Asking Large Language Models (such as ChatGPT or Gemini) to solve a homework problem hinders your learning!
How can you use Large Language Models (LLMs) to support your learning?
Academic Integrity Pledge
I am committed to being a person of integrity. I pledge, as a member of the Santa Clara University community, to abide by and uphold the standards of academic integrity contained in the Student Conduct Code.
Abide by Academic Integrity. Use LLMs to help you learn rather than solve your homework problems.
How does a Large Language Model work?
LLMs use data from millions of books, articles, and conversations to see how words fit together. An LLM uses patterns to guess what text should follow a set of preceding words. An LLM does not understand math concepts and does not perform calculations. LLMs can produce different answers to the same prompt.
Fundamentally, LLMs are designed to produce text that sounds right. While they usually do this by producing text which actually is right, they can also confidently make things up, a phenomenon sometimes called hallucination. For example, when asked for sources for a fact, an LLM may refer to nonexistent books and papers with titles that sound like the kinds of sources you would expect. Using an LLM in a professional context requires understanding the subject well enough to check what it’s saying.
How do human problem solvers work?
To reach a reasonable solution, expert problem solvers creatively think, struggle, and revise in the following ways.
- Understanding the problem
- Note what information is given and what is your goal (what is being asked)
- Making a plan to solve the problem
- Stuck? Carefully review similar problems and understand each step.
- Carrying out the plan
- On the wrong track? Revisit previous steps and modify your approach.
- Checking the solution
- Did you answer the question?
- Is your answer reasonable?
An LLM does not use these mathematical problem solving strategies. It relies on textual pattern recognition. Humans rely on making conceptual connections. Drawing a diagram, thinking about the mathematics of similar problems, looking for number or shape patterns, and sketching a graph are some of the ways human thinking differs from the output of an LLM.
How can you use LLMs to support your learning?
1. Write a useful prompt for help in solving a specific problem.
- Assign a role to the LLM. The LLM should act like a kind, thoughtful, experienced tutor.
- Specify the goal. State clearly that you don't want the solution, but rather guidance understanding basic ideas.
- Be specific. Provide details about the problem, the concept, or exactly where you're stuck.
- Explain your thinking. Explain your current work, even if it's not quite right. Ask the LLM to identify your mistake without giving away the answer.
- Ask follow-up questions. Learning is a process. Think about the response and prompt again.
- Connect to prior knowledge. Try to relate what you're learning to concepts you already know.
Here is the start of a prompt related to rational functions. Add some details about your own work and try it out.
Act like a kind, thoughtful, experienced tutor to help me find all the vertical asymptotes for the function f(x) = 2x2 + 3x- 2x2 - 4. I do not know where to start. Do not give me the answer or the solution. Help me know where to begin without moving too fast. Let me complete one step at a time.
Is the LLM response accurate? Continue prompting the LLM until you reach a problem solution which you are able to explain and which you are able to check with a reliable resource like the Desmos graphing calculator.
2. Deepen your understanding.
- Give a real-world example for how two quantities might behave like a rational function.
- How do equations of rational functions with holes differ from those with a vertical asymptote
3. Strengthen your problem solving skills.
- What information should I look for to find the domain of a rational function like f(x)=x2 - 42x + 1?
4. Ask the LLM for more practice problems.
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Give me some more problems to practice sketching rational functions. Do not give me any hints about solving the problems.
Solve problems on your own!
- You should have an overall plan to solve the problem.
- Be able to explain each step and check your answer.
* Always talk directly with your professors about their individual guidelines for using LLMs!
Related Readings
Kosmyna, N., Hauptmann, E., Yuan, Y. T., Situ, J., Liao, X. H., Beresnitzky, A. V., & Maes, P. (2025). Your brain on ChatGPT: Accumulation of cognitive debt when using an ai assistant for essay writing task.
Gerlich, M. (2025). AI Tools in Society: Impacts on Cognitive Offloading and the Future of Critical Thinking. Societies 2025, 15, 6.
Mollick, E. (2024). Co-intelligence: Living and working with AI. Penguin.
Vallor, S. (2024). The AI mirror: How to reclaim our humanity in an age of machine thinking. Oxford University Press.