Sister section
PedagogyPath
Adaptive learning, spaced repetition, knowledge tracing, item-response theory, and intelligent tutoring — explained for educators and instructional designers, with the same rigor TheoremPath applies to ML theory.
TheoremPath is the parent network for the rigorous machine-learning curriculum this section borrows from.
Flagship
Flagship · 22 min
Bayesian Knowledge Tracing for Educators
Bayesian Knowledge Tracing (BKT) is a state-space model that tracks the probability a learner has mastered a skill from a sequence of correct or incorrect responses. The model has four parameters per skill: prior knowledge, learning rate, guess rate, and slip rate. Updates are by Bayes' rule. Originally developed by Corbett and Anderson (1995) for the Cognitive Tutor systems, BKT remains the workhorse model for skill-level mastery tracking in intelligent tutoring systems and is one of the four pillars of the TheoremPath adaptive learning machinery.
Flagship · 22 min
FSRS: Spaced Repetition for Educators
FSRS (Free Spaced Repetition Scheduler) is a modern spaced-repetition algorithm based on the difficulty-stability-retrievability (DSR) model of memory. It schedules review intervals to target a chosen retention rate (typically 90%) and updates parameters per card based on rating history. Originally developed by Jingyong Ye and the open-spaced-repetition project starting around 2022, FSRS has become the default scheduler in the Anki ecosystem and is the algorithm TheoremPath uses for its review-card layer. This page covers how FSRS works, what empirical evidence underwrites it, where it fails, and how to think about it relative to SM-2 and the broader spaced-repetition literature.
Flagship · 22 min
Intelligent Tutoring Systems
An intelligent tutoring system (ITS) is a software system that provides individualized instruction by maintaining an explicit model of the domain, an explicit model of the learner's current knowledge state, and a tutor model that selects what to do next. The architecture goes back to early 1970s research at Stanford and Carnegie Mellon. The most-cited empirical claim, from VanLehn (2011), is that ITS effects approach the magnitude of one-on-one human tutoring. This page covers the architecture, the empirical record (with effect sizes and the boundary conditions that the effect sizes do not reveal), the canonical examples, and how TheoremPath's adaptive components relate to the ITS tradition.
Flagship · 22 min
Item Response Theory for Educators
Item response theory (IRT) models the probability of a correct response as a function of a learner's latent ability and the parameters of the item. The 1PL Rasch, 2PL, and 3PL family is the workhorse of high-stakes psychometric assessment (GRE, GMAT, TOEFL, NAEP) and the foundation of computerized adaptive testing. Item parameters are calibrated from response data; learner ability is then estimated on the calibrated scale. This page covers IRT as a method that educators can use to understand assessment design and the psychometric scale, with explicit treatment of the assumptions, the boundary conditions, and how the TheoremPath assessment items use IRT-style difficulty calibration.
Flagship · 20 min
Plato as Teacher
Plato as a teacher rather than as a philosopher. The Meno's slave-boy episode (Meno 81e-86c) as a worked example of guided discovery in mathematics; recollection (anamnesis) as a pedagogical thesis with a modern echo in retrieval-practice research; the Academy as an institutional model; the Republic's curriculum sequence (gymnastics, music, mathematics, dialectic) as an explicit ordering of subjects by cognitive readiness. Cross-site companion to the PhilosophyPath Plato landing page; the two pages cover the same figure from different angles.
Flagship · 28 min
The TheoremPath Pedagogy Thesis
The TheoremPath site is itself a pedagogical artifact. Its prerequisite DAG, its FSRS-based review scheduler, its BKT-flavoured mastery layer, and its IRT-style item difficulty calibration are not arbitrary engineering choices. Each of them implements a specific finding from the empirical cognitive-science-of-learning literature, and each is open to evaluation against alternative implementations. This page is the canonical statement of which findings underwrite which design choices, where the implementations match the literature, where they diverge, and what is deliberately deferred. It is the page that says: this is why TheoremPath is built this way.