# Analytics map — Completing the Square

## Learning design

- **Outcome:** Solve `x² − 4x − 7 = 0` by completing the square and explain how the exact roots correspond to the graph’s x-intercepts.
- **Architecture:** Existing guided worked example and graph exploration, extended with four diagnostic checkpoints and immediate explanatory feedback.
- **RAT intent:** Amplify. The graph links the symbolic solution to the roots, while the checkpoint evidence identifies the precise reasoning step needing support.
- **Authoritative score source:** The final selected response in the four diagnostic checkpoint cards.
- **Completion trigger:** The learner attempts all four checkpoints, records final confidence, and selects **Complete and save learning**.

## Evidence map

| Evidence | Meaning | Learner use | Teacher use | Stored representation |
|---|---|---|---|---|
| Checkpoint responses | Understanding of completed-square form, ± roots, exact solution and graph meaning | Receive specific feedback and revise | Locate the algebraic or graphical misconception | Stable item and option IDs; first/final response; correctness |
| Revisions | Change after feedback | See improved reasoning | Distinguish an initial error from an unresolved one | Revision count per item |
| Hint use | Scaffolding requested in the worked example or diagnostic | Monitor independence | Target support level | Step/item ID and hint count |
| Confidence before/after | Self-assessment shift | Compare confidence with performance | Identify confidence–accuracy mismatches | 1–4 codes only |
| Graph exploration | Whether the learner tested roots, vertex or other regions | Connect `y=0` to solutions | See whether the graph was used as evidence | Bounded move count and semantic region codes |
| Completion and score | Final current performance and coverage | Confirm submitted result | Review achievement with process evidence | Score/max, progress, success and item records |

## Misconception taxonomy

- `missing-square-compensation` — does not compensate for the `+4` introduced by `(x − 2)²`.
- `reverses-linear-term-sign` — chooses `(x + 2)²`, producing `+4x`.
- `omits-negative-square-root` — includes only the positive root branch.
- `assumes-single-quadratic-root` — assumes a quadratic must have one root.
- `moves-constant-with-wrong-sign` — isolates `x` using the wrong sign.
- `omits-square-root` — uses `11` instead of `√11`.
- `confuses-roots-with-vertex` — treats the vertex as the pair of roots.
- `confuses-x-and-y-intercepts` — reverses the conditions `y=0` and `x=0`.

## Feedback and privacy

The SLS-visible `feedback` contains a visual teacher report with score, accuracy, completion, process evidence, misconception clusters, question-by-question results and targeted teaching moves. The payload stores no raw keystrokes, free-text responses, copied learner identity or launch authentication.

## Reset and recovery

Meaningful evidence is saved after answers, hints, confidence choices, graph changes, completion and pause/exit. A reset clears the activity’s local evidence and the compatible transport cache before a new run, preventing stale marks from being reinstated. A valid prior snapshot can be restored without replaying old events.