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Learner Engine (LE)

Overview​

The Learner Engine is the system's "hippocampus"—responsible for modeling the student's cognitive state. It transforms the ITS from a stateless chatbot into a persistent, adaptive educational companion. By tracking mastery levels and predicting memory decay, it ensures that learning is personalized and durable.

Core Capabilities​

1. Bayesian Knowledge Tracing (BKT)​

BKT is a probabilistic model used to infer latent student knowledge from observed performance.

  • Purpose: To estimate the probability $P(L_n)$ that a student has mastered a skill after $n$ attempts.
  • Parameters:
    • $P(L_0)$: Initial probability of knowing the skill.
    • $P(T)$: Probability of learning the skill at each step.
    • $P(G)$: Probability of guessing correctly (Guess).
    • $P(S)$: Probability of slipping (mistake despite knowing) (Slip).
  • Update Rule: The system updates $P(L)$ after every attempt using Bayes' theorem.

2. Spaced Repetition System (SRS)​

To combat the Ebbinghaus Forgetting Curve, the LE implements a modified SM-2 Algorithm (similar to Anki).

  • Logic:
    • Correct answer $\rightarrow$ Increase interval (e.g., 1 day $\rightarrow$ 3 days $\rightarrow$ 7 days).
    • Incorrect answer $\rightarrow$ Reset interval to 1 day.
  • Goal: Schedule reviews exactly when the student is about to forget the concept (90% retention probability).

3. User Profiling​

The LE maintains a comprehensive profile for each student:

  • Global Readiness Score: An aggregate metric of overall course progress (0.0 - 1.0).
  • Skill Matrix: A detailed map of mastery probabilities for every concept in the Knowledge Graph.
  • Learning Style: Inferred preferences (e.g., visual vs. textual, theoretical vs. practical).

Technical Implementation​

BKT Update Logic​

def update_bkt(p_known, is_correct):
    if is_correct:
        p_learned = (p_known * (1 - p_slip)) / (p_known * (1 - p_slip) + (1 - p_known) * p_guess)
    else:
        p_learned = (p_known * p_slip) / (p_known * p_slip + (1 - p_known) * (1 - p_guess))
    
    return p_learned + (1 - p_learned) * p_transit

SRS Scheduling​

def schedule_next_review(current_interval, performance_rating):
    if performance_rating >= 3:
        if current_interval == 0:
            return 1
        elif current_interval == 1:
            return 6
        else:
            return round(current_interval * ease_factor)
    else:
        return 1 # Reset

Integration with Other Engines​

  • Pedagogy Engine: Uses the student's mastery state ($P(L)$) to decide the next topic.
  • Assessment Engine: Provides the raw performance data (Correct/Incorrect) to trigger updates.
  • Tutor Engine: Uses the user profile to personalize the dialogue style.