A map of one geometry class (MATH 140) Β· the unit on drawing shapes and proving things
Can geometry studentswho fixing proofs they wrote themselvesdoing what use an AI that only points at the first weak stepwith what to find their mistakes before the quizwhy, while every step stays theirs and only the teacher gives gradeswhat stays safe?
DIGI 230 Β· Milestone 1 Β· client course MATH 140 The Geometry of Physical Space Β· unit: Constructions & Proof
How might MATH 140 studentsactor revising their own two-column proofsactivity use a hint-only AI tutor that points to the first unjustified stepcapability to find gaps in their reasoning before the graded quizpurpose, while every proof step stays the student's own and grading stays with the instructorprotected value?
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Paste your proof (at least 2 steps). The helper points at one step that needs a better reason and asks you a question. It won't do it for you, and it can be wrong. If a hint confuses you, mark it Not sure in the list below.
Paste the theorem and your own draft proof (at least 2 steps). The tutor points to the first step that needs a better reason. It won't write any step for you, and it can be wrong, so check every hint against your theorem list.
It points at one weak step. It asks you a question. It never writes a step for you.
Experts checked AI answers to hard proofs. Most AIs got less than 5% right. So the AI never grades.
The student who needs help is the worst at spotting a bad hint. So "Not sure" is a smart answer.
You write 2 steps first. In one study, kids who got answers did 17% worse later. Kids who got hints did not.
Some kids have no computer at home. They use a paper rule list. It counts the same.
A small hint helps your proof grow. A hint that is too exact is the answer. That is not allowed.
A student types "just tell me the next step" again and again. If the helper gives in, it ends up writing the whole proof. The student turns in a perfect proof they don't understand, and the teacher can't tell.
The helper only answers once you've written 2 steps. It gives one hint at a time and isn't allowed to write steps. Every hint is saved, so the teacher can see it.
No computer? Use the paper list of math rules and visit the teacher's office hours. It counts just the same.
Let AI write proofs, finish proofs or give grades. No AI when you draw, explain at the board, or take the quiz.
Do kids who use the helper do as well on the no-computer quiz as kids who use the paper list? We'd find out by splitting a class in half and comparing.
A student pastes only the theorem, with no draft, and keeps asking "what's the next step?" If the tutor gives in, it writes the proof one step at a time. The student hands in a clean proof they can't defend, and the instructor has no way to tell. Risk to test: does the hint-only rule hold up against repeated pushing?
The tutor only responds to a draft of at least 2 steps, names one gap per reply, and never writes a statement or reason. Every hint is logged, and the log goes in with the proof.
Non-AI alternative: a printed justification checklist (the unit's postulates and theorems) plus office hours. Any student can do Step 3 with no AI at all.
This project will not use AI to write, complete or grade proofs, and will not bring AI into compass-and-straightedge constructions, the whiteboard defense or the unit quiz.
Do students who use the hint tutor do as well on the no-device quiz as students who use only the checklist? Test: split one section in half for one unit and compare quiz proof scores. Carried to Milestone 2.
| Who | What they want | What could go wrong | The good part | What we still wonder |
|---|---|---|---|---|
| Students | Pass the class, and really get why proofs work | Leaning on hints so much they can't start a proof alone | Help at night, when the teacher isn't around | How many hints is too many before it's the AI's work? |
| The teacher | Fair grades, and students who can think for themselves | Grading a proof the AI secretly wrote | Can see every hint a student got | Is there time to check every Not sure hint? |
| Partners and tutors | Fair questions and useful help sessions | Asking about a proof the student didn't really write | Tutors can see where students got stuck | Should tutors see the hint list too? |
| Who might be left out | Kids with no computer at home, and kids who use a screen reader (the helper can't see drawings) want the same help as everyone | Falling behind kids who use the helper | The paper rule list keeps it fair | Can the paper way be as fast as the helper? |
| Who gets hurt if it goes wrong | Students (bad habits, cheating worries) and the teacher (unfair grades) want clear rules | A wrong hint sends a student the wrong way | Hints-only rules protect learning | The teacher is responsible for wrong hints. Will kids say "Not sure" honestly? |
| Group | Who | Interests | Risks | Benefits | Concerns | Unresolved questions |
|---|---|---|---|---|---|---|
| Users | MATH 140 students, mostly art and design majors meeting the math requirement assumption | Pass the course; understand why a proof works, not just copy one | Leaning on hints until they can't start a proof alone | Feedback at 11 p.m., not only in office hours | Being accused of cheating for using an allowed tool | How much hinting is too much before it counts as the AI's work? |
| Decision makers | MATH 140 instructor; SCAD math faculty who set the syllabus AI policy | Valid grades; students who can reason on their own | Grading work that was quietly AI-written | A log that shows how each proof was revised | Extra time: reviewing disputed hints within 48 hours | How many disputed hints per week can one instructor review? |
| People affected | Proof partners; SCAD Learning Center tutors assumption | Fair critique; useful tutoring sessions | Partners questioning proofs the author didn't really write | Tutors see where students got stuck | Tutoring demand shifts in unknown ways | Should tutors see the hint log too? |
| May be excluded | Students without a reliable device or internet at home; screen-reader users, because the tutor can't read diagrams | The same help as everyone else | Falling behind classmates who use the tool | The non-AI checklist keeps Step 3 open to them | Their voice isn't in the tool's design | Can the checklist be made as fast and useful as the tutor? |
| May carry the risk | Students (integrity cases, weaker skills); the instructor (grade validity) | Clear rules on what's allowed | A wrong hint sends a student the wrong way evidence: Petrov et al. 2025 | Safeguards cut the learning loss evidence: Bastani et al. 2025 | Responsibility for a wrong hint: the instructor, who adopts the tool and reviews disputed hints | Will students mark "Not sure" honestly, or just accept every hint? |
The helper only reads and writes words. It can't do math calculations, can't see drawings, and can't prove anything is right. Every answer it gives is saved below, so you and your teacher can see it.
The tutor is a text-only language model. It gives hints in words; it doesn't calculate, see drawings or prove anything is correct. Every reply below is logged so the student and instructor can see what the tool did.
| Run | Time | Model | Reply time | Your verdict | Hint wrote a step? |
|---|---|---|---|---|---|
| No runs yet. Every reply from Proof check is logged here. | |||||
Hand the map to another team with no explanation. Tick what they can do unaided.Show the map to someone who has never seen it, and don't explain it. Tick what they can figure out alone.
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We built these 5 steps from the course description, not the real class plan, so they're our best guess until we check with the teacher.
The unit sequence is modeled on the MATH 140 catalog description (proofs, Euclidean constructions, right-triangle theorems, circles, the Golden Ratio). Its steps and roles are assumptions to confirm against the MATH 140 syllabus or with the instructor. Evidence tags: evidence assumption proposed test constructed.