed us to examine the extent of the PTs' transfer of knowledge for teaching, facilitated by the AIM activities, as well as the PTs' experiences with the use of ChatGPT through these activities. Inter‐rater reliability was calculated at 94%. Any discrepancies between the two authors were discussed and resolved.</p> <hd id="AN0191298893-17">RESULTS</hd> <p></p> <hd id="AN0191298893-18">Verification accuracy, verification errors, and error correction by the PTs</hd> <p>To address the first research question—"To what extent do PTs verify the correctness of problems posed by ChatGPT in AIM activities?"—we examined whether the PTs identified and corrected errors in the problems and problem‐solving processes posed and solved by ChatGPT‐3.5. As shown in Table 1, of the total 109 problems, 71 problems (65.1%) were found to contain errors: 29 problems in Task 1, 33 problems in Task 2, and 9 problems in Task 3. Conversely, 38 problems (34.9%) were found to be error‐free: 13 problems in Task 1, 7 problems in Task 2, and 18 problems in Task 3. The errors in problems posed by ChatGPT‐3.5 resemble those typically made by students in traditional problem‐posing activities, as illustrated in Table 2.</p> <p>2 TABLE Samples of the errors in the problems posed by ChatGPT‐3.5.</p> <p> <ephtml> <table><thead valign="bottom"><tr><th align="left">Type of error</th><th align="left">Description</th><th align="left">Error‐containing problems posed by ChatGPT‐3.5</th></tr></thead><tbody valign="top"><tr><td align="left">Incorrect inclusion of required concepts or situations</td><td align="left">Problems that are incorrectly stated, with the required whole parts of fractions or their operations not included correctly (Kar, <xref ref-type="bibr" rid="bibr16">2015</xref>)* This was the most frequently identified error in this study.</td><td align="left">In Task 1, "In a bakery, there are 24 cupcakes available for sale. If 2/3 of the cupcakes are chocolate flavored, how many chocolate cupcakes are there?"This problem was incorrectly stated, with the answer not aligning with the fraction 2/3.</td></tr><tr><td align="left">Incorrect operations used</td><td align="left">Problems where the solution involves operations different from the ones required (Kar, <xref ref-type="bibr" rid="bibr16">2015</xref>; McAllister & Beaver, <xref ref-type="bibr" rid="bibr23">2012</xref>; Osana & Royea, <xref ref-type="bibr" rid="bibr28">2011</xref>)</td><td align="left">In Task 2, "Sarah baked a delicious cake for her family. She cut the cake into two equal parts and gave one part to her brother. Then, she cut the remaining part into three equal pieces and gave two of those pieces to her sister. What fraction of the original cake did Sarah give to her brother and sister altogether?"The problem was solved with the operation 1/2 + (2/3 × 1/2) instead of the correct operation 1/2 + 2/3.</td></tr><tr><td align="left">Unrealistic quantities that exceed the whole</td><td align="left">Situations where the meanings attributed to fractions or their operations do not make sense in daily life, such as using quantities greater than the whole (Kar, <xref ref-type="bibr" rid="bibr16">2015</xref>; McAllister & Beaver, <xref ref-type="bibr" rid="bibr23">2012</xref>)</td><td align="left">In Task 2, "Emma gave one‐half of the cake to her friend Lily and two‐thirds of the cake to her friend Jack. What fraction of the cake did Emma give away in total?"This problem resulted in a total that exceeds a whole cake, which is unrealistic.</td></tr><tr><td align="left">Inconsistent units used</td><td align="left">Problems involving inconsistent units used in the operations (Kar, <xref ref-type="bibr" rid="bibr16">2015</xref>; Kar & Isık, <xref ref-type="bibr" rid="bibr17">2014</xref>)</td><td align="left">In Task 3, "Jessica served 2 and 1/3 pies to her guests for dessert. Then, she ate 1/2 of a pizza herself. What is the total amount of pies and pizzas that Jessica served or ate?"The problem had two quantities with inconsistent units and thus could not be solved.</td></tr></tbody></table> </ephtml> </p> <p>Out of the 38 problems correctly posed by ChatGPT‐3.5, the PTs accurately identified 37 problems as correct, resulting in a verification accuracy rate of 97.4% (37 out of 38). However, among the 71 problems incorrectly posed by ChatGPT‐3.5, 38 were mistakenly identified as correct by the PTs, indicating that 53.5% of the PTs failed to recognize the errors made by ChatGPT‐3.5 (7 problems in Task 1, 24 problems in Task 2, and 7 problems in Task 3). This high rate of failure in recognizing errors could be due to the PTs' lack of solid understanding of fractions. Of the 33 problems (46.5%) that the PTs successfully identified as incorrect, 21 were successfully revised with feedback for the imaginary students (63.6%): 16 problems in Task 1 and 5 problems in Task 2. Meanwhile, 12 remained uncorrected (36.4%): 6 problems in Task 1, 4 problems in Task 2, and 2 problems in Task 3. Table 3 illustrates some PTs' outcomes on the AIM activities, including types of errors, the PTs' verification errors, error correction, and correction failures.</p> <p>3 TABLE Samples of the preservice teachers' (PTs') outcomes on the AI‐integrated mathematical problem‐posing (AIM) activities.</p> <p> <ephtml> <table><thead valign="bottom"><tr><th align="left">AIM activities</th><th align="left">Error‐containing problems posed by ChatGPT‐3.5</th><th align="left">Type of error</th><th align="left">Problems revised by the PTs</th><th align="left">Connection</th></tr></thead><tbody valign="top"><tr><td align="left">Task 1</td><td align="left">Maria has a pie that she wants to share with her friends. She cuts the pie into 6 equal slices. If she gives 4 slices to her friends, what fraction of the pie does she have left?</td><td align="left">Incorrect inclusion of required concept or situation</td><td align="left">Maria has a pie that she wants to share with her friends. She cuts the pie into 6 equal slices. If she gives 2 slices to her friends, what fraction of the pie does she have left?</td><td align="left">Error corrected</td></tr><tr><td align="left">Ruby is making a fruit salad. She uses 4/6 of a cup of strawberries and 1/6 of a cup of blueberries. What fraction of the total fruit salad is made up of strawberries and blueberries combined?</td><td align="left">Ruby is making a fruit salad. She uses 4/6 of a cup of strawberries and 2/6 of a cup of blueberries. What fraction of the total fruit salad is made up of strawberries and blueberries combined?</td><td align="left">Correction failures: Persistent incorrect inclusion</td></tr><tr><td align="left">Task 2</td><td align="left">Sarah has baked some cookies. She gave away half of her cookies to her friend Lisa, and then she gave away two‐thirds of what she had left to her neighbor, John. If Sarah originally had 12 cookies, how many cookies does she have left after giving them away?</td><td align="left">Incorrect operations used</td><td align="left">Sarah has baked some cookies. She gave away half of a dozen to her friend Lisa, and then she gave away two‐thirds of a dozen to her neighbor, John. How many dozens of cookies did she give away?</td><td align="left">Error corrected</td></tr><tr><td align="left">Emma has baked a cake and divided it into two parts. She gave one‐half of the cake to her friend Lily and two‐thirds of the cake to her friend Jack. What fraction of the cake did Emma give away in total?</td><td align="left">Unrealistic quantities that exceed the whole</td><td align="left">No revision made</td><td align="left">Error recognized, no revision made</td></tr><tr><td align="left">Task 3</td><td align="left">Amy baked 2 whole pies. She served 1/3 of one pie to her guests for dessert. Then, she made a batch of cookies and ate 1/2 of them herself. What is the total amount of pies and cookies that Amy served or ate?</td><td align="left">Inconsistent units used</td><td align="left">Amy made 2 different flavors of pies for her classmates. They ate 2 and 1/3 of the chocolate pie and 1/2 of the apple pie. How much did the class eat all together?</td><td align="left">Unrealistic: quantities exceed the whole</td></tr></tbody></table> </ephtml> </p> <hd id="AN0191298893-19">Positive experiences, concerns and critical perspectives, and transfer and connection of know...</hd> <p>To address the second research question on PTs' experiences with ChatGPT in AIM activities and the AIS strategy for supporting problem posing in teaching and learning mathematics, we analyzed the PTs' journal reflections. A thematic analysis identified common themes, providing insights into their perceptions, concerns, and experiences.</p> <hd id="AN0191298893-20">Strengths of an instructional method using ChatGPT</hd> <p>The analysis of PTs' journal reflections reveals several key strengths of using ChatGPT, as valued by the PTs based on their experiences with the AIM activities under study.</p> <hd id="AN0191298893-21">Step‐by‐step guidance</hd> <p>The most frequently mentioned advantage is the step‐by‐step guidance it provides, probably because AI outputs are presented in that form. 21 PTs out of 38 (55.3%) appreciated the breakdown of complex problems into manageable parts, which enhances their understanding and problem‐solving skills. This is evident from the PTs' comments, such as: "...generate new problems with step‐by‐step solutions"; "It breaks down the math step by step to show how you solve the whole equation"; "Step‐by‐step explanations allowed me to dive deeper into the subject matter"; and "...help you break down complex mathematical problems into smaller, more understandable parts."</p> <hd id="AN0191298893-22">Immediate feedback and interactivity</hd> <p>Another significant benefit noted by 18 PTs out of 38 (47.4%) is the quick feedback and interactivity of the platform. This feature allows for real‐time learning, where students can immediately see the results of their work and compare them with the correct solutions. The PTs remarked on the value of this feature in their learning process as follows: "...provides instant feedback on your solutions"; "The immediate feedback and detailed, step‐by‐step explanations allowed me to dive deeper into the subject matter"; "...one of the most powerful is feedback...."; and "...interactive problem‐solving practice sessions, enabling students to engage in real‐time dialogue with the AI..."; and so on.</p> <hd id="AN0191298893-23">Diverse examples and strategies</hd> <p>12 PTs out of 38 (31.6%) also appreciated the availability of various examples and problem‐solving strategies, which help to deepen their understanding and engagement. The platform's ability to present multiple ways to solve a problem or different types of examples for a single concept allows for a more comprehensive learning experience, as indicated by the PTs' comments, such as: "ChatGPT generates a variety of different word problems that can be used for one answer. This can show that there are many different ways to create a word problem with variables we have"; "...presenting information in a different light, which enriched the learning experience"; "ChatGPT provided alternative solutions or methods of solving the same math problem"; and "I've learned to analyze problems from different angles and evaluate various solution strategies."</p> <hd id="AN0191298893-24">Personalized learning paths and tailored assistance</hd> <p>Additionally, the platform's ability to personalize learning experiences was seen as a major advantage. Personalized learning paths and tailored assistance were mentioned by 11 PTs out of 38 (28.9%) as valuable features that cater to individual student needs, enhancing the overall learning experience by adaptive interactions, such as using prompts like "Can you reconsider this step?" and "Provide another problem for practice." This is evident from the PTs' comments, such as: "...offering personalized assistance tailored to each student's needs," "...develop a personalized learning path," "...a unique learning opportunity," "...allowing for flexible and convenient learning opportunities," and "AI can provide personalized support."</p> <hd id="AN0191298893-25">Enhancing understanding and supporting assessments through AIM activities</hd> <p>Finally, the data suggests that using ChatGPT as an instructional method, particularly AIM activities, effectively deepens understanding and supports assessment. However, this was highlighted only by some of the PTs who succeeded in error recognition and correction. They appreciated that AIM activities foster deep exploration of concepts, enhance critical thinking, and reveal students' thought processes. Although this theme overlaps with others, it was separated due to its direct relevance to AIM activities rather than ChatGPT itself. 13 PTs out of 18 (72.2%) who identified errors in at least one problem and corrected them (34.2% of the 38 total PTs) shared how these methods influenced their content and pedagogical knowledge, as reflected in the following quotes: "...influenced my understanding of mathematical concepts, by seeing how the AI can generate practice problems"; "...opened up opportunities for creative problem‐solving and critical thinking"; "...challenge higher‐order thinking students to check if the ChatGPT created is appropriate for the given solution and correctly reflects the concept"; "...generated worksheets and quizzes"; and "...serve as a valuable formative assessment tool."</p> <hd id="AN0191298893-26">Challenges and limitations of an instructional method using ChatGPT</hd> <p>Conversely, the PTs' reflections reveal key concerns about using ChatGPT as well.</p> <hd id="AN0191298893-27">Incorrect answers</hd> <p>A prominent issue highlighted by 15 PTs out of 23 (65.2%) who identified errors in at least one problem (39.5% of the 38 total PTs) is the provision of incorrect answers. Several comments indicated that the platform occasionally delivered wrong solutions, which led to confusion and frustration: "The problems and solutions that were given were not correct," and expressed concern over the accuracy of the answers as follows: "...need to be aware that the program is not always accurate"; and "...does not have all of the answers, in fact, almost all of the prompts I submitted on this assignment came back incorrect." The potential impact of incorrect answers on students' learning is significant, as it may lead to misunderstandings or a lack of confidence in the platform's reliability: "Although AI provides the steps it took to solve the problem, the logic may be there, and the answer may not add up correctly"; and "Having that blind trust in programs like these could cause them [students] a lot of trouble on their assignments, and their overall understanding of the content as well." Such inaccuracies can also result in students losing interest or failing to develop problem‐solving skills independently: "...students may lose interest and the opportunity to learn to find the answer by their own."</p> <hd id="AN0191298893-28">Concerns with clarity and simplicity in solution presentation</hd> <p>A concern raised by seven PTs out of 38 (18.4%) involves the presentation of solutions without sufficient clear explanations, which can confuse learners. For example, one PT noted difficulty in understanding the steps due to excessive words, characters, and symbols: "I found it difficult to read the steps with so many extra words, characters, and symbols." Additionally, feedback indicated that the platform sometimes failed to provide the simplest or most straightforward answer. For example, the PTs mentioned the need for simple and straightforward answers, as reflected in comments such as: "I also did not like how the equation was made harder [by including unnecessary numbers or variables] than it should have been"; and "I would prefer it to be as simple as my question rather than using larger numbers then reducing [simplifying]. This would not be good if I have not taught my students about reducing yet."</p> <p>Overall, while using ChatGPT in mathematics education offers valuable features, the PTs highlighted that improving its effectiveness in teaching and learning mathematics would require addressing specific issues related to accuracy, clarity, and simplicity.</p> <hd id="AN0191298893-29">Transfer and connection of knowledge</hd> <p>Additionally, the PTs' reflections revealed a transfer and connection of knowledge, suggesting that the use of AI in the AIM activities and the AIS strategy contributed to their understanding and integration of the knowledge of mathematics content, pedagogy, and AI‐based tools. This is reflected in comments such as: "...breaking them down into similar steps for explaining to my students..."; "So they could have the chat [Chat GPT] create a problem, they solve it on their own, and then go back and compare their work to how the chat did it. They can compare the differences and see which way they like best"; "...available 24/7 to provide instant support and guidance to students facing challenges with homework or self‐study"; "This could also be a good tool to use for students if they are unable to attend any type of tutoring and their parents do no understand any of the math work at home"; "It allows for me to help the students if they need it and explain the lesson in a different way from lecturing them"; "...use this in many different math methods or topics, evolving this tool"; and "Educators can create dynamic learning environments that promote collaboration, critical thinking, and mastery of mathematical concepts, ultimately empowering students to excel in math and beyond."</p> <p>The comments demonstrate how the PTs transferred and connected their mathematics content knowledge to their pedagogical and instructional practices, contributing to their development as educators. For example, these comments illustrate the PTs' recognition of using ChatGPT to facilitate step‐by‐step guidance, independent problem‐solving, and critical reflection to encourage students to compare solutions and critically evaluate different methods. They also recognized the value of AI in providing tailored feedback, integrating technology into continuous learning, offering free tutoring and support, creating a range of problems and quizzes with various scenarios, and adapting teaching methods to meet students' needs. Overall, these comments show the PTs effectively bridging content knowledge with practical teaching strategies to enhance their instructional effectiveness.</p> <hd id="AN0191298893-30">DISCUSSION AND IMPLICATIONS</hd> <p>This study examined how well the PTs verified and corrected errors in problems posed by ChatGPT‐3.5 within the AIM activities. It also explored their experiences with ChatGPT through the AIM activities and the AIS strategy for supporting problem posing in mathematics education. The findings reveal significant insights into the PTs' capabilities in error recognition and correction, which have implications for their instructional practices and the reliability of AI tools in educational settings. The findings also highlight both positive aspects and notable concerns regarding the use of ChatGPT, as well as how the PTs connect their mathematics content knowledge with pedagogical practices.</p> <p>First, ChatGPT‐3.5 posed 38 error‐free and 71 error‐containing problems within the AIM activities, as the PTs used their own prompts to ask ChatGPT‐3.5 to generate problems related to daily life in given situations. The errors in the problems posed by ChatGPT‐3.5 closely resembled those commonly made by students in traditional mathematical problem‐posing activities, likely due to the AI's training data. This resemblance might seem natural since ChatGPT is a large language model (LLM) trained on human‐produced datasets. The similarity between the errors could provide insights into biases in AI use in education, as these errors reflect biases inherent in the training data, suggesting a tendency to replicate such biases. Therefore, this study illustrates the importance of students maintaining a critical mindset regarding AI outputs (NCTM, [<reflink idref="bib26" id="ref68">26</reflink>]), as well as the need for teacher education programs to incorporate opportunities for PTs to explore and address potential biases in AI use, which is a critical aspect to consider in mathematics education.</p> <p>Second, the PTs demonstrated a high verification accuracy rate of 97.4%, correctly identifying 37 of 38 error‐free problems. This indicates strong proficiency in recognizing valid problems posed by ChatGPT‐3.5. However, they struggled with identifying errors, mistakenly classifying 38 out of 71 erroneous problems as correct, resulting in a 53.5% error recognition failure rate. Task 2 had the highest undetected error rate (33.8%), highlighting variability in error detection capabilities. This suggests that over half of the problematic problems went unnoticed by the PTs. Such high error recognition failure rates highlight a potential gap in the PTs' ability to critically assess and verify the accuracy of AI‐generated problems, due to a lack of solid understanding of fractions. Additionally, the PTs successfully revised 63.6% of the correctly identified incorrect problems, but 36.4% remained uncorrected. This error correction failure rate highlights the PTs' potential challenges in error correction and feedback processes as well. The findings suggest a need to enhance PTs' skills in error recognition and correction, whether using AI tools such as ChatGPT‐3.5 or not, as this capability is strongly linked to their mathematical content knowledge (Hoth et al., [<reflink idref="bib11" id="ref69">11</reflink>]) and is critical for effective teaching and learning in mathematics. Focused training on critical evaluation and error correction, utilizing AIM activities that involve scenarios assuming the problems and problem‐solving processes posed and solved by ChatGPT represent the outcomes of imaginary students, along with a more detailed review process, could improve PTs' ability not only to detect and correct errors that their future students might make but also to provide meaningful scaffolding for mathematics learning.</p> <p>Third, AIM activities, with the metrics used in this study (e.g., error recognition failure rates and error correction failure rates), could serve as a meaningful assessment tool to measure and promote teachers' professional noticing (Jacobs et al., [<reflink idref="bib13" id="ref70">13</reflink>]). The ability to recognize errors and the ability to correct errors with feedback are important facets of CK and PCK, respectively (Türling et al., [<reflink idref="bib36" id="ref71">36</reflink>]; Wuttke & Seifried, [<reflink idref="bib41" id="ref72">41</reflink>]), both of which are major components of teacher knowledge (Shulman, [<reflink idref="bib32" id="ref73">32</reflink>]). Furthermore, AIM activities could serve as an instructional method to facilitate PTs' transfer of CK into practical instructional strategies and their development of TPACK. Significant transfer and connection of knowledge among the PTs within the AIM activities in the study were evident from the following findings in their reflections.</p> <p>Fourth, the PTs identified several strengths in using ChatGPT for mathematics instruction, including its ability to facilitate a deeper understanding of mathematical concepts and enhance problem‐solving skills. They valued the real‐time feedback and interactivity, appreciating the instant responses and corrections that reinforce learning and enable prompt adjustments through dynamic interaction. The PTs also appreciated the tool's personalized learning paths and tailored assistance, which support individual needs and offer a flexible educational experience. These advantages identified by the PTs are supported by prior research (Hwang, [<reflink idref="bib12" id="ref74">12</reflink>]; Mohamed et al., [<reflink idref="bib25" id="ref75">25</reflink>]; Zawacki‐Richter et al., [<reflink idref="bib42" id="ref76">42</reflink>]). Furthermore, the PTs praised ChatGPT's step‐by‐step guidance, which breaks down complex mathematical problems into manageable and understandable parts, promoting clearer explanations and reinforcing comprehension. Additionally, ChatGPT's ability to generate various examples and problem‐solving approaches for a single concept was another advantage highlighted by the PTs, as it provides a richer learning experience and encourages exploration of different methods, thereby supporting a more robust and comprehensive understanding of mathematical concepts. Conversely, the PTs expressed concerns regarding AI use, including frequent inaccuracies in ChatGPT's outputs, which could lead to misunderstandings, erode confidence in the tool's reliability, and hinder the development of independent problem‐solving skills. This is a major concern highlighted by research (NCTM, [<reflink idref="bib26" id="ref77">26</reflink>]; Wardat et al., [<reflink idref="bib40" id="ref78">40</reflink>]). Furthermore, the PTs expressed concerns about the overly complex or cluttered presentation of outputs and lack of sufficient clarity. The findings in the PTs' reflections revealed a significant transfer and connection of knowledge, demonstrating how the AIM activities contributed to their understanding and application of both mathematics content knowledge and pedagogical and instructional practice knowledge.</p> <p>Fifth, as intended in the study, the AIM activities provided the PTs with an opportunity to recognize the importance of students maintaining a critical perspective on AI outputs, which often contain errors, hallucinations, and biases. This was evident from the PTs' accuracy concerns regarding AI use, as presented above. To some extent, this intention was successfully achieved. However, 15 out of the 38 PTs who completed their reflection journals (39.5%) focused solely on the practical benefits of incorporating AI in mathematics education, without offering any critical evaluation of AI outputs. This lack of critical evaluation is likely due to two factors: the failure to recognize errors (11 out of these 15 PTs) and the encounter of only error‐free problems posed by ChatGPT (4 out of these 15 PTs). No PTs directly highlighted the need to develop their mathematics knowledge and effective teaching skills for utilizing AI. These findings indicate that teacher preparation programs need to provide multiple opportunities for PTs to engage in critically evaluating the use of AI in mathematics education, so they can help their future students maintain a critical perspective on AI use. This supports the NCTM ([<reflink idref="bib26" id="ref79">26</reflink>]) recommendations on the continued importance of teachers possessing robust mathematics knowledge and integrating a critical mindset in their assessments and instructional methods.</p> <p>Finally, the study addressed the need for research that incorporates educational perspectives and theories to comprehend the impact of AI on learning and teaching (Bartolomé et al., [<reflink idref="bib1" id="ref80">1</reflink>]; Mohamed et al., [<reflink idref="bib25" id="ref81">25</reflink>]; Zawacki‐Richter et al., [<reflink idref="bib42" id="ref82">42</reflink>]). The findings illustrate how AIM activities can empower students in their learning process by engaging them in the critical evaluation of AI outputs as well as metacognitive activities, during which they consistently self‐monitor and self‐regulate their cognitive processes to pose problems correctly and connect real‐world scenarios with mathematical concepts. This approach could be an educationally valuable strategy for adopting an ethics of care that prioritizes learning, pedagogy, and the human aspects of technology use (NCTM, [<reflink idref="bib26" id="ref83">26</reflink>]; Prinsloo, [<reflink idref="bib29" id="ref84">29</reflink>]; Zawacki‐Richter et al., [<reflink idref="bib42" id="ref85">42</reflink>]).</p> <hd id="AN0191298893-31">LIMITATIONS AND FUTURE RESEARCH</hd> <p>As discussed above, this pilot case study makes significant contributions by exploring the extent to which PTs verify the correctness of problems posed by ChatGPT and their experiences with ChatGPT through AIM activities and the AIS strategy for supporting mathematical problem posing, which is a novel way to incorporate ChatGPT into mathematics education. Despite these contributions, a couple of limitations should be noted. First, the small sample size of 42 PTs from a single university may limit the generalizability of the findings. Second, the study focused on only three AIM activities centered around specific fraction concepts, which may not fully measure the PTs' professional competence in error recognition and correction across a broader range of mathematical concepts.</p> <p>To build on the findings of this study and address its limitations, future research should include studies with larger and more diverse samples from various institutions and educational settings, using sequences of AIM activities that integrate different mathematical concepts, including algebra and geometry. This approach would help determine whether the findings are consistent across different groups of PTs and whether AIM activities and the AIS strategy can be effectively implemented in various teaching contexts. It could also examine how AI can be integrated into a broader range of mathematical activities, providing insights into its impact on different mathematical concepts. Such research would allow for a more in‐depth exploration of the effects of AIM activities and the AIS strategy on PTs' transfer of mathematics content knowledge for teaching, as well as identify areas needing improvement in error recognition. Moreover, comparative studies involving a control group using traditional mathematical problem‐posing activities would be beneficial to assess the effectiveness of AI assistance during AIM activities. This would help identify the unique contributions of AI in the teaching and learning of mathematics and determine whether AI offers advantages over traditional methods.</p> <p>Finally, future research can investigate the effectiveness of AIM activities and the AIS strategy, which are hypothesized to inherently engage students in metacognitive activities and foster deeper understanding, as instructional methods to promote the development of mathematical knowledge and a positive attitude toward mathematics. For example, research could be guided by the following question: "Is there a significant improvement in students' procedural and conceptual knowledge of fundamental mathematical concepts, as well as their problem‐solving skills, through AIM activities?"</p> <hd id="AN0191298893-32">CONCLUSION</hd> <p>This study explored the PTs' ability to verify and correct errors in problems posed by ChatGPT‐3.5, as well as their overall experiences with AI through AIM activities and the AIS strategy for supporting mathematical problem posing. The findings reveal that while the PTs demonstrated high accuracy in verifying error‐free problems, they struggled significantly with identifying and correcting errors, highlighting a gap in their instructional preparedness. The study suggests that AIM activities can be effective for assessing and developing PTs' competence in error recognition and correction, essential for effective mathematics teaching. Additionally, the findings indicate that, to a certain extent, AIM activities can support the transfer of knowledge from PTs' mathematics content knowledge to their pedagogical and instructional practices, contributing to their growth as adaptable and innovative educators. The study suggests the need to provide PTs with opportunities to create and critically evaluate AI use in mathematics education, fostering strong mathematical knowledge and effective teaching skills, which help them integrate a critical mindset into their assessments and instructional methods. Focusing on learning, pedagogy, and human aspects of technology use, AIM activities, and the AIS strategy can empower PTs in their learning process by engaging them in the critical evaluation of AI outputs as well as metacognitive activities.</p> <ref id="AN0191298893-33"> <title> REFERENCES </title> <blist> <bibl id="bib1" idref="ref23" type="bt">1</bibl> <bibtext> Bartolomé, A., Castañeda, L., & Adell, J. (2018). 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  Data: Exploring the Integration of Artificial Intelligence in Math Education: Preservice Teachers' Experiences and Reflections on Problem-Posing Activities with ChatGPT
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  Data: <searchLink fieldCode="AR" term="%22Young+Rae+Kim%22">Young Rae Kim</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0001-9518-0021">0000-0001-9518-0021</externalLink>)<br /><searchLink fieldCode="AR" term="%22Mi+Sun+Park%22">Mi Sun Park</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0002-7564-9133">0000-0002-7564-9133</externalLink>)<br /><searchLink fieldCode="AR" term="%22Eunmi+Joung%22">Eunmi Joung</searchLink>
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  Data: This study addresses the need for research that incorporates educational perspectives and theories to understand the impact of Artificial Intelligence (AI) on learning and teaching. Utilizing AI-integrated mathematical problem-posing (AIM) activities and the AI-powered scaffolding (AIS) strategy, the research investigated preservice teachers' (PTs') experiences with AI and their capacity for error recognition and correction in problems posed by ChatGPT. The findings reveal that while the PTs excelled at verifying error-free problems, they struggled significantly with identifying and correcting errors, indicating a gap in their instructional preparedness. The study demonstrates that AIM activities are effective tools for assessing and developing PTs' error recognition and correction skills. Additionally, AIM activities support the transfer of mathematical knowledge to pedagogical and instructional practices, contributing to PTs' growth as adaptable educators. The research highlights the need to integrate AI-based activities into PT training to build robust mathematical knowledge and teaching skills. Focusing on learning, pedagogy, and the human aspects of technology use, AIM activities and the AIS strategy enable PTs to engage critically with AI outputs and enhance their metacognitive skills. These insights emphasize the importance of incorporating AI-integrated methods into teacher preparation programs to better equip future educators for an AI-driven educational landscape.
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