The problem — teacher vs 22 students

The situation

A math teacher has 22 students in class. Some have their multiplication tables down cold; others mix up signs; others calculate fine until parentheses appear.

The teacher wants each student to get exactly the task that is right for them:

• not so easy it’s boring,
• not so hard it feels like “I’m stupid, I don’t get anything.”

The problem: the teacher cannot see inside the student’s mind. They only see answers — correct / incorrect. From those tiny signals we must infer what the student actually knows.

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flowchart LR
T[Teacher] -- "20-25 students" --> C[Class]
C --> S1[Student 1]
C --> S2[Student 2]
C --> S3[...]
C --> S22[Student 22]
S1 -.-> H1[hidden state]
S2 -.-> H2[hidden state]
S22 -.-> H22[hidden state]
T -- "sees only" --> O[right / wrong]

The teacher runs 22 “black boxes” at once — each learner’s state is hidden; only outcomes are observed.

Cost of the status quo

From 14 MATx team interviews:

• assembling a differentiated worksheet — 60–75 minutes;
• grading work + descriptive feedback — ~2 hours;
• ~10 hours per week on those two tasks alone.

Meanwhile 25% of Estonian basic-school graduates fail the math exam.

Why classical AI tools don’t close the gap

ChatGPT-style tools:

• hallucinate on math — mix signs, slip on arithmetic;
• miss the student’s level — weak learners dragged to elementary tasks, strong ones jumped years ahead;
• give teachers no explanation — teachers still verify everything by hand.

The niche MATx fills is a teacher-centered system built on micro-skills (“mikrooskused”) with descriptive feedback in Estonian.

The main formula we will build

Everything in the chapters ahead boils down to one number per (student, skill) pair:

$$P(L) = \mathbb{P}(\text{student has mastered the skill})$$

And one update rule — Bayes’ formula:

$$P(L \mid \text{correct}) = \frac{P(L) \cdot (1 - P(S))}{P(L) \cdot (1 - P(S)) + (1 - P(L)) \cdot P(G)}$$

If that looks scary — don’t panic. In the next chapter we unpack it: $P(S)$ is “knew but slipped”; $P(G)$ is “didn’t know but guessed”; and that’s the whole story.

What a good adaptive system does

1. Knows each student at micro-skill granularity, not a single “overall level.”
2. Explains to the teacher why this task fits this student now.
3. Sees the whole class in one view.
4. Does not author tasks with AI — the teacher curates problems; AI only selects.
5. Saves hours — the main hackathon metric.