Explain Concepts (explain-concept)
Make an abstract concept as easy to understand as plain language. The core idea is to bridge with what the student already knows, rather than re-copying the definition.
Triggers
- The user asks "what does XX mean / how do I understand it / why is it like this"
- The user wants to understand the how and why of a formula, theorem, or definition
- The user hits a knowledge point they can't explain clearly while previewing / reviewing
Teaching Flow
Step 1: Confirm the object and level
- Make clear the knowledge point to explain (if needed, ask where it comes from / which subject)
- Ask "where are you in your learning / what feels off", and set the depth accordingly
Step 2: Three-layer explanation
Organize by "what it is → why → how to use":
- One-sentence definition: explain what it is in plain words (intuition first, then rigorous statement)
- Analogy / diagram: use a familiar real-life example or a clear diagram to make the abstract concrete
- Why it holds: explain the reason or derivation behind it, not just "remember it"
- How to use / common traps: give typical usage, applicable conditions, and the traps people most often fall into
Step 3: Easy-to-confuse comparison
- List nearby, easily-confused concepts and clarify the difference with a comparison table
(e.g., prime vs composite; displacement vs distance)
Step 4: Self-check
- Give the student 1-2 true/false or fill-in questions to answer in their own words
- Correct restatement → confirm mastery; deviation → re-explain the specific gap
Style
- The first time a term appears, follow it with a plain-language explanation before the formal definition.
- Prefer real-life analogies, diagrams, and graph-number fusion; avoid jargon stacking.
- After giving a formula, explain the meaning and unit of each symbol.
- Don't go beyond the syllabus: decide how deep to go by the student's grade; don't overload at once.
Graph-Number Fusion: Draw a Picture Instead of Text Alone
- For functions, geometry, trigonometry (e.g., quadratic graphs, monotonicity, axis of symmetry, extrema, circles, triangles), first draw a coordinate graph with the script:
node scripts/plot.mjs fn --fn "-(x^2)+4x" # explicit function
node scripts/plot.mjs impl --impl "x^2+y^2-9" # circle/ellipse/hyperbola/line
node scripts/plot.mjs pts --pts "0,0 4,0 4,3" # triangle/polygon/segment
- Mark key points on the graph (vertex, axis of symmetry, axis intersections, center/radius, etc.), and write next to it how these points are computed.
- To save an image for the user: add
--svg ./out.svg.
- If the environment has no Node, fall back to ASCII/text sketch, but prefer the script for accuracy.
Output Template
【One-Sentence Understanding】
XX is <plain words>
【Analogy】
<real-life analogy or diagram>
【Why It's Like This】
<reason / derivation>
【How to Use · Common Traps】
- Applicable conditions: <...>
- Most common traps: <...>
【Easy-to-Confuse Comparison】
| Concept | Difference |
| ... | ... |
【Self-Check】
<1-2 small questions for the student to answer in their own words>
Notes
- If the concept depends on prerequisite knowledge, briefly review the prerequisite first, then get to the point.
- After explaining, proactively ask "is there any sentence you didn't get", and invite follow-up questions.
1---2name: explain-concept3description: Explain Concepts (explain-concept)4---56# Explain Concepts (explain-concept)78Make an abstract concept as easy to understand as plain language. The core idea is to bridge with **what the student already knows**, rather than re-copying the definition.910## Triggers1112- The user asks "what does XX mean / how do I understand it / why is it like this"13- The user wants to understand the how and why of a formula, theorem, or definition14- The user hits a knowledge point they can't explain clearly while previewing / reviewing1516## Teaching Flow1718### Step 1: Confirm the object and level19- Make clear the knowledge point to explain (if needed, ask where it comes from / which subject)20- Ask "where are you in your learning / what feels off", and set the depth accordingly2122### Step 2: Three-layer explanation23Organize by "what it is → why → how to use":24251. **One-sentence definition**: explain what it is in plain words (intuition first, then rigorous statement)262. **Analogy / diagram**: use a familiar real-life example or a clear diagram to make the abstract concrete273. **Why it holds**: explain the reason or derivation behind it, not just "remember it"284. **How to use / common traps**: give typical usage, applicable conditions, and the traps people most often fall into2930### Step 3: Easy-to-confuse comparison31- List nearby, easily-confused concepts and clarify the difference with a comparison table32 (e.g., prime vs composite; displacement vs distance)3334### Step 4: Self-check35- Give the student 1-2 true/false or fill-in questions to answer in their own words36- Correct restatement → confirm mastery; deviation → re-explain the specific gap3738## Style3940- The first time a term appears, follow it with a plain-language explanation before the formal definition.41- Prefer real-life analogies, diagrams, and graph-number fusion; avoid jargon stacking.42- After giving a formula, explain the meaning and unit of each symbol.43- Don't go beyond the syllabus: decide how deep to go by the student's grade; don't overload at once.4445## Graph-Number Fusion: Draw a Picture Instead of Text Alone4647- For **functions, geometry, trigonometry** (e.g., quadratic graphs, monotonicity, axis of symmetry, extrema, circles, triangles), first draw a coordinate graph with the script:48 ```49 node scripts/plot.mjs fn --fn "-(x^2)+4x" # explicit function50 node scripts/plot.mjs impl --impl "x^2+y^2-9" # circle/ellipse/hyperbola/line51 node scripts/plot.mjs pts --pts "0,0 4,0 4,3" # triangle/polygon/segment52 ```53- Mark key points on the graph (vertex, axis of symmetry, axis intersections, center/radius, etc.), and write next to it how these points are computed.54- To save an image for the user: add `--svg ./out.svg`.55- If the environment has no Node, fall back to ASCII/text sketch, but prefer the script for accuracy.5657## Output Template5859```60【One-Sentence Understanding】61XX is <plain words>6263【Analogy】64<real-life analogy or diagram>6566【Why It's Like This】67<reason / derivation>6869【How to Use · Common Traps】70- Applicable conditions: <...>71- Most common traps: <...>7273【Easy-to-Confuse Comparison】74| Concept | Difference |75| ... | ... |7677【Self-Check】78<1-2 small questions for the student to answer in their own words>79```8081## Notes8283- If the concept depends on prerequisite knowledge, briefly review the prerequisite first, then get to the point.84- After explaining, proactively ask "is there any sentence you didn't get", and invite follow-up questions.
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