How a Simple Algebra Problem Turned AI Into a Detective for Reasoning
In 2023, I was in the faculty lounge, sipping lukewarm coffee between classes, when the topic of AI came up. Every teacher in the room had an opinion, and nearly all of them circled back to the same concern: cheating, cheating, and more cheating. To my colleagues, tools like ChatGPTA generative AI assistant created by OpenAI that can answer questions, write, brainstorm, explain ideas, and help with everyday tasks. More were little more than answer machines, ready to hand students the work without the thinking.
I saw it differently then—and I still do now. Maybe the problem isn’t AI. Maybe it’s how we ask questions and structure learning. If AI can produce answers in seconds, the real challenge for educators is to design questions where the reasoning is the star of the show.
As a high school math teacher, I decided to test this idea with a simple multi-step equation:4(3x – 5) = –60
The learning objective wasn’t just “get x.” It was:
Students will be able to solve a multi-step equation with parentheses, explain each step, and investigate alternate solutions.
Turning AI into a Reasoning Detective
Instead of letting AI spit out an answer, I prompted it to act like a detective—only revealing the next clue when the student provided both a step and a reason.
Here’s what that interaction looked like:
AI: “What’s your first step, and why?”
Student: “Multiplication… I don’t know why.”
AI: “Look at 3x. What does the 3 mean when it’s next to x?”
Student: “It means 3 times x.”
AI: “Exactly. Can you reword that so another student could understand it?”
The AI doesn’t move forward unless the reasoning is solid. A correct number without an explanation is treated as incomplete—no free passes.
Why This Works
- Slows down guessing. Students can’t skip to the answer—they have to justify.
- Builds math vocabulary. They explain operations in their own words.
- Encourages metacognition. Rewording forces them to think about how they think.
- Opens space for alternatives. Once they find one method, they can explore others.
A Quick Example for Teachers to Try
Here’s a condensed “Detective Mode” promptThe instruction, question, or request a person gives to an AI system. The better the prompt the better the outcome. More teachers can copy into ChatGPT:
Prompt: You are a math reasoning detective. Your job is to help the student solve the equation 4(3x – 5) = –60, but you can only reveal one step at a time. After each step, ask the student for their reason in words. If they answer correctly, ask them to reword it for clarity. Do not reveal the final answer until all steps and reasons are complete. If a student gives a numerical step without a reason, ask for the reasoning first.
I encourage teachers to adapt this idea, experiment with it, and create their own lessons. Try it with your students and see where it leads.
The Bigger Picture
If we introduce this type of AI use early, chatbots will automatically be seen as thought companions—partners in thinking, not just answer keys. Students will grow up seeing AI as a coach for reasoning, logic, and problem-solving.
They’ll stop memorizing for the test and start thinking for life.
I welcome comments, questions, and experiences from other educators who are experimenting with AI in the classroom. Let’s share ideas on how to make reasoning—not just answers—the goal.
List of terms
- ChatGPT
- prompt
