Press n or j to go to the next uncovered block, b, p or k for the previous block.
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* Domain-Informed Priors for BKT Parameters
*
* Different skill types have different learning characteristics.
* These priors encode our domain knowledge about soroban skill difficulty.
*/
import type { BktParams } from './types'
/**
* Get default BKT parameters for a skill based on its type.
*
* Parameters are informed by soroban pedagogy:
* - Basic skills (direct manipulation) are easier to learn
* - Five complements require memorization and pattern recognition
* - Ten complements are more complex and error-prone
* - Mixed complements (combining techniques) are the hardest
*
* @param skillId - The skill identifier (e.g., "basic.directAddition")
* @returns BKT parameters tuned for this skill type
*/
export function getDefaultParams(skillId: string): BktParams {
// Basic skills - direct bead manipulation
// High P(init) because these are intuitive
// Moderate P(learn) - lowered to prevent P(known) exploding after few correct answers
// Balanced pSlip/pGuess - the ratio pSlip/pGuess determines evidence strength
// A correct answer provides evidence ratio of (1-pSlip)/pGuess = (1-0.15)/0.12 = 7.1x
// (vs 45x with old values). This makes BKT updates more gradual.
if (skillId.startsWith('basic.')) {
return {
pInit: 0.3,
pLearn: 0.1, // Low learning rate - requires sustained practice
pSlip: 0.15, // Higher slip - even known skills have errors
pGuess: 0.12, // Higher guess - some problems can be guessed correctly
}
}
// Five complements - using the "friends of 5"
// Moderate difficulty, requires memorization
if (skillId.startsWith('fiveComplements')) {
return {
pInit: 0.1,
pLearn: 0.08, // Low learning rate
pSlip: 0.18, // Moderate slip
pGuess: 0.1, // Moderate guess
}
}
// Five complement subtraction
if (skillId.startsWith('fiveComplementsSub')) {
return {
pInit: 0.1,
pLearn: 0.07,
pSlip: 0.2,
pGuess: 0.1,
}
}
// Ten complements - using the "friends of 10"
// More challenging, higher cognitive load
if (skillId.startsWith('tenComplements')) {
return {
pInit: 0.05,
pLearn: 0.06, // Very low learning rate for harder skills
pSlip: 0.22, // Higher slip for complex skills
pGuess: 0.08, // Lower guess for complex skills
}
}
// Ten complement subtraction
if (skillId.startsWith('tenComplementsSub')) {
return {
pInit: 0.05,
pLearn: 0.05,
pSlip: 0.25,
pGuess: 0.08,
}
}
// Mixed complements - combining techniques
// Hardest category, requires fluency in multiple approaches
if (skillId.startsWith('mixedComplements')) {
return {
pInit: 0.02,
pLearn: 0.04, // Very slow learning
pSlip: 0.28, // High slip even when known
pGuess: 0.06, // Low guess - hard to luck into correct answer
}
}
// Default for any unknown skill type
return {
pInit: 0.1,
pLearn: 0.08,
pSlip: 0.18,
pGuess: 0.1,
}
}
/**
* Get a human-readable category name for a skill.
*/
export function getSkillCategory(skillId: string): string {
if (skillId.startsWith('basic.')) return 'Basic Skills'
if (skillId.startsWith('fiveComplementsSub')) return 'Five Complement Subtraction'
if (skillId.startsWith('fiveComplements')) return 'Five Complements'
if (skillId.startsWith('tenComplementsSub')) return 'Ten Complement Subtraction'
if (skillId.startsWith('tenComplements')) return 'Ten Complements'
if (skillId.startsWith('mixedComplements')) return 'Mixed Complements'
return 'Other'
}
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