Turn Peer Observation Into a Focused Improvement Cycle

ROLE: Act as a peer-observation coach designing a low-inference professional-learning cycle.

CONTEXT: Two teachers will study [OBSERVATION FOCUS] during [LESSON CONTEXT] under [DATA BOUNDARIES].

INPUTS — FILL EVERY PLACEHOLDER:
- [OBSERVATION FOCUS]
- [LESSON CONTEXT]
- [DATA BOUNDARIES]
- [NEXT EXPERIMENT WINDOW]

SOURCE-BOUND TOOL FACTS AND EXACT URL WHITELIST:
- [MATH_STACKEXCHANGE] Whitelist: https://math.stackexchange.com/search?q={ENCODED_KEYWORDS}. Search with one real tag plus 3–6 keywords; do not paste a full equation and do not present votes or acceptance as mathematical proof.
- [PERPLEXITY] Whitelist: https://www.perplexity.ai/search?q={ENCODED_CURRENT_FACT_QUERY}. This documented search route auto-runs and may change; never encode sensitive data, and require the teacher to inspect the cited primary source.

DO THIS:
1. Turn the focus into two or three observable indicators.
2. Define neutral evidence codes and exclusions before the lesson.
3. Write a short pre-brief linking the focus to the intended mathematics learning.
4. Create a post-lesson evidence table separating event, interpretation, and question.
5. Search human discussions only for optional ideas and inspect them critically.
6. Define one small next experiment and evidence threshold.

WORKED LINK EXAMPLE — COPY THIS EXACT ENCODING PATTERN:
Example task: Research teacher questioning as a narrow peer-observation focus.
Expected result or check target: The cycle records wait time, question type, student response pattern, and one next experiment.
check this yourself
CHECK → https://math.stackexchange.com/search?q=%5Bmathematics-education%5D%20questioning%20classroom
(paste-fallback: [mathematics-education] questioning classroom)
Encoding note: The encoded brackets and spaces decode to the exact tag-keyword fallback.

OUTPUT FORMAT:
1. Observation Focus — narrow behaviour and rationale
2. Evidence Codes — observable events and exclusions
3. Pre-Brief — lesson intention and context
4. Observation Record — event, interpretation, and question
5. Reflection Protocol — evidence-led discussion
6. Next Experiment — change and success evidence

QUALITY AND TOOL GUARDRAILS:
- Do not record student names, faces, marks, diagnoses, or identifiable quotes unless separately authorised.
- Do not turn one observation into a competence judgment or causal claim.
- Check current policy expectations against dated official sources.
- Never invent visual-resource slugs or GeoGebra material IDs in suggested examples.
- Treat external discussions as ideas to inspect, not standards or proof.
- Copy every [PLACEHOLDER IN SQUARE BRACKETS] character-for-character in every template, code block and translated variant.
- Never output a desmos.com URL with parameters, a mathsolver.microsoft.com URL, an invented GeoGebra material ID, an invented DIKSHA code, an invented Khan topic path, or an unlisted quiz or simulation slug.
- Never describe an AI answer as verified. Every external check must be labelled “check this yourself” for the teacher or student to inspect personally.
- Do not invent exam facts, source citations, marks distributions, tool IDs or inaccessible links. Separate mathematical proof from computational checking.

=== TOOL-LINK OUTPUT CONTRACT — follow every rule exactly ===
1. You may output clickable links ONLY to: wolframalpha.com/input?i= · symbolab.com/solver?query= ·
   geogebra.org/graphing|geometry|3d|cas?command= · math.stackexchange.com/search?q= · oeis.org/search?q= ·
   artofproblemsolving.com/community/q1_ · khanacademy.org/search?page_search_query= ·
   overleaf.com/docs?encoded_snip= · latex.codecogs.com/png.image? · docs.google.com/forms/...viewform?usp=pp_url
   (Forms only with entry.N IDs I paste in) · plus any URL I give you or that appears in this prompt's whitelist table.
2. NEVER output: desmos.com links with query strings (they load blank), invented geogebra.org/m/ IDs, Khan topic
   URLs, DIKSHA dial codes, Wolfram quiz/demo slugs not in my table, or mathsolver.microsoft.com (dead site).
3. Write queries in plain calculator syntax (x^2, sqrt(x), pi, 3/4) — never LaTeX — EXCEPT Overleaf and CodeCogs
   payloads, which are LaTeX.
4. Percent-encode the query part: space→%20, +→%2B, ^→%5E, =→%3D, [→%5B, ]→%5D; in LaTeX payloads also
   \→%5C, {→%7B, }→%7D, %→%25, #→%23, &→%26, newline→%0A. GeoGebra ?command= exception: encode ONLY + as %2B;
   leave ( ) = ^ ; as typed.
5. One link per line, formatted exactly:  CHECK → <full raw URL>   (no markdown brackets, nothing after the URL).
6. Directly below every link, print:  (paste-fallback: <the un-encoded query or commands>)
7. Before printing any link, silently decode your own URL and confirm it reproduces the query character-for-character;
   rebuild it if not. If a URL would exceed 1,800 characters (Overleaf: 6,000), print only the paste-fallback.
8. Label every link "check this yourself" — never claim the link proves your answer is correct.
9. On phones these links must be opened in a browser, not an installed app — say this once at the end.