Blame for docs/project.prd

The app is written from scratch. Kept from the current app:
- the exercises (app/math_algebra9.json)
- the drawing board (static/math-board.js, static/board-math.js, static/vendor/mathlive)



Glossary:

- skill (מיומנות): a specific topic like פירוק טרינום
- exercise (תרגיל): a qustion on a certain topic, can be either open ended or multiple choice
- lesson (שיעור): set of skills like טכניקה אלגברית 1
- quiz (בוחן): a test on a single lesson, can be retaken, best grade wins. each retake draws new questions.
  it is the only quiz type (no one-time summary quiz); its best grade is the lesson's grade
- exrcise test (מבחן תרגול): a timed test on a set of a lessons, can be retaken, best grade wins
- simulation test (מבחן סימלוציה): a timed test on a set of a lessons, one time only
- test: real life test, appears in app as a date + the lessons it covers + number of questions and time limit
  (default 12 questions, 90 minutes). set by the teacher



Goals:

The app helps the student to:
1. master the skills - done by the path
2. get ready for the real life tests - done by the test countdown plan



Goal 1: Mastering the skills (the path)

Each skill goes through these stages:
1. worked example: the student sees a full solution and is asked "why this step?"
2. faded examples: steps are removed one at a time, the student fills them in
3. practice: immediate feedback that names the specific mistake.
   after a wrong answer, the student gets a similar question (not the same one)
4. mastered: 3 correct answers in a row, without hints, across at least 2 different days.
   a mastered skill stays mastered (math does not rot)

Skill states:
- not started
- learning
- mastered

Path rules:
- all lessons are open: the student can enter any lesson at any time, in any order



Goal 2: Getting ready for the real test

The teacher sets the test date and the lessons it covers.
The app plans backwards from the date:

- until 9 days before: finish the path for all the covered lessons
- 9-7 days before: exercise tests (מבחן תרגול) - timed, mixing all the covered lessons.
  each result points back to the weak skills in the path (see "Exercise tests" below)
- final week: simulation test (מבחן סימלוציה) - required. one attempt, open until the test day,
  same length and timing as the real test, feedback only at the end
- last days: targeted review of the skills that failed in the simulation,
  light mixed review the day before

Exercise tests:
- assigned by the app: created automatically when the teacher sets the test,
  and placed on the student's countdown
- the teacher can also send one to the class as an assignment
- the student can start or retake one at any time. each retake draws new questions, best grade wins
- same length and timing as the simulation test, feedback only at the end
- weak skill: a skill in "learning" state, or one failed in a previous exercise test
- 2 exercise tests, then the simulation test:

  | days before the test | step                       | weak skills | other covered skills |
  |----------------------|----------------------------|-------------|----------------------|
  | ~9                   | exercise test 1            | 60%         | 40%                  |
  | ~7                   | exercise test 2            | 30%         | 70%                  |
  | ~5                   | simulation test (required) | -           | like the real test   |
  | 4 -> 1               | review the skills that failed in the simulation                         |

- if the test is set less than 9 days ahead, keep the same order with shorter gaps

Readiness meter (per test):
- % of the covered skills that are mastered
- recent exercise test grades
- simulation test grade



Student Screen:
- home
  - my assignments (המשימות שלי): homewords submitted by the teacher
  - remider on the upcoming test: days left, readiness meter, today's task (from the closest test)
  -

- path
- grades
- collection



Teacher Screen:
- assignments
  - give an assignment. load it from:
    - the computer (file upload)
    - the app's drawing board (math-board.js)
    - a picture (camera)
  - check assignments: review each student's submitted answers and give feedback/grade
- tests
  - set a real life test: date + the lessons it covers
  - see who took the required simulation test
- class heat map
  - rows: students, columns: skills
  - each cell is colored by the skill state (not started / learning / mastered)
  - period tabs: sep-dec, jan-jun
- student lesson coverage
  - rows: students, columns: lessons
  - each cell shows how much of the lesson the student covered: % of its skills mastered + the best quiz (בוחן) grade
  - period tabs: sep-dec, jan-jun