Research InitiativeSpace to keep going.
A valid step does not need another question. When the math is progressing, ARIA stays quiet.
Valid step3x − 3 = 9ARIA watches without interrupting.
Method
How the tutor decides what to do.
Four stages, one kind of hint, and a policy that treats staying quiet as a decision. Everything here describes the live tutor as built for the October 2026 demonstration; the timing model behind the policy is documented on the ARIA-Pace page.
For the learner
A next step that is still yours.
ARIA supports mathematical thinking by giving students room to plan, check their work, and try again.
A small hint when it matters.
A wrong step or a request for help can trigger one hint that points at the next step, never the answer.
Hint from the demo“Write (x + 3)(x + 3) and multiply each term. What do you get?”
Keep the thinking yours.
Explain a plan, notice an error, and choose your next move. ARIA is designed to support that process rather than complete the problem for you.
The goalStudents plan, check their work, and revise their approach.
Method
Notice, verify, scaffold, step back.
The cycle stays on the step in front of the student. ARIA reads what they write, checks the mathematics, decides whether to say anything, and looks for the support to become unnecessary.
- 01Notice
The student works the problem out loud.
A plan, a revision, a pause, or a question gives ARIA more to work with than a final answer alone.
The student’s words stay central. - 02Verify
A symbolic engine checks the step.
Each step the student writes is checked for correctness before ARIA decides whether to speak. A correct step is never treated as stuck, and a wrong step is never treated as progress.
Correctness comes from the math, not from the student’s tone. - 03Scaffold
ARIA offers one hint, or none.
While the student is making progress, ARIA stays quiet and shows that it is watching. After a verified wrong step it gives one hint that points at the next authored step, or a short note without a hint while the risk is still below the profile’s bar. The student’s own answer is never given.
The student keeps ownership of the work. - 04Transfer
The support should fade.
ARIA looks for the student to begin planning and checking without being prompted.
Success means ARIA can step back.
Student says“Wait, I multiplied too early.”→ARIA noticesSelf-correction→ARIA asks“What will you check before trying again?”
Intervention design
One hint at a time, aimed at the next step.
Once ARIA has decided to speak after a verified wrong step, it gives one hint at a time. The student’s own answer is never given. Keeping each hint to one step is a design choice informed by work on cognitive load during problem solving (Sweller, 1988); it is a design influence, not evidence that ARIA works. Ideas this builds on.
- Built01
One hint after a verified wrong step
When a step is verified wrong, ARIA gives one hint that points at the next authored step of the problem that the student has not yet produced. The wording comes from a few templates and rotates, so consecutive replies differ: some are a plain question, some name the step, and some also name that step’s result. The student’s final answer is never given, and every reply is checked for it before it is shown.
“Try this: apply the power rule to 3x^4. What do you get?”
In the summit demo - Built02
A counter picks the next step, not a higher level
Each hint moves a counter forward, so the next hint points at the next authored step the student has not produced yet. When every authored step is done, the hint falls back to a general question. There is no fixed sequence of levels: nothing moves from a question to an explanation.
“What is the smallest useful next step?”
In the summit demo - Future work03
A three-level scaffold is an idea, not a feature
A gate with three levels (silence, a prompt with no mathematical content, an execution hint) could be built on the same checks. It has not been built or tested, no offline data can set its thresholds, and ARIA does not generate a worked example on a different problem. It needs a reviewed study with students first.
Design note only: docs/aria_pace/SCAFFOLD_LEVELS.md in the aria.kls repository
Intervention policy
Quiet does not always mean stuck.
ARIA decides whether to speak before it decides what to say. The state comes from verified correctness first; the student’s words add flags on top. In the live tutor, these are the situations the policy distinguishes.
Making progress
The math engine verifies that the step is correct or partially correct.
ResponseStay quiet and show a “watching” indicator. Interrupting productive work is treated as an error, not a missed opportunity.
Planning
The student restates the problem or sets up an approach before computing.
ResponseLet it run. No prompt is offered while a plan is forming.
Stuck
The math engine marks a step wrong, or the student stalls after a verified error.
ResponseARIA can offer one hint aimed at the next step the student has not produced. From the third attempt, a profile with a high bar may show a short note first and hold the hint until the risk is high enough.
Frustrated or confused
The student uses explicit words to express frustration or confusion. These language flags never replace the mathematical correctness check.
ResponseThe tone of the help changes. The correctness verdict does not.
Asking for the answer
The student directly asks to be told the result.
ResponseARIA declines to give the answer and gives a hint toward the first step. Every reply is checked so the answer cannot leak.
Finished
The student gives a correct final answer.
ResponseARIA asks one short reflection question and then stops prompting.
Privacy-aware interaction
Text and lightweight choices first. Voice is optional.
Most interactions are a tap, a selected step, or one short line of text. Voice input is never required. Students work in classrooms, shared rooms, and beside peers, and asking someone to talk through a problem out loud can be exposing rather than helpful. Speaking should be a preference the student chooses, not a condition of getting help.
Language signals
Different moments. Different questions.
Example interactionSelect a student message
Student says
“I know I have seen this kind of equation before, but I cannot tell which step comes next.”
Observed: uncertainty + help-seeking→
ARIA asks“Which step still feels solid? Start there, then name the first line where it stops making sense.”
Whether a step is right or wrong comes from the math checker. The student’s words are used only to notice uncertainty, frustration, and requests for help. ARIA does not diagnose a hidden mental state, ability, emotion, or disability.