Diagnostic mathematical assessment records

Mathematical statement

Here a diagnostic record consists of an item identity, expected mathematical result, observed synthetic response and judgment rule. The rule may label whether the response matches the expectation, but one response cannot establish a real student’s ability, error cause, personality or learning outcome.

Representative formula (exact TeX)

D(q,r)

Assumptions

• All exercise responses are synthetic; no real learners, personal data or behavioral records are used.
• Judgment codes describe only agreement with the explicit mathematical rule and make no psychological or causal interpretation of an incorrect result.

Symbol scope

• D — rule-based diagnostic record
• q — item and expectation
• r — synthetic response

Intuition, definition, and misconceptions

A replayable record must retain the item, expectation, response and rule. Missing fields license only an incomplete-record label.

Integer sums, fraction equivalence and substitution values can be recomputed exactly. The judgment code only distinguishes agreement from disagreement with the rule’s expectation.

Broader educational inferences would require multi-item evidence, teaching histories and valid measurement models. This slice establishes none of those claims.

Do not infer a learning difficulty, missing concept or ineffective teaching from one incorrect response.

Adopted derivation guide

The original MKO is retained. The guide has its own append-only revision and verification boundaries, not a new Lean proof.

Prerequisites

• Proposition — Expectations and judgments can be stated as true-or-false propositions.
• Counterexamples and domain eligibility — A counterexample can refute a universal assertion without diagnosing a person’s traits.
• Mathematical representation — Compare responses and expectations under the same representation and interpretation rules.

Verification boundary

Synthetic rule classification is neither a diagnosis of a real student nor evidence of learning effectiveness.

not_formalized

This does not mean the content is false; it means no replayable computational or formal evidence is registered yet.

Next obligation

Add multi-item scales, validity, reliability, human review and privacy governance while keeping them separate from single-item rule records.

Same-source structured data

This page and the interactive view use the same object and existing language edition; this adds no proof or human review.