Purpose
Turn "guessing the setter's thoughts" into a reusable, verifiable proposition research process.
The goal is not to claim knowledge of the setter's true psychology, but to infer the most evidence-supported testing intent based on the question text, curriculum requirements, question structure, solution paths, scoring points and similar questions from past years, and to transform the conclusions into identification skills that students can train.
Setup
No additional installation required.
Prioritize the past exam questions, answers, scoring rubrics and year/paper information provided by the user. When the material is incomplete, clearly state which conclusions are inferences, and do not present guesses as facts.
Core Principle
Try to ground every conclusion in this chain:
题面证据 → 结构识别 → 所需能力 → 典型错误 → 区分度 → 教学动作
When aimed at students, ultimately compress it to:
看到什么 → 想到什么 → 为什么这样想
Workflow
1. Establish the question's identity
First record:
- Year, paper, question number, question type, score
- Main knowledge points and related knowledge points
- Known answers or scoring points (if provided)
If the source of the question is unclear, do not fabricate the year, paper or official source.
2. Do a "bare question dissection"
Do not rush to solve it first; analyze the question text itself:
- What conditions are given? Which conditions are explicit, and which need to be translated?
- Does the question ask for evaluation, proof, existence, range, extremum, zeros, parameter discussion or structural judgment?
- Is a familiar structure wrapped in new symbols, a new context or new wording?
- Which condition is most likely to be the breakthrough? Which condition is most easily overlooked?
- In the information, which parts are core, and which may be used to create cognitive load?
3. Reconstruct the standard solution path
Give the most natural and most scorable main path, and explain:
- Why the first step should start this way
- The basis for each intermediate transformation
- Which step reflects core ability rather than mere calculation
- Whether there is a clearly longer path that students are prone to take by mistake
- If there are multiple solutions, compare what mathematical structure each one exposes
Do not just give the answer; focus on explaining "why you think of this from here".
4. Infer the propositional intent
Judge item by item from the following six dimensions:
- What is tested: What are the core knowledge, methods and mathematical ideas.
- Why it is packaged this way: Whether it tests transfer, reading, modeling, graphical transformation, symbol understanding or adaptation to unfamiliar contexts.
- The real breakthrough: What structure, condition or invariant excellent candidates will identify first.
- Preset error paths: Where students with weak foundations or poor strategies are most likely to lose points.
- Location of discrimination: Which step distinguishes students of different levels, and whether it distinguishes knowledge, strategy, computation or expression.
- Question gradient: If there are multiple sub-questions, how the later question uses, generalizes, reverses or abstracts the previous one.
Use evidence-based wording for statements of "propositional intent", for example:
- "From the gradient of the questions, it is more likely testing..."
- "The role of this condition shows that the focus of the problem is not just computation, but..."
- "If combined with the previous question, it can be inferred that the second question mainly tests..."
Avoid asserting without evidence that "the test writer just wanted students to...".
5. Build a student error map
Distinguish at least four types of point loss:
- Conceptual error: unclear definitions, properties, or applicable conditions.
- Recognition error: saw the condition but did not recognize the structure.
- Strategic error: chose an inefficient, unsustainable path or one that missed cases.
- Execution error: errors in calculation, signs, writing, case analysis, or boundary handling.
Give one teaching corrective action for each type of error, rather than just writing "careless".
6. Extract transferable rules for students
Translate teacher analysis into student language:
- What signal do you see?
- What should your first reaction be?
- Why is this reaction valid?
- Under what conditions can it not be applied mechanically?
Prioritize forming short rules rather than piling up mnemonics.
7. Generate minimal variants
Design at least 2 variant directions for each typical problem:
- Keep structure, change packaging: the core method stays the same; only the context, symbols, figures, or wording change.
- Change one key condition: force the original method to fail or branch, testing whether students truly understand the boundary of applicability.
If necessary, add: reverse questioning, parameterization, open-endedness, or cross-topic combinations.
For each variant, explain "what was changed, why it was changed, and what is intended to be tested"; do not make it harder just for the sake of difficulty.
Longitudinal Research
When the user provides past exam questions from multiple years on the same topic, conduct a longitudinal study:
- Build a sequence of questions by year.
- Uniformly label knowledge points, core methods, entry signals, contextual packaging, computational load, question levels, and discrimination points.
- Distinguish the "stable core" from the "changing shell".
- Identify recurring ability requirements and the ways of expression that change year by year.
- Summarize the abilities that future review should train, without directly predicting specific years.
Output focus:
多年没变的是什么？近年变化的是什么？学生应该练什么不变量？
Horizontal Research
When the user provides different paper versions or regional papers from the same year:
- Compare the common abilities tested in the same module
- Compare different packaging and entry designs
- Compare whether the source of difficulty is knowledge, recognition, computation, reading, or synthesis
- Identify changes that cannot be covered by a single "question-type routine"
Standard Output
When analyzing a single question, prioritize the following structure:
Question positioning
- Source:
- Module:
- Core knowledge:
- Core method:
Proposition structure
- Surface wording:
- Hidden structure:
- Key conditions:
- Breakthrough point:
Inference of proposition intent
- Main assessment:
- Purpose of packaging:
- Where discrimination lies:
- Evidence:
Candidate psychology and error map
- First sticking point:
- Typical misconception:
- Error type:
- Correction action:
Standard breakthrough path
Three sentences for the student
- See:
- Think:
- Because:
Variation directions
Research Table
Use unified fields for batch research:
年份｜卷别｜题号｜知识点｜核心方法｜入口信号｜关键条件｜命题意图｜典型错误｜区分点｜设问梯度｜变式方向｜同类题
Quality Rules
- Distinguish "facts", "question evidence", and "reasonable inference".
- Do not equate the standard answer path with the only correct line of thinking.
- Do not use "carelessness" or "didn't think of it" as the endpoint for the cause of an error; continue to probe the specific cognitive gap.
- Do not prioritize obscure solutions just to demonstrate technique.
- Do not claim stable question-setting patterns directly based on a small number of real exam questions.
- When drawing cross-year conclusions, state the sample scope and exceptions.
- Ultimately serve students' ability transfer, rather than creating the illusion of predicting exam questions.