File size: 4,604 Bytes
0e2e9ee | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 | """tutor/adaptive.py — LearnerState with Bayesian Knowledge Tracing."""
from __future__ import annotations
import random
from collections import defaultdict
from typing import List, Dict, Any
BKT_DEFAULTS = {"p_init": 0.30, "p_learn": 0.10, "p_guess": 0.20, "p_slip": 0.10}
AGE_CONFIG = {
5: {"diff_min": 1, "diff_max": 3, "target_acc": 0.70},
6: {"diff_min": 1, "diff_max": 4, "target_acc": 0.72},
7: {"diff_min": 2, "diff_max": 6, "target_acc": 0.75},
8: {"diff_min": 3, "diff_max": 7, "target_acc": 0.75},
9: {"diff_min": 4, "diff_max": 9, "target_acc": 0.78},
}
DYSC_STREAK_THRESHOLD = 5
DYSC_MIN_ATTEMPTS = 8
class SkillBKT:
def __init__(self, skill: str, params: Dict | None = None):
self.skill = skill
p = params or BKT_DEFAULTS
self.p_init = p["p_init"]
self.p_learn = p["p_learn"]
self.p_guess = p["p_guess"]
self.p_slip = p["p_slip"]
self.p_know = self.p_init
self.attempts = 0
self.correct = 0
self.streak_wrong = 0
def update(self, is_correct: bool):
self.attempts += 1
if is_correct:
self.correct += 1
self.streak_wrong = 0
else:
self.streak_wrong += 1
p_ok = (1 - self.p_slip) if is_correct else self.p_slip
p_nok = self.p_guess if is_correct else (1 - self.p_guess)
num = p_ok * self.p_know
den = num + p_nok * (1 - self.p_know)
p_kno = num / (den + 1e-9)
self.p_know = p_kno + (1 - p_kno) * self.p_learn
def mastery(self) -> float:
return self.p_know
def to_dict(self):
return {k: getattr(self, k) for k in
("skill","p_know","p_init","p_learn","p_guess","p_slip",
"attempts","correct","streak_wrong")}
@classmethod
def from_dict(cls, d):
obj = cls(d["skill"], {k: d[k] for k in ("p_init","p_learn","p_guess","p_slip")})
obj.p_know = d["p_know"]
obj.attempts = d["attempts"]
obj.correct = d["correct"]
obj.streak_wrong = d.get("streak_wrong", 0)
return obj
class LearnerState:
def __init__(self, learner_id: str, lang: str = "en", age: int = 7):
self.learner_id = learner_id
self.lang = lang
self.age = max(5, min(9, age))
self.bkt: Dict[str, SkillBKT] = {}
self._history: List[Dict] = []
@property
def age_config(self):
return AGE_CONFIG.get(self.age, AGE_CONFIG[7])
def _bkt(self, skill: str) -> SkillBKT:
if skill not in self.bkt:
self.bkt[skill] = SkillBKT(skill)
return self.bkt[skill]
def record_response(self, item: Dict, is_correct: bool):
self._bkt(item.get("skill", "unknown")).update(is_correct)
self._history.append({"item_id": item.get("id"), "correct": is_correct})
def mastery(self, skill: str) -> float:
return self._bkt(skill).mastery()
def select_next_item(self, all_items: List[Dict], use_bkt: bool = True) -> Dict:
cfg = self.age_config
by_skill: Dict[str, List[Dict]] = defaultdict(list)
for item in all_items:
d = item.get("difficulty", 5)
if cfg["diff_min"] <= d <= cfg["diff_max"]:
by_skill[item.get("skill", "unknown")].append(item)
if not by_skill:
return random.choice(all_items)
skills = sorted(by_skill.keys(), key=lambda s: self.mastery(s)) if use_bkt \
else list(by_skill.keys())
for skill in skills:
cands = by_skill[skill]
if cands:
m = self.mastery(skill)
t = cfg["diff_min"] + m * (cfg["diff_max"] - cfg["diff_min"])
cands.sort(key=lambda i: abs(i.get("difficulty", 5) - t))
return cands[0]
return random.choice(all_items)
def dyscalculia_warning(self) -> List[str]:
return [s for s, b in self.bkt.items()
if b.attempts >= DYSC_MIN_ATTEMPTS and b.streak_wrong >= DYSC_STREAK_THRESHOLD]
def to_dict(self):
return {
"learner_id": self.learner_id, "lang": self.lang, "age": self.age,
"bkt": {k: v.to_dict() for k, v in self.bkt.items()},
"history_len": len(self._history),
}
@classmethod
def from_dict(cls, d):
obj = cls(d["learner_id"], d.get("lang","en"), d.get("age",7))
for skill, bd in d.get("bkt", {}).items():
obj.bkt[skill] = SkillBKT.from_dict(bd)
return obj
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