1. Read for intent
The Word document supplied the syllabus objective, mathematical language and question evidence. Each item was analysed for the concept, representation and likely misconception it could reveal.
Complex roots of quadratic equations
What is groundbreaking here?
The discriminant, exact algebra and Argand locations are linked in one progression. Non-real roots become interpretable points with symmetry and magnitude, so the quadratic formula is not an isolated manipulation.
The AI did not merely generate answers. It translated a static assessment document into an instrumented learning progression: learners predict, attempt, receive misconception-specific feedback, open a visual tutorial, retry, and leave semantic evidence that a teacher can inspect.
The six-stage learning journey
- Pure imaginary rootsSolve z² + 3 = 0.
- Quadratic formulaSolve z² − z + 1 = 0.
- Complex coefficientSolve z² + iz − 7 = 0.
- Leading i coefficientSolve iz² + 3z − 2i = 0.
- Square a complex numberThe number z satisfies z² = 3 − 4i. Find both values.
- Reverse engineerWhich quadratic has roots 2+3i and 2−3i?
From a Word document to an expert learning experience
2. Add a learning-design prompt
Build from negative discriminants to exact complex roots and then plot the pair. Preserve plus-minus structure, show i squared reasoning, handle complex coefficients carefully, include reverse engineering from roots to a quadratic, and diagnose missing i, denominator and sign errors.
3. Build for the SLS frame
The payload is self-contained and responsive, with touch targets, keyboard access, read-aloud support, closed overlays on launch and no dependency on a network library.
4. Preserve proven xAPI know-how
The supplied reference ZIP was treated as a contract. lib/xapiwrapper.min.js, lib/xAPI.js and the injected xAPI head block were copied byte-for-byte; only the learning payload was redesigned.
How a teacher can use it
Pause after the discriminant is found and ask learners to sketch where the two roots should lie before completing the exact calculation.
- Use stages 1–2 for diagnosis before formal teaching.
- Ask students to narrate what changes in the visual model before they calculate.
- Use the tutorial and retry trail as evidence of self-correction, not just the final score.
- Upload the accompanying ZIP directly as an SLS interactive resource when xAPI evidence is required.
Quality evidence
Every activity was checked at desktop, mobile and narrow-phone sizes; incorrect-feedback, visual-tutorial and correct-retry paths were exercised; and the package validator confirmed six stages, root-level ZIP entries, offline assets and byte-identical xAPI integration.
MathematicsComplex NumbersAI GeneratedSLSQuadratic Equations