> ## Documentation Index
> Fetch the complete documentation index at: https://docs.prepst.com/llms.txt
> Use this file to discover all available pages before exploring further.

# Cognitive Efficiency

> Measure how effectively students learn

## What is Cognitive Efficiency?

Cognitive efficiency is a comprehensive metric that measures how effectively students process information, combining correctness, time spent, and confidence to provide a holistic view of learning effectiveness.

## The Efficiency Formula

Cognitive efficiency combines multiple factors:

```
Efficiency = (Correctness × Confidence) / Time
```

Where:

* **Correctness**: 1 for correct, 0 for incorrect
* **Confidence**: Self-reported 1-5 scale
* **Time**: Time spent on question in seconds

<Info>
  Higher efficiency scores indicate students who answer correctly, with high confidence, and minimal time - the ideal learning state.
</Info>

## Efficiency Dimensions

### Time Efficiency

How quickly students solve problems without sacrificing accuracy:

```python theme={null}
time_efficiency = {
    "fast_correct": 25,      # <30s, correct
    "moderate_correct": 15,  # 30-60s, correct
    "slow_correct": 10,      # >60s, correct
    "incorrect": 0           # Any time, wrong
}
```

### Confidence Accuracy

Alignment between confidence and correctness:

```python theme={null}
confidence_alignment = {
    "high_conf_correct": 1.0,      # Confident and right
    "low_conf_correct": 0.6,       # Uncertain but right
    "high_conf_wrong": 0.0,        # Confident but wrong
    "low_conf_wrong": 0.2          # Uncertain and wrong
}
```

### Learning Efficiency Trends

Track efficiency over time to identify improvement or decline:

```python theme={null}
efficiency_trend = {
    "current_efficiency": 0.75,
    "trend_7_days": "improving",
    "trend_30_days": "stable",
    "peak_efficiency": 0.85
}
```

## Usage Example

```python theme={null}
from cognition_engine import CognitionEngine

engine = CognitionEngine(supabase_url, supabase_key)

# Get efficiency metrics
efficiency = await engine.get_cognitive_efficiency("student_123")

print(f"Overall efficiency: {efficiency['overall_efficiency']:.2f}")
print(f"Time efficiency: {efficiency['time_efficiency']:.2f}")
print(f"Trend: {efficiency['efficiency_trend']}")
```

## Efficiency Patterns

### High Efficiency Pattern

<AccordionGroup>
  <Accordion title="Characteristics">
    Quick correct answers with high confidence. Students understand concepts deeply and apply them efficiently.
  </Accordion>

  <Accordion title="Implications">
    Ready for increased difficulty or new topics. Strong foundation allows faster advancement.
  </Accordion>

  <Accordion title="Recommendations">
    Challenge with harder problems. Introduce advanced topics.
  </Accordion>
</AccordionGroup>

### Moderate Efficiency Pattern

<AccordionGroup>
  <Accordion title="Characteristics">
    Correct answers but take longer or show uncertainty. Students understand but need reinforcement.
  </Accordion>

  <Accordion title="Implications">
    Good grasp of concepts but not yet automatic. More practice will improve speed and confidence.
  </Accordion>

  <Accordion title="Recommendations">
    Continue current difficulty level. Focus on similar problems to build fluency.
  </Accordion>
</AccordionGroup>

### Low Efficiency Pattern

<AccordionGroup>
  <Accordion title="Characteristics">
    Slow progress with frequent errors or low confidence. Students struggle with concepts.
  </Accordion>

  <Accordion title="Implications">
    Foundation skills may be weak. May need review or easier problems.
  </Accordion>

  <Accordion title="Recommendations">
    Lower difficulty. Review fundamentals. Increase practice frequency.
  </Accordion>
</AccordionGroup>

## Efficiency by Skill

Track efficiency across different topics:

```python theme={null}
skill_efficiency = {
    "algebra": 0.85,        # Strong efficiency
    "geometry": 0.72,       # Good efficiency
    "trigonometry": 0.45,   # Low efficiency - needs attention
    "statistics": 0.78      # Good efficiency
}

# Identify skills needing improvement
weak_skills = [skill for skill, eff in skill_efficiency.items() 
               if eff < 0.60]
print(f"Skills to focus on: {weak_skills}")
```

## Integration with BKT

Cognitive efficiency enhances BKT mastery estimates:

<ComparisonTable>
  <ComparisonRow feature="BKT Only" whatOursDoes="Mastery probability" whatOursShouldDo="Based on correctness" />

  <ComparisonRow feature="BKT + Efficiency" whatOursDoes="Weighted mastery" whatOursShouldDo="Correctness, time, confidence" />

  <ComparisonRow feature="Accuracy" whatOursDoes="Good" whatOursShouldDo="Better" />

  <ComparisonRow feature="Granularity" whatOursDoes="Know/Don't know" whatOursShouldDo="Fluency levels" />
</ComparisonTable>

## Cognitive Load Indicators

Monitor signs of cognitive overload:

### Warning Signs

* **Increasing time**: Problems taking longer than expected
* **Answer changes**: Frequent corrections suggest uncertainty
* **Low confidence**: Despite correct answers
* **Declining efficiency**: Trend over recent sessions

### Intervention Triggers

```python theme={null}
if efficiency['cognitive_load_warning']:
    print("High cognitive load detected")
    print("Recommendations:")
    print("- Reduce session length")
    print("- Lower difficulty temporarily")
    print("- Increase breaks between problems")
```

## Performance Snapshots

Capture comprehensive efficiency profiles:

```python theme={null}
snapshot = await engine.create_performance_snapshot("student_123")

efficiency_profile = {
    "overall_efficiency": 0.75,
    "cognitive_efficiency_score": 0.68,
    "time_efficiency": 0.82,
    "confidence_accuracy": 0.91,
    "peak_performance_time": "morning",
    "cognitive_load": "moderate"
}
```

## Best Practices

<Tip>
  Monitor efficiency trends over 7-day periods. Short-term fluctuations are normal, but sustained patterns indicate real changes.
</Tip>

<Warning>
  Don't prioritize efficiency over understanding. Some problems naturally take more time. High efficiency is good, but mastery is the goal.
</Warning>

<Info>
  Combine efficiency metrics with mastery probability and velocity for the most complete picture of student learning.
</Info>

## Next Steps

<CardGroup cols={2}>
  <Card title="Learning Velocity" icon="gauge" href="/guides/velocity">
    See how efficiency influences velocity calculations
  </Card>

  <Card title="Plateau Detection" icon="exclamation-triangle" href="/guides/plateaus">
    Understand how efficiency helps detect plateaus
  </Card>
</CardGroup>