Worked example

A calculus tutor for someone who does not yet understand

Consider an application that explains derivatives, proposes an exercise, offers a hint and finally shows the solution. The flow looks complete. However, if the person gets the exercise wrong after reading the explanation and still does not understand the solution, they reach a dead end. The application delivered content, but it did not produce progress.

From a feature request to the circumstance

Weak formulation. As a student I want to receive hints so that I can solve derivatives. The role is generic, the hint already prescribes the response, and the outcome does not distinguish understanding from mechanical progress.

Main Job Story. When I have read an explanation and I still do not know which rule to apply, I need to identify the prior concept I do not understand, so that I can resume the exercise without depending on being shown the solution.

Recovery Job Story. When I see the solution and I still do not understand why the next step was chosen, I need to reconstruct a single decision using a different representation, so that I can explain the rule in my own words.

Both stories belong to the same higher-level Jobs to Be Done: developing enough understanding to solve an equivalent exercise with growing autonomy. They describe different blockages, however, and may call for different responses.

Diagnosis from the manifesto

Principle	Problem observed
Progress	The system measures steps consumed, not understanding achieved.
Experience	The person ends up frustrated and with no route to recovery.
Complexity	The explanation preserves the expert's model instead of rebuilding the concept.
Interface	Numbers or stages without meaning add incidental learning.
Trust	The final solution is presented as closure, even though understanding is still absent.

Evidence that completes the Job Story

Element	Observation
Current behavior	The person asks for a hint, then the solution, and still cannot decide which rule to apply.
Obstacle and anxiety	They do not identify the missing prerequisite and are afraid to move on without understanding.
Evidence of success	They can choose and explain the rule in an equivalent exercise with less help.

Redesign of the journey

1. Detect the type of blockage: concept, notation, prior operation or interpretation of the problem statement.

2. Reformulate using a different representation, rather than repeating the same explanation with more words.

3. Check an earlier micro-skill through a brief, diagnostic question.

4. Offer a worked example step by step, with one decision at a time and in the student's language.

5. Ask them to explain the reasoning or complete an equivalent step before moving on.

6. Always keep a route to go back, switch explanation or ask for human help.

What stays deterministic and what may use AI

Layer	Responsibility
Deterministic	Sequence of states; mathematical validation; mastery of prerequisites; record of attempts; progression rules; prevention of dead ends.
AI-assisted	Reformulating an explanation; generating an analogy; classifying the blockage; adapting the tone; proposing an equivalent exercise within validated limits.
Human control	Letting the student or tutor choose another route, review the history and correct a mistaken inference by the system.

Success criterion

The goal is not for the student to reach the end of the sequence. It is for them to be able to solve or explain an equivalent exercise with less help. That difference changes the interface, the logic, the measurement and the use of AI.