第3篇：题库不是堆砌！——构建智能分级题库的底层逻辑

import spacy, textstat
from collections import Counter

nlp = spacy.load("zh_core_web_sm")
cefr_map = {"A1": 0.1, "A2": 0.3, "B1": 0.5, "B2": 0.7, "C1": 0.85, "C2": 1.0}

def cognitive_load(text: str) -> float:
    doc = nlp(text)
    # 统计从句嵌套深度（简化版）
    clause_depth = max([len([t for t in sent if t.dep_ in ["relcl", "ccomp"]]) 
                        for sent in doc.sents], default=0)
    
    # CEFR词汇抽象度（示例：用预加载的中文CEFR词典）
    words = [token.lemma_.lower() for token in doc if not token.is_punct]
    cefr_scores = [cefr_map.get(get_cefr_level(w), 0.2) for w in words]
    vocab_abstraction = sum(cefr_scores) / len(words) if words else 0.2
    
    return min(1.0, (clause_depth * 0.4 + vocab_abstraction * 0.6))

from sympy import symbols, parse_expr, preorder_traversal
import networkx as nx

def solution_path_complexity(expr_str: str) -> float:
    try:
        expr = parse_expr(expr_str.replace("×", "*").replace("÷", "/"))
        # 运算符嵌套深度
        depth = 0
        for node in preorder_traversal(expr):
            if hasattr(node, 'func') and node.func.__name__ != 'Symbol':
                depth = max(depth, len(list(preorder_traversal(node))) - 1)
        
        # 变量依赖图直径（简化：仅处理赋值链）
        G = nx.DiGraph()
        # ...（实际实现需解析赋值语句，此处略）
        diameter = nx.diameter(G) if nx.is_strongly_connected(G) else 3
        
        return min(1.0, (depth * 0.5 + diameter * 0.5) / 8.0)
    except:
        return 0.5  # fallback

from sentence_transformers import SentenceTransformer
import numpy as np

model = SentenceTransformer('sentence-transformers/all-MiniLM-L6-v2')
anchor_embeddings = model.encode(anchor_questions)  # 形状: (1000, 768)
kmeans = KMeans(n_clusters=12).fit(anchor_embeddings)

def knowledge_span(text: str) -> float:
    vec = model.encode([text])[0]
    distances = np.array([1 - cosine(vec, center) for center in kmeans.cluster_centers_])
    top3_dist = np.sort(distances)[-3:]
    return np.std(top3_dist)  # [0, 0.35] → 归一化到[0,1]

你是一名教育测量专家。请严格按以下JSON Schema分析题目，禁止任何额外字符：
{
  "difficulty_score": "float [0,1]",
  "reasoning": ["string", "..."],
  "dimension_breakdown": {
    "cognitive_load": "float [0,1]",
    "solution_path": "float [0,1]",
    "knowledge_span": "float [0,1]"
  }
}
题目：小明用3米长的绳子围成一个正方形，又用同样长度的绳子围成一个圆。问哪个图形面积更大？（π取3.14）

from scipy.stats import spearmanr
import json

# 模拟教师标注数据
teacher_labels = [0.32, 0.67, ..., 0.81]  # 长度500
llm_outputs = [json.loads(resp)["difficulty_score"] for resp in llm_responses]

rho, pval = spearmanr(teacher_labels, llm_outputs)
print(f"Spearman ρ={rho:.3f}, p={pval:.3f}")  # Qwen2: 0.78, gpt-4: 0.86

def lambda_handler(event, context):
    # event: {"question_id": "q_12345", "is_correct": False, "response_time": 287}
    df = load_attempts(question_id=event["question_id"], window="7d")
    
    # 触发重评条件：正确率骤降 & 响应时间飙升
    if (df["is_correct"].mean() < 0.4 and 
        df["response_time"].mean() > 300 and
        len(df) > 20):
        
        # 调用分级Pipeline重评估
        new_score = run_full_pipeline(question_id=event["question_id"])
        update_question_difficulty(question_id=event["question_id"], score=new_score)

import plotly.express as px
import numpy as np

# 当前题库难度分布
scores = get_all_difficulty_scores()
fig = px.histogram(
    x=scores, nbins=20,
    title="题库难度分布（当前 vs 教育学基准）",
    labels={'x': '难度分', 'y': '题目数量'}
)
# 添加正态分布基准线（μ=0.5, σ=0.15）
x_norm = np.linspace(0, 1, 100)
y_norm = 100 * np.exp(-0.5 * ((x_norm - 0.5) / 0.15)**2)
fig.add_scatter(x=x_norm, y=y_norm, mode='lines', name='理想正态分布')
fig.show()

from scipy import stats

# 学习增益率（标准化提升）
gain_rate = (post_test - pre_test) / baseline_std
t_stat, p_val = stats.ttest_rel(gain_exp, gain_ctrl)
print(f"增益率提升: {np.mean(gain_exp)-np.mean(gain_ctrl):.3f}, p={p_val:.3f}")

# 挫败率（响应超5分钟且答错）
df['is_friction'] = (df['response_time'] > 300) & (~df['is_correct'])
friction_rate = df.groupby('group')['is_friction'].mean()
print(f"挫败率下降: {friction_rate['ctrl'] - friction_rate['exp']:.3%}")