# Pedagogy Brief for LessonKit (K-12 Vietnam Classroom Simulator)

**Audience:** CTO. **Purpose:** check the five-step LessonKit model (S0 intuition_trap → S1 productive_failure → S2 prediction_lock → S3 causal_insight → S4 mastery_test) against well-supported learning research, and say what the tutor should do and say at each point.

LessonKit in one line: every lesson has five phases. Mastery of a knowledge component (KC) comes **only** from observed attempts (item_result flags: correct, constraints_hold, first_try, not_scaffolded, not_auto_dealt; rules consecutive(n) or at_least(n)). Tutor speech never earns evidence. Misconceptions are first-class and tied to constraints. FSRS schedules review across sessions.

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## 1. Productive failure (Kapur)
**(a) Finding.** Students who try to solve a new, rich problem *before* instruction, and mostly fail, then do better on conceptual understanding and transfer than students taught first. Procedural skill stays about the same (Kapur 2008; Kapur 2014; meta-analysis Sinha & Kapur 2021). The benefit depends on a good debrief that compares the students' own attempts with the correct idea.
**(b) Mapping.** This is S1. Failure in S1 must **not** count as negative evidence toward mastery. S1 attempts are diagnostic: violated constraints show which misconceptions are active. The debrief belongs at the S1→S3 boundary.
**(c) Do/say.** Give one open task, let the learner make several attempts, and don't correct each one. Then compare their attempt with the canonical solution.
> *"Em thử nhiều cách xem. Sai cũng không sao, cô muốn xem em nghĩ thế nào."*

**Tension:** see §2 (expertise reversal).

## 2. Worked examples and fading (Sweller; Renkl & Atkinson)
**(a) Finding.** For novices, studying worked examples beats unguided problem solving because it lowers extraneous cognitive load (Sweller & Cooper 1985; Sweller 1988). Gradually removing steps, so the learner moves from example to completion problem to independent problem, helps transfer (Renkl & Atkinson 2003; Atkinson, Derry, Renkl & Wortham 2000). Self-explaining the examples adds more benefit (Chi et al. 1989).
**(b) Mapping.** S3 causal_insight is the "worked form". LessonKit currently has a single S3 and no fading ladder between S3 and S4. The hint ladder can serve as fading in reverse. Assists that complete steps should set `not_scaffolded=false`, which is correct.
**(c) Do/say.** In S3, show one fully worked example and ask the learner to explain one step. Then give a version with the last step blank before moving to S4.
> *"Đây là cách giải đầy đủ. Em giải thích giúp cô: vì sao bước hai lại nhân cả hai vế?"*

**Tension (expertise reversal, Kalyuga et al. 2003; Kalyuga 2007).** Guidance that helps novices can hurt more knowledgeable learners. Productive failure says "problem first", while the worked-example effect says "example first". The two can be reconciled. Productive failure aims at *conceptual* understanding and assumes some prior knowledge plus a strong debrief. Worked examples aim at *procedural* fluency for true novices. **Engineering implication:** let S1 be shortened or skipped by learner state. If FSRS/KC data shows a novice failing repeatedly, cap S1 attempts and move to S3. If the learner is already strong, skip the S3 worked example and go straight to completion problems.

## 3. Retrieval practice (Roediger & Karpicke)
**(a) Finding.** Recalling information from memory makes long-term retention much stronger than restudying, even without feedback. The effect is larger with feedback (Roediger & Karpicke 2006; Karpicke & Blunt 2011; Dunlosky et al. 2013).
**(b) Mapping.** S4 mastery_test and FSRS reviews are retrieval events. The `first_try` and `not_scaffolded` flags correctly separate retrieval from recognition. Gap: retrieval only happens in S4. Short retrieval items at the start of the *next* lesson (S0 of lesson n+1 recalling KCs from lesson n) would add value at low cost.
**(c) Do/say.** Ask the learner to produce the answer, not pick or reread it. Give feedback after the attempt.
> *"Không nhìn lại nhé, em nhớ xem công thức tính diện tích hình thang là gì?"*

## 4. Spacing (Cepeda et al.)
**(a) Finding.** Spreading practice over time gives better retention than massing it. The best gap grows with how long the learner needs to remember: roughly 10–20% of the retention interval for intervals of a week or more (Cepeda et al. 2006; Cepeda et al. 2008).
**(b) Mapping.** FSRS with `target_retention` implements this directly. Two cautions. FSRS was tuned on adult flashcard data, so K-12 parameters are an open question. Review items should be *generative problems* tied to KCs, not recall of facts.
**(c) Do/say.** Open each session with 2–3 due review items before new content, and explain why.
> *"Trước khi học bài mới, mình ôn nhanh ba câu của tuần trước để não giữ lâu hơn nhé."*

## 5. Formative assessment and feedback (Black & Wiliam; Hattie & Timperley; Wiliam)
**(a) Finding.** Using evidence of learning to adjust teaching during instruction produces substantial gains (Black & Wiliam 1998). Effective feedback answers three questions: where am I going, how am I going, where to next. Feedback about the task, the process and self-regulation helps. Praise aimed at the self ("giỏi quá") mostly does not (Hattie & Timperley 2007). Wiliam (2011) adds "eliciting evidence" and "activating students as owners of their learning". Kluger & DeNisi (1996) show that roughly a third of feedback interventions *reduce* performance.
**(b) Mapping.** Strong fit. Per-attempt constraint status (satisfied/violated/unevaluated) gives task- and process-level feedback. The rule that tutor words never earn evidence is exactly right. Risk: the `praise` act on `mastery_passed` should praise the *process*, not the person.
**(c) Do/say.** Name what was right and what to fix next. Avoid generic praise.
> *"Em đặt đúng đơn vị rồi. Bước tiếp theo, kiểm tra lại dấu khi chuyển vế xem."*

## 6. Misconception-driven instruction / conceptual change (Posner et al. 1982)
**(a) Finding.** Learners give up a prior conception only when they are dissatisfied with it and the new one is intelligible, plausible and fruitful (Posner, Strike, Hewson & Gertzog 1982). Refutation texts that state the misconception and directly counter it outperform plain exposition (Tippett 2010). Simply confronting a learner with an anomaly often fails (Chinn & Brewer 1993).
**(b) Mapping.** Very strong fit. S0 intuition_trap creates dissatisfaction. Each misconception's `counter_example` provides the anomaly. `scaffold` plus S3 make the new conception intelligible and plausible. The constraint → misconception link lets the system *detect* the active misconception. Gap: "fruitful" (the new idea solves new problems) depends on S4 items showing transfer, so authors should include at least one far-transfer item.
**(c) Do/say.** State the intuitive belief kindly, show the counter-example, then ask the learner to reconcile the two.
> *"Nhiều bạn nghĩ vật nặng rơi nhanh hơn. Nhưng xem hai quả bóng này rơi cùng lúc. Em giải thích sao?"*

## 7. Predict–Observe–Explain (White & Gunstone)
**(a) Finding.** Having learners commit to a prediction, observe the result and then reconcile the two surfaces their prior ideas and engages them (White & Gunstone 1992). Committing publicly or explicitly matters.
**(b) Mapping.** This is S2 prediction_lock, implemented correctly as long as the prediction is *locked* before the reveal. Add a required "explain" turn after the observation. Without it, POE reduces to guessing.
**(c) Do/say.**
> *"Em chốt dự đoán trước nhé: nước sẽ dâng lên hay hạ xuống? Chốt rồi mới xem."*

## 8. Socratic questioning and wait time (Rowe)
**(a) Finding.** Raising teacher wait time from about 1 second to 3–5 seconds, both after a question and after a student answer, increases how long answers are, how many students respond and how much they reason (Rowe 1974; Rowe 1986; Tobin 1987).
**(b) Mapping.** This is covered by the `ask` act, `waits_for_student`, and the cue cooldown. **Tension:** on a tablet, silence reads as "app frozen", and children tap away. Treat wait time as *a visible thinking state*: a `think` animation, no new cue, input still open. Use a minimum of about 3 s before any `prompt`/`encourage`, and longer for open "why" questions. The `thinking` event should *suppress* cues, not trigger them.
**(c) Do/say.** Ask one question, then stay quiet. Follow up with "why", not with the answer.
> *"Vì sao em nghĩ vậy? … Cô đợi em suy nghĩ nhé."*

## 9. CPA: Concrete–Pictorial–Abstract (Bruner; Singapore maths)
**(a) Finding.** Bruner (1966) described three modes of representation: enactive, iconic and symbolic. Singapore mathematics turned this into the CPA sequence: objects, then drawings or bar models, then symbols. There is reasonable evidence for concreteness fading, i.e. starting concrete and fading to abstract (Fyfe, McNeil, Son & Goldstone 2014).
**(b) Mapping.** Partial fit. LessonKit's phases describe *function* (trap, failure, prediction, insight, test), not *representation*. The simulator is naturally concrete and pictorial, and S3 "symbol" is the abstract step. Recommend a per-step `representation` tag (concrete/pictorial/abstract) checked by the verifier, so S4 does not assess only at the concrete level.
**(c) Do/say.**
> *"Mình xếp 3 nhóm, mỗi nhóm 4 khối. Giờ vẽ thành sơ đồ, rồi viết thành phép tính 3 × 4."*

## 10. Scaffolding and ZPD (Vygotsky; Wood, Bruner & Ross 1976)
**(a) Finding.** Learners can do with help what they cannot yet do alone, which is the zone of proximal development (Vygotsky 1978). Wood, Bruner & Ross (1976) listed tutor scaffolding functions: recruiting interest, reducing degrees of freedom, maintaining direction, marking critical features, controlling frustration and demonstrating. Scaffolding must be *contingent*: more help after failure, less after success (Wood & Middleton 1975; van de Pol, Volman & Beishuizen 2010).
**(b) Mapping.** The hint ladder plus the misconception `scaffold` cover this. The evidence rule `not_scaffolded` correctly ensures help is eventually withdrawn. Gap: the ladder should move *down* after success. Assist level should be per-learner state, not reset to zero on each item.
**(c) Do/say.** Start with the least help (a question), and escalate only if needed.
> *"Gợi ý nhỏ: em thử nhìn vào mẫu số trước xem."*

## 11. Vietnam GDPT 2018 framing
The general education curriculum (Chương trình giáo dục phổ thông 2018) was issued by **Thông tư 32/2018/TT-BGDĐT** (26/12/2018). It is competence-based (phát triển phẩm chất và năng lực) rather than content-transmission. It defines:
- **5 phẩm chất chủ yếu:** yêu nước, nhân ái, chăm chỉ, trung thực, trách nhiệm.
- **3 năng lực chung:** tự chủ và tự học; giao tiếp và hợp tác; giải quyết vấn đề và sáng tạo.
- **7 năng lực đặc thù:** ngôn ngữ, tính toán, khoa học, công nghệ, tin học, thẩm mỹ, thể chất.

Each subject program (e.g. Toán) further specifies subject competences. For Toán these are tư duy và lập luận toán học, mô hình hoá toán học, giải quyết vấn đề toán học, giao tiếp toán học, and sử dụng công cụ, phương tiện học toán. The exact per-grade "yêu cầu cần đạt" wording must be taken from the official subject documents. I have not verified grade-level details here.
**Mapping.** KCs should carry tags for GDPT năng lực and yêu cầu cần đạt, so teacher and parent reports use the national vocabulary. S1/S2 naturally evidence *giải quyết vấn đề và sáng tạo*. Explain turns evidence *giao tiếp*. FSRS self-review supports *tự chủ và tự học*. Phẩm chất such as *trung thực* and *chăm chỉ* should **not** be inferred from attempt data. Behavioural labelling of children is ethically risky and not what the attempt evidence measures.
> *"Em tự kiểm tra lại bài của mình trước khi nộp nhé, đó là cách tự học tốt đấy."*

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## Key tensions (summary)
1. **Productive failure vs worked examples / expertise reversal.** Make S1 adaptive (cap attempts, allow skipping) using KC and FSRS state.
2. **Wait time vs tablet engagement.** Show visible thinking and suppress cues during waits. Don't fill silence.
3. **Retrieval rigour vs motivation.** No-hint S4 items can frustrate. Use `reassure` on `mastery_failed` with a concrete next step, and re-test after spacing rather than immediately.
4. **Praise vs feedback quality.** Praise for process only. Avoid "con thông minh quá".
5. **Adult-tuned FSRS vs children.** Validate retention targets on real K-12 data.

## Implications for LessonKit
- **Keep the evidence rule absolute.** Only observed, unassisted, first-try, constraint-satisfying attempts count. Never let S1 failure count *against* mastery.
- **Make S1 and S3 adaptive (expertise reversal).** Novices with repeated S1 failure jump to the worked example. Proficient learners skip to completion items. Add a faded completion step between S3 and S4.
- **Require an "explain" turn after S2 reveal and after the S3 worked example** (POE + self-explanation). Store it as `unevaluated` evidence unless it can be scored.
- **Wait-time contract in the cue scheduler.** At least 3 s before any follow-up cue after `ask`. The `thinking` event suppresses cues. Show a visible think state.
- **Contingent hint ladder.** Assist level persists per learner and steps *down* after success. The verifier should flag lessons where every misconception lacks a counter_example or scaffold.
- **Retrieval at the start of each session.** Due FSRS items plus a recall of the previous lesson's KC before the S0 of the new one.
- **Representation tags (C/P/A) and GDPT năng lực tags on steps and KCs.** The verifier checks that S4 includes abstract and transfer items. Reports speak GDPT language and never infer phẩm chất.
- **Feedback lines follow Hattie & Timperley.** Every `correct`/`affirm` line names the specific thing done right. Every `incorrect` line gives a next step, not just "sai rồi".

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