SIAM Session at JMM 2024 Addresses Artificial Intelligence in the Education Sector

By Alvaro Ortiz Lugo

The Joint Mathematics Meetings (JMM) have long served as an opportunity for mathematicians, educators, and enthusiasts to convene, exchange ideas, and explore the latest advancements in the field. At JMM 2024, which took place in January in San Francisco, Ca., the SIAM Education Committee organized a comprehensive “Session on Artificial Intelligence and its Uses in Mathematical Education, Research, and Automation in the Industry.” The session provided a platform for artificial intelligence (AI) experts and practitioners from various backgrounds to share insights and innovations across four primary domains: research, education, undergraduate experiences, and academic partnerships with industry. Eight individual talks delved into inventive methods, pedagogical techniques, and emerging technologies that are actively revolutionizing the landscape of mathematics.

Education, Course Design, and the Classroom

Alvaro Ortiz of the University of Cincinnati showcased AI’s transformative impact in educational environments. Studies show that a large percentage of students now define themselves as AI users and claim that they will not stop utilizing the technology even if university-level restrictions forbid it [1]. But despite this surge in use, a surprisingly small number of institutions are actively establishing policies that address AI and its corresponding academic challenges — often leaving educators to fend for themselves. Ortiz emphasized the necessity of comprehensive professional development that prepares educators to effectively include AI tools in their lesson plans, moderate student interactions with AI, and mitigate AI-related ethical issues. He also exhibited innovative course and instructional design approaches that leverage AI’s capabilities, and articulated the importance of personalized, engaging learning experiences that meet diverse student needs.

In addition, Ortiz’s presentation briefly explored educational AI tools like intelligent tutoring systems; automated grading platforms; and natural language processors, chatbots, and adaptive learning platforms that may actually augment the learning process without simply providing students with the answer. Ortiz highlighted the potential of these tools to enhance student learning and streamline teaching tasks, but he also acknowledged the inherent complexities and concerns about data privacy, ethics, and algorithmic biases.

Undergraduate Experiences

The JMM 2024 session provided ample time for participants to discuss AI’s profound influence on undergraduate research and survey future opportunities for learning and creativity. To begin, Mihhail Berezovski of Embry-Riddle Aeronautical University shared some results from the integration of ChatGPT into the educational landscape, and focused on the chatbot’s implementation within Embry-Riddle’s project-based classes and Research Experiences for Undergraduates (REU) program. Berezovski recapped student REU experiences over the past two years and explained how the utilization of ChatGPT has created transformative opportunities to boost learning outcomes; foster collaborative experiences; and assist with coding tasks, report writing, and the structure of research publications. Additionally, the incentive of authorship and research ownership made REU students more careful with their use of ChatGPT. To stimulate a sense of transparency in their methods, they only employed it to access public knowledge and technical information for necessary tasks.

Although Berezovski highlighted ChatGPT’s advantages as a cutting-edge research tool, ethical considerations are nonetheless paramount. As such, he also examined the moral implications and addressed topics like data privacy, transparency, and possible biases in AI models. Berezovski concluded his talk by reflecting on prospective approaches for AI integration that retain a nuanced understanding of ethical dilemmas and ensure an equitable and inclusive learning environment.

During the SIAM Education Committee’s “Session on Artificial Intelligence and its Uses in Mathematical Education, Research, and Automation in the Industry” at the 2024 Joint Mathematics Meetings—which took place in January in San Francisco, Ca.—speakers explored the impact of artificial intelligence on applied mathematics students and educators. Top row, left to right: Mihhail Berezovski (Embry-Riddle Aeronautical University), Lake Bookman (Monash University), and Patricio Gallardo (University of California, Riverside). Middle row, left to right: Sergio García-Morán (Universidad del Rosario), Javier González Anaya (Harvey Mudd College), and Rafael Alberto Méndez-Romero (Universidad del Rosario). Bottom row, left to right: Sudhir Murthy (University of California, Riverside), Alvaro Ortiz (University of Cincinnati), and Yofer Quintanilla-Gómez (Universidad del Rosario). Photos courtesy of the speakers.

In a similar vein, Javier González Anaya of Harvey Mudd College spoke about convolutional neural networks (CNNs), which are prominent in audio, image, and text processing because of their ability to identify characteristic features of complex datasets at a relatively low computational cost. Their success is partly due to the robustness of the pooling layers within CNN architectures. González Anaya then overviewed his role as a co-mentor to three undergraduate students on a project about the combinatorial complexity of max pooling layers, which can serve as piecewise linear functions. To tackle this problem, the students employed a novel technique that relates the linear regions in a max pooling layer to the issue of counting vertices in some concrete polytopes.

All of these presentations emphasized the potential of AI-assisted coding and machine learning methodologies to enhance student productivity by effectively reducing the time of mathematical calculations, which impacts the entire learning and research development process.

AI-assisted Research

The integration of AI technology and mathematical research also holds immense promise in areas like data analysis and theorem-proving methodologies. Lake Bookman of Monash University considered the versatility of Gaussian mixture models (GMMs) in data clustering, acknowledged the challenges of fitting these models to large datasets, and identified the classical expectation-maximization (EM) scheme as an efficient, widely applicable method for GMM fitting. Despite the prevalence of data from multiple underlying models in many scenarios, GMMs’ potential for regression remains unknown. Bookman addressed the need for accurate parameter inference in such settings, discussed the extension of EM methods to fully nonlinear models, and noted variations in noise models. He also explored these algorithms’ utility in multi-target tracking and image processing applications, which illuminated their broader applicability beyond traditional clustering tasks.

Sudhir Murthy of the University of California, Riverside demonstrated how AI might possibly assist with mathematical proofs. For example, he showcased the efficacy of Lean—an interactive theorem prover—in organizing mathematical knowledge and rigorously verifying proofs, ultimately underscoring its versatility across disciplines like number theory, analysis, and algebra. Murthy’s talk offered insights into student experiences with the tool, outlined the advantages of interactive theorem-provers in the world of undergraduate mathematics and interdisciplinary curricula, commented on education’s relationship with proof automation and AI-generated mathematics, and introduced ongoing endeavors to enrich training data for seamless integration with large language models. AI tools like Lean hint at the imminent arrival of a future where conferences will likely feature AI-proven results.

Academic Partnerships With Industry

The SIAM Education Session at JMM 2024 also included talks by several members of the Colombia Section of SIAM, who illustrated AI’s capacity to encourage creative, innovative research and reinvigorate the relationship between industry and academia in Latin America. For instance, the traditional emphasis on disciplinary competencies in Colombian higher education often sidelines crucial industry-academia collaborations and hinders the holistic preparation of students for the workforce. However, the rise of AI has sparked a newfound convergence of interests between academia and industry.

Rafael Alberto Méndez-Romero of Universidad del Rosario spoke about industry’s significance as a vital partner in shaping well-rounded technological professionals. He highlighted a successful collaboration between Universidad del Rosario and DevSavant that exemplified the potential of such partnerships to drive gender equity and nurture talent in software engineering. One notable outcome of this collaboration is CodeSavant: a groundbreaking hackathon that leverages generative AI to innovate software development processes. By sharing this paradigmatic success, Méndez-Romero aimed to inspire other institutions and companies to adopt similar collaborative models and foster exceptional young talent in the technology sector.

Yofer Quintanilla-Gómez and Sergio García-Morán, both students at Universidad del Rosario, presented their three-step methodology to establish protocols for emotional support in learning environments. Universities are increasingly prioritizing mental and emotional health within learner-centered frameworks, recognizing its pivotal role in academic success. The intricate relationship between emotions and cognitive processes has thus become a critical research focus in education. While existing literature suggests that peak learning occurs when students are in optimal emotional states, the creation of effective protocols that cultivate such states remains a challenge.

Quintanilla-Gómez and García-Morán’s approach encompasses emotional stimulus generation, student response assessment, and educator emotion detection and classification. A specialized center for emotional education at Universidad del Rosario fosters student wellbeing and bolsters this effort, but the speakers want to further refine existing procedures with an automated system that acquires and processes biosignal-based emotional data—such as heart rate and skin conductivity—and utilizes machine learning algorithms to classify emotions. Quintanilla-Gómez and García-Morán aim to advance their university’s emotional health protocols and enhance the student body’s wellbeing with this innovative emotional acquisition system.

§

Overall, the SIAM Education Session at JMM 2024 comprehensively explored current trends and innovations in education and AI technology — from changes in the classroom to industry collaborations, cutting-edge research, and unique undergraduate experiences. These insights are just a small sample of the many developments that will pave the way for future advancements and collaborations within this landscape.

Alvaro Ortiz Lugo is an assistant professor of mathematics at the University of Cincinnati. He was previously a SIAM-sponsored Fellow of Project NExT (New Experiences in Teaching) and is currently a member of the SIAM Education Committee.