From thinking-frameworks-skills
Produces step-by-step computational walkthroughs of vector and matrix operations as numbered frames, showing explicit state at each step. Use when a learner needs to see a computation unfold.
How this skill is triggered — by the user, by Claude, or both
Slash command
/thinking-frameworks-skills:worked-example-walkthroughThe summary Claude sees in its skill listing — used to decide when to auto-load this skill
1. [Workflow](#workflow)
A walkthrough is a sequence of numbered frames showing the state of a computation at each step. Each frame answers three questions: what's the current state?, what operation produced it?, and what should the learner notice?
This is the closest pure text gets to a 3Blue1Brown animation. The learner can re-trace the operation by hand, and the explicit intermediate states catch confusions that a final-result-only treatment hides.
Quick example (Eigenvalues of a 2×2 matrix):
Compute the eigenvalues of A = [[4, 1], [2, 3]].
Frame 1. State: A = [[4, 1], [2, 3]]. We want λ such that det(A − λI) = 0.
Frame 2. Form A − λI:
A - λI = [[4-λ, 1 ], [ 2, 3-λ]]Frame 3. Compute the determinant: det = (4 − λ)(3 − λ) − 1·2 = (12 − 7λ + λ²) − 2 = λ² − 7λ + 10
Frame 4. Solve λ² − 7λ + 10 = 0: Factor: (λ − 5)(λ − 2) = 0. So λ = 5 or λ = 2.
Frame 5. Eigenvalues: 5 and 2. Quick sanity check: trace(A) = 4 + 3 = 7 = sum of eigenvalues ✓; det(A) = 12 − 2 = 10 = product of eigenvalues ✓.
What to notice: The characteristic polynomial is just det(A − λI) expanded; finding eigenvalues is just root-finding. No magic.
Five frames, ~80 words. The learner can redo this on paper in under a minute.
Copy this checklist and track your progress:
Walkthrough Progress:
- [ ] Step 1: Pick the smallest possible example that exercises the concept
- [ ] Step 2: Write the goal — what we'll compute and why
- [ ] Step 3: Plan the frames (3-7 typically)
- [ ] Step 4: Write each frame: state, operation, notice
- [ ] Step 5: End with a sanity check or invitation to verify
- [ ] Step 6: Optional — invite the learner to redo with a variant
Step 1: Pick the smallest possible example that exercises the concept
The example must be small. 2×2 matrices, 3-vector inputs, 3-token sequences. Bigger examples obscure the structure with arithmetic.
The example must also exercise the concept — not just trivially demonstrate it. A diagonal matrix has trivial eigenvectors; pick a 2×2 that's not diagonal. A scalar attention is trivial; pick at least 3 tokens.
For a catalog of recommended example sizes per concept, see resources/examples.md.
Step 2: Write the goal — what we'll compute and why
Single sentence. "Compute the eigenvalues of A = [[4, 1], [2, 3]]." or "Apply attention to a 3-token sequence with random Q, K, V vectors." The goal frames everything that follows.
Step 3: Plan the frames (3-7 typically)
Each frame is one operation. Sketch the frames before writing them out — this catches the "skipped step" problem before it hits the page.
A frame budget that works for most operations:
If you find yourself wanting >7 frames, either the example is too big (shrink) or the operation has multiple sub-operations that each deserve their own walkthrough.
Step 4: Write each frame: state, operation, notice
Each frame has three parts (see Frame Anatomy):
The "notice" is what distinguishes a walkthrough from a worked solution. A worked solution shows the steps; a walkthrough also says what to look at.
Step 5: End with a sanity check or invitation to verify
Every walkthrough ends with one of:
The sanity check is what tells the learner the result is right. It also doubles as a reusable verification trick they can apply to similar problems.
Step 6 (optional): Invite the learner to redo with a variant
If the learner has time and the example is short, invite them to redo with a small change:
Variants check whether the picture transferred, not just the arithmetic.
Each frame has three parts. Keep them visually distinct.
**Frame N.** [Operation: short verb phrase, what we're doing.]
[State: explicit values, in a code block if needed.]
[Notice: one sentence — what to look at.]
Use a code block for matrices, vectors, and equations. Show actual numbers; resist the urge to leave things symbolic. The point is concreteness.
v = (3, 4)
|v| = √(3² + 4²) = √25 = 5
Short verb phrase: "Compute…", "Apply…", "Substitute…", "Solve…". One line.
One sentence pointing at the most important feature of this frame.
If a frame doesn't earn a notice sentence, it might not need to be its own frame. Consider merging.
The example you choose makes or breaks the walkthrough. Heuristics for choosing:
A walkthrough with a, b, c, d is a derivation, not a walkthrough. Pick numbers like 2, 3, 1, −1 — small enough to compute by eye, varied enough to expose pattern.
Identity matrix, zero vector, all-equal scores — these are too trivial; they don't exercise the operation. The walkthrough learner needs to see what happens when the operation is non-trivially active.
Symmetric matrices have real eigenvalues — easy to spot a bug. Stochastic matrices have a stationary distribution — easy to verify. Pick examples with these checkable properties so Step 5's sanity check is meaningful.
For a recommended example per concept, see resources/examples.md.
Used for one-shot operations: eigenvalue compute, single SGD step, single attention forward pass, softmax of a vector. Length: 3-5 frames. Closing: sanity check.
Used for processes that loop: gradient descent over multiple steps, power iteration finding eigenvectors, diffusion sampling. Length: 5-7 frames showing 2-3 iterations explicitly, then "and so on…". Closing: convergence comment + invitation to predict the limit.
Used to show the contrast between two operations: matrix-vector mul as row-dot vs as column-combination; layer norm vs batch norm; SGD vs Adam on the same gradient. Length: parallel frames in two columns or two passes. Closing: bridge sentence on what makes them equivalent or different.
For one filled walkthrough per pattern, see resources/examples.md.
Av is a derivation; a walkthrough with [5, 11] is a walkthrough. The learner needs to see the values.| Operation | Recommended example | Frame count |
|---|---|---|
| Matrix-vector mul | A = [[1, 2], [3, 4]], v = (5, 6) | 3 |
| Eigenvalues | A = [[4, 1], [2, 3]] | 5 |
| Eigenvector for known λ | Same A, λ = 5 | 4 |
| SVD | A = [[3, 1], [1, 3]] (symmetric for clean SVD) | 6 |
| Softmax | x = (2, 1, -1) | 4 |
| Cross-entropy | p = (1, 0, 0), q = (0.7, 0.2, 0.1) | 3 |
| Single SGD step | Loss x², start at x = 4, η = 0.5 | 4 |
| Attention forward | 3 tokens, d = 2 | 7 |
| LayerNorm | x = (1, 5, 9) | 5 |
| Backprop on tiny net | y = w₂σ(w₁x), one input/output | 6 |
| PCA on tiny dataset | 4 points in 2D | 6 |
For full filled-in walkthroughs of each, see resources/examples.md.
npx claudepluginhub lyndonkl/claude --plugin thinking-frameworks-skillsGuides a learner to invent a math/ML concept themselves through Socratic questioning, ending with them stating the formal definition. Use when teaching foundational concepts or when the user wants deep understanding.
Coaches a 13-year-old advanced math student through problems without giving answers, hooks interest with real-world applications, and catches skipped workbook instructions. Trigger on first math turn.
Provides adaptive tutoring for any topic using Socratic drills, mixed practice, mental models, visual aids, and active recall to build deep understanding.