The peer-reviewed concepts, algorithms, and studies that power our engine.

We believe that language learning software should be as rigorous as the science it is built upon. Below is the complete index of the neurobiological frameworks and algorithmic principles used in our platform, categorized by function.

How the brain encodes and retrieves information.

The Illusion of Competence

• Definition: The cognitive bias where learners mistake "familiarity" (recognizing a word) for "mastery" (being able to use it).
• Primary Source: Roediger & Karpicke (2006); Bjork (1994).

The Testing Effect

• Definition: The finding that the act of effortful retrieval strengthens neural pathways significantly more than passive review.
• Primary Source: Roediger & Karpicke (2006).

Generative Processing (ICAP)

• Definition: The hierarchy of engagement (Interactive > Constructive > Active > Passive) that predicts learning depth. We optimize for Constructive engagement.
• Primary Source: Chi (2009).

Transfer-Appropriate Processing

• Definition: The principle that memory performance is optimized when study methods match the final application (e.g., typing answers to practice speaking).
• Primary Source: Morris, Bransford, & Franks (1977).

The Hypercorrection Effect

• Definition: The phenomenon where high-confidence errors, when corrected immediately, result in the strongest memory retention.
• Primary Source: Butterfield & Metcalfe (2001).

The mathematics of memory decay and optimization.

The FSRS Algorithm

• Definition: The Free Spaced Repetition Scheduler—a probabilistic model that calculates memory stability ($S$) and retrievability ($R$) to predict the exact moment of forgetting.
• Primary Source: Jarosz (SuperMemo); FSRS Documentation.

Memory Stability ($S$)

• Definition: A metric quantifying the durability of a memory trace (how long it lasts), distinct from Retrieval Strength (how accessible it is now).
• Primary Source: Bjork’s New Theory of Disuse (1992).

The Spacing Effect

• Definition: The robust finding that distributing practice over time yields superior retention compared to massed practice (cramming).
• Primary Source: Ebbinghaus (1885); Cepeda et al. (2006).

Sleep-Dependent Consolidation

• Definition: The biological process during Slow-Wave Sleep (SWS) and REM sleep that transfers memory traces from the hippocampus to the neocortex.
• Primary Source: Walker & Stickgold (2006).

Managing the biological bottlenecks of the brain.

Working Memory Capacity

• Definition: The biological limit of processing (often cited as $7 \pm 2$ chunks) that dictates optimal session length to avoid cognitive overload.
• Primary Source: Miller (1956); Sweller (1988).

The Tripartite Load Model

• Definition: The balance between Intrinsic (necessary difficulty), Extraneous (harmful distractions), and Germane (beneficial processing) cognitive load.
• Primary Source: Sweller (Cognitive Load Theory).

Desirable Difficulties

• Definition: Learning tasks that require considerable but desirable effort, thereby improving long-term performance.
• Primary Source: Bjork (1994).

Building flexible, robust knowledge networks.

Interleaving

• Definition: Mixing different topics or problem types within a session (e.g., A-B-C vs A-A-A) to improve discrimination skills.
• Primary Source: Taylor & Rohrer (2010); Kang (2016).

Dual Coding Theory

• Definition: The theory that pairing verbal and visual information creates two distinct retrieval paths, doubling retention probability.
• Primary Source: Paivio (1971).

The Frayer Model

• Definition: A four-quadrant graphic organizer used to define the boundaries of a concept (Definition, Characteristics, Examples, Non-Examples).

Primary Source: Frayer, Frederick, & Klausmeier (1969).

Bridging the gap to real-world application.

Comprehensible Input ($i+1$)

• Definition: The hypothesis that acquisition occurs when learners are exposed to content slightly above their current competence.
• Primary Source: Krashen (1982).

Zone of Proximal Development (ZPD)

• Definition: The range of tasks a learner can perform with guidance (scaffolding) but cannot yet perform alone.
• Primary Source: Vygotsky (1978).