The one move, every time
Everything below serves a single teaching loop. A new hire learns this loop first, then the vocabulary that fills it.
First: is this a current-concept gap, or an upstream prerequisite gap? Rule out the prerequisite before naming anything else — then say which of the eight gap types fits. Teachers speak Gap Types.
→Each gap type has a method the research supports — reteach, represent, restate, check, transfer, or adjust. Match the method to the mechanism, not the surface error.
→Log what was observed, not what was felt. A reaction in the moment is not an outcome; verify with a delayed, spaced retention/transfer check.
The eight gap types
The teacher-facing language. Behind each sits one or more research process-codes (P01–P13). Ask the question; the answer names the gap; the gap names the method.
Methods that cut across every gap
The highest-yield learning-science moves aren't tied to one gap — train them as defaults.
The learner profile · 八维侧画像
How a learner is seen — across eight dimensions, plus what they know. Eight readings, held together. Never summed into a rank.
◇ These eight standing dimensions are a different lens from the eight momentary gap types (§02): the profile is how a learner tends to be; a gap is what's happening on this task. They don't map one-to-one — Retention has no gap type; Representation, Interpretation, Strategy and Challenge have no profile dimension.
Learner profiles in practice · 侧画像案例
Five recurring shapes teachers meet. Each is a profile signature + a dominant gap type + the method that fits. These are teaching composites — not real children.
Solves quickly and often correctly, but skips the check — drops a sign, misses a number, never asks "is this reasonable?"
Understands the idea aloud, but can't hold it in symbols or diagrams — can't draw the model that would unlock the concept. (Messy handwriting or reversal is separate — that's legibility, not this.)
Each skill works on its own; put two together, or change the surface of the problem, and it collapses.
Capable, but performance swings with focus, fatigue, and whether progress is visible — not with what they can actually do.
The arithmetic is fine — but answers a different question than the one asked; rushes the reading, computes the wrong quantity.
Freezes on a test and "forgets", yet explains it calmly afterwards. Anxiety suppresses working memory and mimics a knowledge gap — with a real monitoring gap underneath. The single-code reflex would mislabel this child.
◇ Illustrative composites for training — de-identified, not real children. Real gaps are momentary, method-linked states — never a permanent label for a child ("a Monitoring-gap kid"). Real profiles live in m8208 (internal · never customer-facing) under alias RUDO-MATH-####.
Worked cases · 黄金标准案例
The move, run end to end. These are the calibration key — a new coder must reach the same codes on cases like these. Composite, de-identified.
Content × process · how a case is classified
Two axes. What the math is (content) crosses why it broke (process / gap type). Content codes are owned by m453; we only reference them.
| Content group | Codes | Commonly co-occurring process |
|---|---|---|
| Algebra symbols · variables · equations | E001–E008 | P01 · P03 · P05 · P07 · P08 |
| Geometry angles · area · proof | E009–E014 | P02 · P05 · P10 |
| Statistics probability · distribution | E015–E020 | P06 · P09 |
| Fractions · Ratios · Number sense (K–8) | E021+ proposed | P01 · P05 · P06 · P10 · P11 |
Coding order: set observation type first — gap / developing / strength / context. A strength carries no gap code. Each gap row takes one primary code (a second only if a second mechanism is clearly present); never code from a "feeling" or from detail not in the record.
Common confusions · 消歧
The pairs coders most often mix up. Rule of thumb: rule out prerequisite → interpretation → then the mechanism. If two still fit and the evidence can't separate them, code P12.
| You see… | Could be | Tell them apart by |
|---|---|---|
| A dropped sign | Monitoring vs Representation | Notation broke (Rep) vs it was written fine but never checked (Mon)? |
| Answers the wrong quantity | Interpretation vs Strategy | Misread what's asked (Interp) vs read it right but chose a poor method (Strat)? |
| Performance swings | Environment/Motivation vs Challenge Fit | Focus / affect / anxiety (Env) vs task too easy or hard to show true state (Chal)? |
| Fails when skills combine | Transfer vs automaticity (Knowledge) | Component fluent but won't transfer (Transfer) vs component not automatic → working-memory overload (load)? |
| Same error keeps returning | absent Knowledge vs a misconception | Never learned it (worked example) vs learned it wrong (elicit → confront)? |
The disciplines · 员工培训铁律
What a teacher is trained to hold — the honesty rules that keep the method trustworthy.
No total score, ever. Eight dimensions read and shown separately.
A child lighting up in the moment is not yet a learning result. Log it as a reaction, verify the outcome later.
"Not enough evidence" is an honest state, never a verdict on the child.
Code only from what's in the record; strengths never get a gap code; at most two codes.
Names serve teaching only; analysis and reporting run on aliases. One learner is never merged with a same-name other.
Every gap type and method traces to published learning-science, not opinion.
Traceability · P-codes reference: NRC (How People Learn) · IES Practice Guides (math / fractions / algebra / problem-solving) · NMAP · EEF (metacognition / feedback) · SDT (motivation) · ETS (learning progressions) · transfer research.
How a new teacher learns this
Sequenced, not dumped. Week 1 is the loop + the four highest-frequency gaps (Knowledge, Monitoring, Interpretation, Representation) learned through the personas & worked cases; P-codes, the E×P grid, and the rarer gaps come later. Each step has a pass gate before the next.
Learn the loop & the four core questions
See → Teach → Confirm, and the teacher-question for the four highest-frequency gaps. Gate: can state the loop and match each question to its gap.
Shadow & name gaps aloud
Watch real sessions; call the gap type before the mentor does. Gate: agrees with mentor on ≥8 of 10 live calls.
Method drills + the confusions
Practice the fitting method and the five confusable pairs until the move is automatic. Gate: picks the right method + tiebreak on drill cases.
Log to standard
Record to the coding rules — evidence not feeling, primary code, alias, no total score — on a log with separate "reaction" and "outcome" fields so I4 is enforced by the form.
Calibration & sign-off
Blind-code shared cases against the gold-standard bank with a second reader. Certified when: ≥80% code agreement (or Cohen's κ ≥ 0.7) across ≥15 cases. Fail → coaching + re-attempt.
Stay calibrated
Quarterly blind re-code of sampled production cases; drift below threshold triggers re-calibration. Certification is not one-and-done.