AI policy for a calculus course, with examples

Sample AI syllabus policies for calculus courses at three levels of use, with clauses for showing work, course methods and disclosure.

Short answer: calculus instructors have dealt with answer-producing tools for years, from graphing calculators to online solvers. What is new is that AI tools also write out the steps, so “show your work” no longer proves the work is the student’s. Your policy should say whether homework is practice or assessment, what counts as acceptable help, and how you will check understanding. Pick one of the three policies below, then add the calculus-specific clauses that fit your course.

What makes calculus different

  • Current models do well on first-year exam questions. A University College London case study gave the 2024 to 2025 first-year mathematics exams to one model (chatgpt-4o-latest). In the calculus modules its average marks matched or exceeded the student averages, for example 86.2 against 63.7 in Multivariable Calculus (Walker et al., 2025).
  • Shown work is now easy to generate. Written steps used to be good evidence of understanding. An AI tool produces a tidy derivation on request, so the steps on a homework submission tell you less than they did.
  • Calculus is cumulative. Limits feed derivatives, derivatives feed optimization and integration. A student who skips the practice early runs into trouble later in the course and in courses that build on it, a point Stanford’s Math 51 guidance makes about mathematics in general (Stanford Math 51).

Three sample policies

Copy the one closest to your course and edit the bracketed parts.

1. No generative AI on graded work

Generative AI tools (for example ChatGPT, Claude, Gemini or Copilot) may not be used on homework, quizzes or exams in this course. Working problems yourself, including getting stuck and trying again, is how you learn calculus, and these tools skip that step. You may use the textbook, lecture notes, [a graphing calculator / approved software], classmates [if allowed] and office hours. If you are unsure whether something is allowed, ask before you submit.

2. AI for studying, not for submitted work

You may use generative AI tools to study: to explain a concept such as the chain rule, generate extra practice problems, or check your understanding after you have attempted a problem on your own. You may not use them to produce solutions you submit. Write your homework solutions yourself, without looking at AI output while you write. If you used an AI tool while studying for an assignment, add one sentence at the end saying how.

3. AI allowed with disclosure

On [homework / the project], you may use generative AI tools if you disclose it. For each problem where you used one, name the tool and include the prompts you entered. You are responsible for every step you submit: check each one, and use only methods covered in this course. AI tools may not be used on [quizzes / exams], where you show your understanding on your own.

Clauses worth adding for calculus

  • Explain-your-solution check. “I may ask you to explain any submitted solution in person. If you cannot, that part of the work may receive no credit.” Stanford’s Math 51 guidance includes a similar rule and sums it up as “Do not submit what you do not understand” (Stanford Math 51).
  • Course methods only. Say that solutions must use methods taught in the course. AI tools sometimes reach for advanced results: in the UCL study, some of the model’s answers in Integration, its lowest-scoring module, used results taught in the third year (Walker et al., 2025).
  • Calculators and solvers versus AI chatbots. If you allow a graphing calculator or a computer algebra system, say whether AI chatbots fall under the same rule or a different one.
  • What to disclose. Name the tool, what it was used for and the prompts that shaped the answer (KU CTE). Stanford’s Math 51 asks for screenshots of the prompts below the solution.

What one recent study found

The UCL case study (Walker et al., 2025) compared one AI model with students on all eight first-year core mathematics modules, using 33 closed-book exam questions from 2024 to 2025:

  • Across all modules, the model’s mean mark (71.1) was close to the students’ (69.1), and its marks were far more consistent (standard deviation 1.5 against 15.1).
  • In the calculus modules it scored 76.8 against 75.4 (Calculus and Probability) and 86.2 against 63.7 (Multivariable Calculus). The authors attribute much of the Multivariable Calculus result to a Python programming question it answered almost perfectly.
  • Typical errors were arithmetic slips in final steps, misapplied theorems, unreliable “prove or disprove” answers and ignoring constraints set in the question.

Keep the limits in mind: one model, one short prompt, no course materials, text-only questions, one UK department, and a paper that does not state a peer-reviewed venue. The authors call their results a lower bound and expect them to date quickly. The practical takeaway is the same as for any quantitative course: if a grade needs to reflect what a student can do alone, at least part of it should come from work you can observe.

Write yours in a few minutes

The free AI policy generator asks a few questions about your course and assessments and produces a policy you can paste into your syllabus.

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