📘 Learning Efficiency API

A Django REST API for measuring and tracking research preparation efficiency — grounded in three interlocking learning science theories.

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The Model

$$ L_e = \frac{K_g \times R_q}{T_s \times C_l} $$

Symbol	Variable	Range	Theoretical Grounding
Le	Learning Efficiency	computed	Composite output score
Kg	Knowledge gained	0–100	Ebbinghaus — retained knowledge after forgetting decay
Rq	Research quality weight	0.0–1.0	Bibliometric credibility weighting (h-index, field normalisation)
Ts	Study time (hours)	> 0	Ebbinghaus — time-on-task relative to retention curve
Cl	Cognitive load index	1–10	Sweller's CLT — intrinsic + extraneous + germane load

Compression Rate:

Lc = PapersRead / StudyTime

The formula encodes a key insight: efficiency is not just about how much you study — it is about what you retain (Kg), how reliable your sources are (Rq), and how much mental overhead you carry (Cl). Each variable maps directly to one of the three theoretical pillars below.

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Theoretical Foundations

1 · Cognitive Load Theory — Sweller (1988)

The Cl (cognitive load index, 1–10) is a direct operationalisation of Sweller's framework. Working memory holds roughly 4 chunks at a time. When it overflows, learning halts — no matter how many hours are logged.

Sweller identified three load types that together must not exceed working memory capacity:

┌──────────────────┬────────────────────┬──────────────────────┐
│  INTRINSIC       │  EXTRANEOUS        │  GERMANE             │
│                  │                    │                      │
│ Complexity of    │  Caused by poor    │  Schema-building     │
│ the material     │  presentation,     │  effort — the goal   │
│ itself           │  split attention,  │  of all instruction  │
│                  │  redundancy        │                      │
│  Fixed — managed │  Minimise this     │  Maximise this       │
│  via sequencing  │                    │                      │
└──────────────────┴────────────────────┴──────────────────────┘
  Total Load  =  Intrinsic  +  Extraneous  +  Germane  ≤  Capacity

How Cl maps to load types:

Cl Score	Interpretation
1–3	Low load — germane processing dominates, deep schema formation likely
4–6	Moderate load — efficient study under normal conditions
7–8	High load — extraneous sources likely present; review session design
9–10	Overload — learning efficiency collapses; split sessions recommended

A session with Cl = 9 and Kg = 80 scores lower than one with Cl = 3 and Kg = 70. The model correctly penalises cognitive overload even when perceived knowledge gain appears high.

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2 · Ebbinghaus Forgetting Curve (1885)

Kg is not raw input — it represents retained knowledge, shaped by the forgetting curve. Ebbinghaus showed that without reinforcement, memory decays exponentially:

$$ R = e^{-t/S} $$

Where R = retention, t = time elapsed, S = memory stability (grows with each successful retrieval).

Retention
  100% │▓
       │ ▓▓
   75% │    ▓▓▓
       │        ▓▓▓▓
   50% │             ▓▓▓▓▓
       │                   ▓▓▓▓▓▓▓▓
   25% │                            ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓
       └────────────────────────────────────────────────▶ Time
         20min  1hr   9hr  1day  2days  6days  31days

Spaced repetition optimal review intervals:

Review #	Interval	Rationale
1st	1 day	Catch decay before the steepest drop
2nd	6 days	Stability S has grown — safe to wait longer
3rd	14 days	Each retrieval flattens the next curve
4th	30 days	Long-term consolidation phase
5th+	60+ days	Near-permanent retention

Implication for the API: Kg scores logged immediately after a session will be higher than true retained knowledge measured days later. A planned forgetting_decay field — calculated as Kg × e^(−t/S) — is in the roadmap to model this drift over time.

Bjork (1994) — Desirable Difficulties: Retrieval practice is more powerful than re-reading. A session involving active recall yields higher true Kg than passive review of the same duration, even when the immediate subjective score feels lower.

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3 · Bibliometric Credibility Weighting

Rq (research quality weight, 0.0–1.0) encodes the credibility of sources consulted in a session. It is informed by bibliometric indices drawn from the literature on research quality measurement.

Credibility tiers — how to assign Rq:

Rq Range     Source Tier        Bibliometric Signal
──────────────────────────────────────────────────────────────────
0.90–1.00    Tier 1 journals    High Eigenfactor, Q1 SCImago,
                                field-normalised citation score > 2.0

0.70–0.89    Peer-reviewed      h-index authors, i10-index > 10,
             conferences        cited in systematic reviews

0.50–0.69    Preprints /        arXiv, SSRN — traceable but
             working papers     not yet peer-reviewed

0.30–0.49    Grey literature    Technical reports, white papers,
                                institutional publications

0.10–0.29    Informal sources   Blogs, forum posts, undated content

0.00–0.09    Uncredentialed     No author, no date, no citations

Key bibliometric indices that inform Rq:

Index	Definition	Strength
h-index (Hirsch, 2005)	h papers each cited ≥ h times	Balances breadth and depth of output
Field-normalised score	Paper citations ÷ field & year average	Corrects for discipline citation norms
Eigenfactor	PageRank-style weighting by journal influence	High-impact citing journals count more
Altmetrics	Policy, media, and social mention tracking	Captures real-world and societal impact

A session reading 4 Nature papers (Rq = 0.95) outscores a session reading 12 blog posts (Rq = 0.20) at identical Kg and Cl. The model correctly reflects that source quality mediates knowledge reliability.

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How the Three Theories Interact

  WHAT to trust          HOW efficiently         WHEN to revisit
  ─────────────          ───────────────         ───────────────
  Bibliometrics    ───►   CLT-aware study   ───►  Spaced repetition
  sets Rq                 minimises Cl            schedules Kg decay

  Poor Rq contaminates    High Cl wastes          Without review,
  Kg — bad sources        capacity even on        Kg decays to ~25%
  corrupt retained        good material           within a week
  knowledge

The formula Le = (Kg × Rq) / (Ts × Cl) is not arbitrary — it is a compression of this three-way interaction. Maximising Le requires attending to all three simultaneously: credible sources, managed cognitive load, and retention-aware scheduling.

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Project Structure

project/
├── manage.py
├── requirements.txt
├── learning_efficiency/
│   ├── __init__.py
│   ├── settings.py
│   ├── urls.py
│   └── wsgi.py
└── research/
    ├── __init__.py
    ├── models.py
    ├── serializers.py
    ├── views.py
    ├── services.py          ← Le formula + grade logic lives here
    ├── urls.py
    └── migrations/

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Setup

pip install -r requirements.txt
python manage.py makemigrations
python manage.py migrate
python manage.py runserver

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API Endpoints

Method	Endpoint	Description
GET	/api/sessions/	List all sessions
POST	/api/sessions/	Create new session
GET	/api/sessions/{id}/	Retrieve session
PUT	/api/sessions/{id}/	Update session
DELETE	/api/sessions/{id}/	Delete session
GET	/api/sessions/analytics/	Aggregate statistics
GET	/api/sessions/top/	Top 5 most efficient sessions

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Example Request

POST /api/sessions/
Content-Type: application/json

{
    "title": "AI Security Papers",
    "papers_read": 6,
    "study_time_hours": 4,
    "knowledge_score": 85,
    "research_quality": 0.92,
    "cognitive_load": 5,
    "notes": "Focused on adversarial ML and prompt injection"
}

Example Response

{
    "id": 1,
    "title": "AI Security Papers",
    "papers_read": 6,
    "study_time_hours": 4.0,
    "knowledge_score": 85.0,
    "research_quality": 0.92,
    "cognitive_load": 5.0,
    "notes": "Focused on adversarial ML and prompt injection",
    "learning_efficiency": 3.91,
    "compression_rate": 1.5,
    "efficiency_grade": "Moderate",
    "created_at": "2025-03-01T08:00:00Z",
    "updated_at": "2025-03-01T08:00:00Z"
}

Analytics Response

GET /api/sessions/analytics/

{
    "total_sessions": 12,
    "mean_efficiency": 4.23,
    "max_efficiency": 9.75,
    "min_efficiency": 1.20,
    "stdev_efficiency": 2.14,
    "mean_compression_rate": 1.85,
    "total_papers_read": 72,
    "total_study_hours": 38.5
}

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Efficiency Grade Scale

Le Score	Grade	CLT Interpretation
≥ 15	🟢 Exceptional	Low Cl, high Rq, strong retention
≥ 10	🔵 High	Well-managed load, credible sources
≥ 5	🟡 Moderate	Typical research session
≥ 2	🟠 Low	High cognitive load or weak sources
< 2	🔴 Very Low	Overload or low-credibility material

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Roadmap

• forgetting_decay field — apply R = e^(−t/S) to Kg over time (Ebbinghaus)
• Spaced repetition scheduler — surface sessions due for review at optimal intervals
• Rq auto-scoring via DOI lookup against Crossref / Semantic Scholar APIs
• Cl variance analysis — flag sessions where load spikes correlate with score drops
• Statistical validation (Pearson correlation, regression across sessions)
• Predictive efficiency forecasting (linear regression / ML)
• JWT multi-user authentication
• PDF research report export with per-session breakdown
• Dockerized deployment

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References

Theory	Citation
Cognitive Load Theory	Sweller, J. (1988). Cognitive load during problem solving. Cognitive Science, 12(2), 257–285
Forgetting Curve	Ebbinghaus, H. (1885). Über das Gedächtnis. Leipzig: Duncker & Humblot
Desirable Difficulties	Bjork, R.A. (1994). Memory and metamemory considerations in the training of human beings. In Metacognition
Testing Effect	Roediger, H.L. & Karpicke, J.D. (2006). Test-enhanced learning. Psychological Science, 17(3), 249–255
h-index	Hirsch, J.E. (2005). An index to quantify an individual's scientific research output. PNAS, 102(46)
Eigenfactor	Bergstrom, C.T. (2007). Eigenfactor: Measuring the value and prestige of scholarly journals. College & Research Libraries News

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_{Built by @mngugi · Learning Science × Software Engineering}