TutLM
Pedagogy · Cognitive Science · Learning Science

The Science Behind TutLM

Every element of the system is grounded in decades of research in cognitive psychology and pedagogy. This is not just an AI chatbot — it's an implementation of proven learning methods.

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SM-2 Algorithm

Spaced Repetition

Each topic gets a next-review date based on answer quality. Intervals grow exponentially for well-mastered material.

Why it works

Ebbinghaus's forgetting curve shows: without review, 70% of information is lost within a day. SM-2 schedules reviews at the moment when the memory is still intact but beginning to fade — the optimal point for reinforcement.

In TutLM

  • After each answer the algorithm receives a quality score (0–5)
  • Next interval: interval × ease_factor (1.3–2.5)
  • Correct answer increases ease_factor; error resets interval to 1 day
  • Mastery score stored in user_topic_mastery, updated after each session

References

  • Wozniak P.A. (1990). Optimization of learning. SM-2 Algorithm.
  • Cepeda et al. (2006). Distributed practice in verbal recall tasks. Psychol. Bull.
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Feynman Method

Elaborative Interrogation

Before testing, AI explains the topic and asks guiding questions. The student can ask follow-ups. Only after understanding do they move to exercises.

Why it works

Research shows passive reading yields 10% retention, while explaining to someone else yields up to 90%. The conversational format with clarifying questions mimics learning by teaching.

In TutLM

  • Explain phase: AI streams explanation, student can ask questions in chat
  • After each exchange AI assesses readiness (0–100%) and updates progress bar
  • "Check knowledge" button activates when readiness ≥ 70%
  • Student decides when ready — not the system

References

  • Chi M.T.H. et al. (1994). Eliciting self-explanations improves understanding. Cogn. Sci.
  • Fiorella & Mayer (2016). Eight ways to promote generative learning. Educ. Psychol. Rev.
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Interleaving

Interleaved Practice

Tasks from different topics are mixed, not grouped. Each session starts with a topic different from the last one answered.

Why it works

Blocked practice (all tasks on topic A, then all on topic B) creates an illusion of understanding. Interleaved practice forces the brain to retrieve the right approach each time — harder, but leads to long-term retention.

In TutLM

  • get_due_topic() fetches top-3 candidates by SM-2 date
  • The topic most recently answered is excluded
  • If another topic is available — it is selected

References

  • Rohrer D. & Taylor K. (2007). The shuffling of mathematics problems improves learning. Instr. Sci.
  • Kornell & Bjork (2008). Learning concepts and categories. Psychol. Sci.
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Pre-assessment

Pre-Assessment

On first contact with a topic, AI asks one quick question. Correct answer — explanation is skipped, student goes straight to practice.

Why it works

A boring explanation of something the student already knows is demotivating and wastes time. A quick check respects existing knowledge and speeds up familiar material.

In TutLM

  • mastery IS NULL → pre_assess phase
  • LLM generates a short question on the topic
  • Score ≥ 3/5 → pre_assessed = true, interval = 6 days (skip explanation)
  • Score < 3 → transition to explain phase

References

  • Ausubel D.P. (1968). Educational psychology: A cognitive view.
  • Roediger & Karpicke (2006). Test-enhanced learning. Psychol. Sci.
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Adaptive Difficulty

Adaptive Difficulty

Task difficulty is calibrated based on the current mastery score. Higher mastery — harder question.

Why it works

Flow theory (Csikszentmihalyi): learning is most effective in the zone of optimal challenge — not too easy (boredom) and not too hard (anxiety). Adaptation keeps the student in this zone.

In TutLM

  • difficulty = mastery_score (0.0–1.0)
  • difficulty_label: easy (<0.35), medium (0.35–0.65), hard (>0.65)
  • Prompt passes difficulty_label and exact value
  • LLM selects task format according to distribution table

References

  • Csikszentmihalyi M. (1990). Flow: The psychology of optimal experience.
  • VanLehn K. (2011). The relative effectiveness of human tutoring, ITS, and other tutoring systems. Educ. Psychol.
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Knowledge Graph

Prerequisite Chains

Topics are linked through prerequisites. The next topic is only available when previous ones are sufficiently mastered (mastery ≥ 20%).

Why it works

Learning is nonlinear but structured. The knowledge graph ensures the foundation is laid before building on it. Visualization helps students understand where they are.

In TutLM

  • Topic.prereq_ids: UUID[] — list of prerequisites
  • get_unlocked_topic_ids(): checks mastery ≥ 0.2 for all prereqs
  • SM-2 considers only unlocked topics when selecting the next one
  • SVG graph with topological sort (layered DAG) at /app/courses/[id]/graph

References

  • Chi M.T.H. (1997). Quantifying qualitative analyses of verbal data. J. Learn. Sci.

See it in action

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