During a special presentation at the 2026 SIAM Annual Meeting this July in Cleveland, Ohio, a new framework for integrating artificial intelligence into education was outlined in a forthcoming book, Learning with AI: A Framework for Students, Instructors, and Universities. The approach addresses a fundamental shift in educational workload, moving to AI tools and “human work” to judgment.
This change stems from a question posed by Tamara Kolda: “what remains for mathematicians when AI can produce plausible mathematics on demand?”; her answer was that mathematicians add judgment in choosing the question, owning the result, and vetting the tool’s output.
AI Shifts Educational Trilemmas: Sustainability, Honesty, Understanding
The redistribution of educational workload now frames assessment as prioritizing judgment over routine tasks; artificial intelligence handles the former, while humans focus on the latter. Students now face a tension between achieving high grades, maintaining academic honesty, and genuinely understanding the material, a balance previously more easily maintained.
Instructors grapple with a parallel trilemma, balancing professional sustainability with trustworthy judgment and authentic student learning; AI’s emergence has not created these tensions, but rather “sharpened every edge simultaneously.” The book identifies three ways the trilemma manifests for students: work appearing polished yet lacking understanding, strategic concealment of AI assistance, and unfair judgment of honest students who openly acknowledge using AI. The first two issues fall to students to resolve, while the third represents a systemic problem requiring institutional attention.
A key concept outlined in Learning with AI is the distinction between recognition and production; a fluent AI explanation can create a false sense of understanding that exceeds actual ability. To bridge this gap, the guide advocates for an approach where students verify AI-generated answers through self-testing. Closing the AI window and explaining the concept aloud is a rapid assessment of true comprehension, identifying areas requiring further study.
This approach reframes AI output not as a definitive answer, but as a draft requiring human evaluation and refinement. The framework proposes a shared structure and vocabulary applicable across student, instructor, and institutional levels, recognizing that a rule designed for one scale often fails at others.
Honesty, specifically what a student reports, what a grade certifies, and what a degree attests, forms a critical thread throughout all three scales. Institutions, too, face a trilemma balancing financial sustainability with the meaning of credentials and their educational mission, a challenge exacerbated by the potential for AI to create the appearance of learning without actual knowledge acquisition.
The CAT Framework: Core Competence, AI Assistance, Trustworthiness
This approach moves beyond simply permitting or prohibiting AI tools, instead categorizing appropriate usage levels for different assignments, with instructors designating one of four levels: NAI (no AI), AIT (AI as tutor), AIC (AI as collaborator), and AIS (AI as the object of study). Expectation of some AI use for homework is suggested as a default setting, acknowledging student access and potential benefit from the technology.
Assessment, according to the guide, should separate independent competence from responsible AI-assisted work, recognizing that a polished final product alone provides insufficient evidence of either. This framework extends to the consistent application of these categories across learning and teaching activities. Further resources are cited.
Learning Spiral for Students: From Question to Independent Production
The Learning with AI guide proposes a five-step learning spiral to cultivate judgment alongside AI assistance, beginning with students independently framing a question before seeking support. This process isn’t about prohibiting tools, but structuring their use to bridge the gap between recognizing a correct answer and genuinely understanding the underlying concepts, a distinction the guide terms.
Students are encouraged to view AI outputs as drafts requiring independent verification, not definitive solutions, a shift intended to foster deeper engagement with the material. A core component of this verification is a simple self-test, the blank-page test, requiring students to explain a concept aloud without the AI interface open; failure to do so immediately identifies areas needing further study.
NAI, AIT, AIC, AIS: Explicit AI Use Categories for Instructors
Institutions can now establish clear policies regarding AI use with a new vocabulary designed to align expectations across students, instructors, and governing bodies. The framework, detailed in Learning with AI, proposes four explicit categories, NAI, AIT, AIC, and AIS, to define acceptable levels of AI assistance for different assignments, moving beyond simple prohibitions toward structured integration.
This approach acknowledges the inherent tensions between fostering independent competence, ensuring honest assessment, and verifying genuine understanding, issues artificial intelligence has not created but rather intensified. The core of the system rests on a shared understanding of these categories; NAI designates assignments requiring no AI assistance to protect independent skill development, while AIT permits AI as a study aid but not for submitted work.
AIC allows AI collaboration on submissions, contingent on verification and full disclosure of its use, and AIS frames AI itself as the subject of study. “The book recommends giving departments the four categories—NAI, AIT, AIC, and AIS—and the disclosure norms; letting each course choose its mix; and requiring every syllabus to state what is permitted, what must be done independently, and how to disclose AI use,” according to the guide’s authors.
This vocabulary aims to address a fundamental challenge: the difficulty of balancing honesty, competence, and institutional attestation in an era of readily available AI tools. Rather than attempting a universal rule, the guide advocates for a departmental approach, allowing individual courses to tailor AI usage to their specific learning objectives while maintaining a common language for discussing expectations.
A suggested default assumes students have access to AI for homework, anticipating some level of integration into their study habits, and shifting the focus to responsible and transparent application. The authors emphasize that AI can assist at every step of a five-step learning spiral, trying, asking for help, working independently, verifying, and reflecting, but cannot replace any of them.
The framework’s success hinges on institutional adoption and consistent application of these categories, transforming the trilemma from an intractable problem into a discussable issue with shared terminology. Tamara Kolda’s research, cited as a resource within the guide, further illuminates the evolving landscape of AI in education and provides additional context for informed decision-making.
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