Skill: daigxok/calculus-error-analyzer (version 1.0.0)

# calculus-error-analyzer - 高等数学错题深度分析Skill ## 概述 专门针对高等数学错题的深度分析系统，通过错误模式识别、知识点关联分析、学习路径优化，实现从错题到学习改进的智能转化。 ## 核心功能 ### 1. 错误模式深度挖掘 - **错误类型分类**: 概念错误、计算错误、逻辑错误、理解偏差 - **错误根源分析**: 追溯错误的知识点根源和思维误区 - **错误模式聚类**: 发现学生个性化的错误模式 - **错误演变追踪**: 分析错误随时间的演变规律 ### 2. 个性化错题本生成 - **智能错题归类**: 按知识点、错误类型、难度自动分类 - **错题标签系统**: 多维标签标记错题特征 - **错题难度评估**: 评估错题的典型性和重要性 - **错题复习计划**: 基于遗忘曲线的智能复习安排 ### 3. 学习路径优化 - **薄弱点诊断**: 精准定位知识体系中的薄弱环节 - **学习路径推荐**: 基于错误分析的个性化学习路径 - **干预策略生成**: 针对不同错误类型的教学干预 - **进步预测**: 基于错误纠正的进步可能性预测 ## 工具定义 ### analyze_error_patterns 深度分析错误模式 **参数**： - `error_data` (array): 错误数据列表 - `analysis_level` (string): 分析级别，"basic"、"standard"、"deep" - `include_causes` (boolean): 是否包含错误原因分析 - `generate_solutions` (boolean): 是否生成解决方案 **返回**： ```json { "analysis_id": "ea_001", "summary": { "total_errors": 24, "unique_error_types": 8, "most_common_error": "积分公式记错", "error_frequency": 6 }, "error_categories": [ { "category": "概念理解错误", "count": 10, "percentage": 41.7, "subtypes": [ { "subtype": "定理条件混淆", "examples": ["误用罗尔定理条件", "拉格朗日定理应用错误"], "root_cause": "对定理成立条件理解不深", "recommendation": "重点复习定理的几何意义和适用条件" } ] }, { "category": "计算执行错误", "count": 8, "percentage": 33.3, "subtypes": [ { "subtype": "符号运算错误", "examples": ["正负号错误", "括号展开错误"], "root_cause": "计算粗心，检查习惯不好", "recommendation": "建立计算检查清单，放慢计算速度" } ] } ], "knowledge_gaps": [ { "topic": "微分中值定理", "gap_level": "严重", "affected_questions": 5, "prerequisite_topics": ["函数连续性", "导数概念"], "remediation_path": [ "第一步：复习函数连续性定义", "第二步：理解导数几何意义", "第三步：学习中值定理证明", "第四步：练习典型应用题" ] } ], "personalized_insights": { "learning_style_issues": "倾向于记忆公式而非理解推导", "thinking_patterns": "在证明题中容易跳过关键步骤", "time_management": "复杂题目后期容易出现计算错误", "confidence_level": "中等偏下，需要成功体验提升" } } ``` ### generate_personalized_error_book 生成个性化错题本 **参数**： - `student_id` (string): 学生ID - `time_range` (string): 时间范围，"week"、"month"、"all" - `organization_method` (string): 组织方式，"by_topic"、"by_error_type"、"by_difficulty" - `include_explanations` (boolean): 是否包含详细解析 **返回**： ```json { "error_book_id": "eb_001", "student_info": { "student_id": "stu001", "name": "张三", "total_errors_collected": 42, "time_period": "2026-03-01 至 2026-04-15" }, "error_book_structure": { "sections": [ { "section_title": "第一章 函数与极限", "error_count": 8, "priority": "高", "topics": [ { "topic": "函数极限计算", "error_examples": [ { "original_question": "求lim(x→0) (sinx/x)", "student_answer": "0", "correct_answer": "1", "error_type": "重要极限记错", "detailed_explanation": "这是第一个重要极限，值为1...", "similar_questions": [ "lim(x→0) (tanx/x)", "lim(x→0) (arcsinx/x)" ], "learning_resources": [ { "type": "video", "title": "重要极限的几何解释", "url": "https://example.com/video1" } ] } ], "mastery_exercises": [ { "exercise": "计算lim(x→0) (1-cosx)/x²", "hint": "使用半角公式或洛必达法则", "answer": "1/2" } ] } ] } ] }, "review_schedule": { "spaced_repetition": [ { "review_date": "2026-04-16", "topics": ["函数极限", "导数定义"], "estimated_time": 30 }, { "review_date": "2026-04-20", "topics": ["微分中值定理"], "estimated_time": 45 } ], "review_strategies": { "immediate": "24小时内复习新错题", "short_term": "3天后第二次复习", "long_term": "每周系统性回顾" } }, "progress_tracking": { "error_reduction_rate": 35.2, "mastery_improvement": [ {"topic": "导数计算", "from": 65, "to": 82}, {"topic": "积分应用", "from": 58, "to": 71} ], "confidence_change": "显著提升" } } ``` ### recommend_intervention_strategies 推荐教学干预策略 **参数**： - `error_analysis` (object): 错误分析结果 - `student_profile` (object): 学生画像 - `intervention_type` (string): 干预类型，"immediate"、"short_term"、"long_term" - `available_resources` (array): 可用教学资源 **返回**： ```json { "intervention_plan_id": "ip_001", "student_profile_summary": { "learning_style": "视觉型学习者", "motivation_level": "中等", "self_efficacy": "需要提升", "time_availability": "每周5-7小时" }, "immediate_interventions": [ { "strategy": "概念澄清会议", "description": "一对一讲解微分中值定理的几何意义", "duration": 30, "materials": [ "GeoGebra动态演示文件", "定理证明动画视频" ], "expected_outcome": "理解定理条件和几何解释" }, { "strategy": "计算规范化训练", "description": "建立标准计算步骤检查表", "duration": 20, "materials": ["计算检查清单", "典型错误案例集"], "expected_outcome": "减少符号运算错误50%" } ], "short_term_strategies": [ { "strategy": "错题重做计划", "description": "系统性重做最近10个错题", "schedule": "每天2题，连续5天", "monitoring": "每天提交重做结果", "success_criteria": "正确率达到90%" }, { "strategy": "同伴学习小组", "description": "与同水平同学组成学习小组", "activities": ["互相批改作业", "讨论解题思路", "分享学习资源"], "frequency": "每周2次，每次60分钟" } ], "long_term_development": [ { "strategy": "数学思维训练", "description": "培养严谨的数学推理习惯", "activities": [ "每周完成1道证明题", "学习数学证明写作规范", "阅读数学史相关材料" ], "timeline": "8周计划", "milestones": [ "第2周：掌握基本证明结构", "第4周：能独立完成中等难度证明", "第8周：形成系统的数学思维" ] } ], "resource_recommendations": { "targeted_practice": [ { "resource_type": "练习册", "name": "微分中值定理专项练习", "difficulty": "基础到提高", "estimated_time": "4小时" } ], "conceptual_understanding": [ { "resource_type": "视频课程", "name": "微积分核心概念可视化", "duration": "3小时", "focus": "几何直观理解" } ], "motivational": [ { "resource_type": "阅读材料", "name": "数学之美：从微积分看世界", "purpose": "激发学习兴趣，理解数学应用" } ] }, "monitoring_and_evaluation": { "key_metrics": [ "错题重做正确率", "同类错误重复率", "学习时间投入", "自我效能感变化" ], "evaluation_schedule": [ {"time": "1周后", "focus": "计算错误减少情况"}, {"time": "2周后", "focus": "概念理解提升"}, {"time": "1月后", "focus": "综合能力进步"} ], "adjustment_criteria": "如果2周后进步小于20%，调整干预策略" } } ``` ## 使用示例 ### 示例1：深度错误模式分析 ```bash # 分析学生错误模式 openclaw skill calculus-error-analyzer analyze_error_patterns \ --error-data '[{"question":"求导数","error":"链式法则应用错误"},{"question":"计算积分","error":"积分公式记错"}]' \ --analysis-level "deep" \ --include-causes true \ --generate-solutions true ``` ### 示例2：生成个性化错题本 ```bash # 为学生生成月度错题本 openclaw skill calculus-error-analyzer generate_personalized_error_book \ --student-id "stu001" \ --time-range "month" \ --organization-method "by_topic" \ --include-explanations true ``` ### 示例3：推荐干预策略 ```bash # 基于错误分析推荐教学干预 openclaw skill calculus-error-analyzer recommend_intervention_strategies \ --error-analysis '{"error_categories":[{"category":"概念错误","count":10}]}' \ --student-profile '{"learning_style":"visual","motivation":"medium"}' \ --intervention-type "comprehensive" \ --available-resources '["geogebra","video_course","practice_sheets"]' ``` ## 错误分析模型 ### 错误分类体系 ```python class ErrorTaxonomy: """高等数学错误分类体系""" def __init__(self): self.categories = { 'conceptual_errors': { 'definition_misunderstanding': { 'description': '概念定义理解错误', 'examples': ['极限定义混淆', '导数概念误解'], 'severity': '高' }, 'theorem_misapplication': { 'description': '定理条件或应用错误', 'examples': ['误用中值定理', '洛必达法则滥用'], 'severity': '高' }, 'logical_fallacies': { 'description': '逻辑推理错误', 'examples': ['循环论证', '充分必要条件混淆'], 'severity': '中' } }, 'computational_errors': { 'algebraic_mistakes': { 'description': '代数运算错误', 'examples': ['符号错误', '因式分解错误'], 'severity': '中' }, 'formula_misremembering': { 'description': '公式记忆错误', 'examples': ['积分公式记错', '导数公式错误'], 'severity': '中' }, 'procedural_errors': { 'description': '计算步骤错误', 'examples': ['积分上下限错误', '变量替换错误'], 'severity': '低' } }, 'strategic_errors': { 'method_selection': { 'description': '解题方法选择不当', 'examples': ['复杂方法代替简单方法', '方法不适用'], 'severity': '中' }, 'problem_analysis': { 'description': '问题分析不充分', 'examples': ['未识别关键条件', '误解问题要求'], 'severity': '高' } } } def classify_error(self, error_description, context): """分类错误类型""" for category, subcategories in self.categories.items(): for subtype, config in subcategories.items(): if self.matches_pattern(error_description, config['examples']): return { 'category': category, 'subtype': subtype, 'description': config['description'], 'severity': config['severity'], 'confidence': self.calculate_confidence(error_description, config) } return {'category': 'unknown', 'subtype': 'other'} ``` ### 错误根源分析 ```python class RootCauseAnalyzer: """错误根源分析引擎""" def analyze_root_cause(self, error_instance, student_history): """分析错误根本原因""" causes = [] # 1. 知识点缺陷分析 knowledge_gaps = self.identify_knowledge_gaps(error_instance) if knowledge_gaps: causes.append({ 'type': 'knowledge_gap', 'description': '相关知识点掌握不足', 'specific_gaps': knowledge_gaps, 'evidence': self.find_evidence(student_history, knowledge_gaps) }) # 2. 思维习惯分析 thinking_patterns = self.analyze_thinking_patterns(error_instance, student_history) if thinking_patterns: causes.append({ 'type': 'thinking_habit', 'description': '不良思维习惯', 'patterns': thinking_patterns, 'frequency': self.calculate_frequency(student_history, thinking_patterns) }) # 3. 心理因素分析 psychological_factors = self.assess_psychological_factors(student_history) if psychological_factors: causes.append({ 'type': 'psychological', 'description': '心理因素影响', 'factors': psychological_factors, 'impact_level': self.estimate_impact(psychological_factors) }) # 4. 学习策略分析 strategy_issues = self.evaluate_learning_strategies(student_history) if strategy_issues: causes.append({ 'type': 'strategy', 'description': '学习策略不当', 'issues': strategy_issues, 'recommendations': self.suggest_strategy_improvements(strategy_issues) }) return { 'primary_cause': self.identify_primary_cause(causes), 'contributing_factors': causes, 'interdependencies': self.analyze_interdependencies(causes) } ``` ### 错题本智能生成 ```python class ErrorBookGenerator: """个性化错题本生成器""" def __init__(self): self.organizers = { 'by_topic': TopicOrganizer(), 'by_error_type': ErrorTypeOrganizer(), 'by_difficulty': DifficultyOrganizer(), 'by_priority': PriorityOrganizer() } def generate_error_book(self, student_errors, organization_method='by_topic'): """生成错题本""" organizer = self.organizers.get(organization_method, self.organizers['by_topic']) # 1. 错题分类组织 organized_errors = organizer.organize(student_errors) # 2. 添加详细解析 enriched_errors = self.enrich_with_explanations(organized_errors) # 3. 生成学习资源链接 errors_with_resources = self.link_learning_resources(enriched_errors) # 4. 设计复习计划 review_plan = self.create_review_plan(errors_with_resources) # 5. 生成错题本文档 error_book = self.compile_error_book( errors_with_resources, review_plan ) return error_book def create_review_plan(self, errors, algorithm='spaced_repetition'): """基于遗忘曲线创建复习计划""" if algorithm == 'spaced_repetition': plan = SpacedRepetitionScheduler().schedule(errors) elif algorithm == 'adaptive': plan = AdaptiveScheduler().schedule(errors) else: plan = FixedIntervalScheduler().schedule(errors) return { 'schedule': plan['intervals'], 'estimated_time': plan['total_time'], 'success_criteria': self.define_success_criteria(errors), 'adjustment_rules': self.get_adjustment_rules() } ``` ## 与现有Skill集成 ### 集成calculus-learning-anal


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