STEM Guidance & Problem-Solving

It’s tempting to ask AI for answers in STEM—but learning happens when you use it for guidance, not solutions.

When working through math, physics, chemistry, or engineering problems, your goal should be learning how to think like a problem-solver. This page shows how to use AI so it helps you grow your analytical skills instead of replacing them.

By the end, you’ll know how to craft prompts & follow workflows that lead to deep understanding, not just correct answers.

1. Ask for Hints / Next Steps Instead of Full Solutions

What it is: Instead of posting a whole question and expecting AI to solve it, ask for partial guidance—hints, strategy, or which principle applies.

How you can use it:

Prompt: “I’m stuck on this algebra/derivative/integration question. What would be a good first step to try?”
Prompt: “List possible methods to solve this problem (e.g. substitution, graphical approach), then I’ll pick one.”
After you try something, send what you did and ask: “Here’s what I tried; where did I go wrong?”

Example Prompt:

Problem: The integral of x^2 * ln x with respect to x.

Instead of giving me the full solution, can you suggest a strategy and outline the steps I should attempt? Then I’ll try it and share what I got.

ChatGPT is not perfect at handling very complicated integrals. If your integral is complex, consider checking it with Wolfram Alpha to verify. (See the Tools section for details.)

2. Use Chain-of-Thought for Understanding

What it is: Ask the AI to walk through reasoning step by step. Use these steps to check your own reasoning or to see where you might make mistakes.

Example:

Walk me through how you’d solve this step by step, explaining each decision.

Compare AI’s reasoning with yours and see differences.
If AI or you skip something, pause and explore that part more deeply.

3. Interactive / Incremental Problem Solving

What it is: Break a tough problem into parts; solve it piece by piece with AI’s help.

Example:

Let’s divide this problem into sub-problems: identify what info is given, draw any diagrams, simplify, then solve.

After each sub-part, check correctness, then move on.
For physics or engineering, sketch diagrams, units, constants, then check with AI.

4. Use AI Tools & Simulations

What it is: Use AI to visualize, simulate, or test what you’re doing—for example, graphing functions, running physics simulations, or dynamically altering parameters.

Example:

Create a plot of this function for x from 0 to 10; highlight where it crosses the x-axis.

ChatGPT can use Python to draw complex graphs.
Use free simulation tools and ask AI to explain what changes if you tweak a parameter.
For chemistry: molecular geometry; for engineering: forces, tension, etc.

5. Error Analysis & Feedback Loop

What it is: Use AI to check your work, explain mistakes, and then generate similar problems.

How you can use it:

After solving, show your work: “Here’s how I solved it. Please check for mistakes and suggest corrections.”
Then ask for “two to three similar problems, slightly harder, so I can practice.”

6. Prompts & Templates You Can Reuse

Here is problem X. Could you guide me through solving it without giving the full answer, but make sure to explain why each step works?

I want to understand concept Y in physics better. Please explain it and give me three practice problems with increasing difficulty.

Create a flowchart or checklist for solving integration (or linear algebra / circuit analysis) problems.

7. Apply it!

Imagine you have this question:

“A tank is filling at rate dV/dt = k * sqrt(V), where V is volume. Solve for V as a function of t, given initial volume V₀.”

You could use this workflow:

Ask what kind of differential equation this is.
Ask what substitution or separation of variables might help.
Try solving based on the hint; send your attempt.
Ask AI to review your steps.
Generate a similar equation (maybe with different exponent) to practice and test yourself.

8. Why This Matters

You build problem-solving skills instead of becoming dependent.
You understand underlying principles, not just memorized steps.
It boosts confidence when you can work through challenging problems and see why things hold (or don’t).

9. Summary

In STEM subjects, treat AI like a tutor who asks questions, provides scaffolding, and nudges you forward—not like a calculator that does all the work. Use hints, reason step by step, simulate, check mistakes, and then practice more. That’s how mastery happens.