digitalboy/mathGPT_graph_data

# 说明

本数据集属于 **数学根因分析与练习系统（Root Cause Analysis and Exercises for Mathematics, RCAE）** 的基础子项目之一。旨在可以高效的发现学生数学学业错误的根本原因。


## 总项目介绍

**数学根因分析与练习系统（RCAE）** 是一款利用先进的图数据库技术和强大的数据分析算法，旨在革新数学教育的系统。通过对学生答题记录的分析，RCAE能够快速定位学生掌握不牢固的知识点，并生成个性化的练习计划，帮助学生高效提升数学成绩。

## 此数据集的意义

本数据集是“数学根因分析与练习系统（RCAE）”的一个子项目，包含由中国北京师范大学出版社出版的小学数学全部知识点的详尽知识图谱。通过这个数据集，可以实现对小学数学知识点的全面了解和掌握，辅助RCAE系统进行更准确的根因分析和个性化练习推荐。

## 此数据集的优势
1. **充分MECE**：已经尽可能的将知识点做到不缺失，不遗漏，不重复，相互独立。
2. **关系充分**：从先决关系、包含关系、互补关系等12种关系。基本覆盖了数学领域的所有关系。
3. **拓展**：比如统计某种关系的数量，判断节点的重要性和复杂性等。

## 后续发展计划
1. **更多数据**：继续拓展初中，高中各个年级；人教出版社，北美数学……
2. **知识点解释**：为每个知识点提供生动、传神、有趣的解释，提高可理解性并降低学生的认知负荷。
3. **题目设计**：根据布鲁姆目标分类和孩子的认知规律，为每个知识点设计题目，难度分层。
4. **根因溯源**：可以快速的找到错题的根因，谨防无效刷题（我最恨这个了）。
5. **教师界面**：老师可以随时查看各种数据透视，快速掌握群体、个体的学业水平。
6. **结合脑科学**：学习尽快不能很快乐，但是尽量不要伤害孩子的学习热情。

## 节点数量
742

## 边数量
2990

## 使用方法
1. **下载数据集**：从GitHub仓库下载JSON格式的知识点图数据。
2. **加载数据**：将下载的JSON数据导入图数据库（如Neo4j）。
3. **构建知识图谱**：使用图数据库工具构建知识点之间的关系图谱。
4. **使用API**：如下。

## API
https://math.beike.ai/api/graph/get_nodes_edges
### Params:
grades (小学六年级上册,小学六年级下册)
subject (数学)

## 版权声明
本数据集和相关代码由[张扬]创建，采用 **[Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)](https://creativecommons.org/licenses/by-nc/4.0/deed.zh)** 许可证进行许可。

### 您可以自由地：
- **共享** — 在任何媒介以任何形式复制、分发和传播本数据集和相关代码。
- **演绎** — 修改、转换或以本数据集和相关代码为基础进行创作。

### 在以下条件下：
- **署名** — 您必须给出适当的署名，提供指向本声明的链接，并指明是否对作品进行了修改。您可以以任何合理方式进行，但不得以任何方式暗示许可人认可您或您的使用。
- **非商业性使用** — 您不得将本数据集和相关代码用于商业目的。

### 没有附加限制：
- 您不得适用法律术语或技术措施从而限制其他人做许可证允许的任何事情。

### 免责声明：
- 本数据集和相关代码按“原样”提供，不附带任何明示或暗示的担保。使用者需自行承担使用风险。作者不对因使用本数据集和相关代码而产生的任何索赔、损害或其他责任负责，无论是在合同诉讼、侵权诉讼或其他诉讼中。

有关详细信息，请参见[Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) 许可证](https://creativecommons.org/licenses/by-nc/4.0/deed.zh)。

## 目前存在的问题
尽管已经具备的相当的可用性，但是由于本人精力有限，才疏学浅，难免疏漏。

1. **数据完整性**：数据集可能存在某些知识点的缺失或描述不完整的情况，需要持续完善。
2. **关系准确性**：知识点之间的关系需要进一步验证和优化，确保其准确性和逻辑性。
3. **系统兼容性**：不同图数据库的兼容性和性能差异可能影响知识图谱的构建和查询效率。
4. **用户反馈**：需要更多的用户反馈来优化系统的算法和数据结构，提高整体效果。

## 需要的帮助
1. **编程**：如果您有编程能力，并热爱AI+教育，联系我。
2. **一线教师**：如果您能在一线实践并检测这个系统，联系我。
3. **脑科学**：如果您对教育+认知科学有兴趣，联系我。

## 联系作者

如有任何问题或建议，请通过以下方式联系作者：

- **微信**：13510546101
- **邮箱**：[e-mail]
- **Twitter**：https://x.com/freethisslave

欢迎大家提供宝贵意见和建议，共同完善数学根因分析与练习系统！

## 关系(edge)表：
```
[
{
"type": "Prerequisite",
"direction": "directed",
"description": "描述一个概念是理解另一个概念的先决条件。",
"example": {"from": "加法", "to": "乘法"}
},
{
"type": "Includes",
"direction": "directed",
"description": "表明一个概念是另一个更广泛概念的一部分。",
"example": {"from": "三角形", "to": "几何图形"}
},
{
"type": "RelatedTo",
"direction": "undirected",
"description": "表示两个概念之间的相关性或关联性。",
"example": {"from": "概率", "to": "统计"}
},
{
"type": "AppliedIn",
"direction": "directed",
"description": "指一个概念如何在另一个领域或实例中被应用。",
"example": {"from": "几何学", "to": "建筑设计"}
},
{
"type": "AdvancesTo",
"direction": "directed",
"description": "表明一个概念是另一个概念的深入或拓展。",
"example": {"from": "基础代数", "to": "高等代数"}
},
{
"type": "ContrastsWith",
"direction": "undirected",
"description": "描述两个概念之间的对比或差异。",
"example": {"from": "离散数学", "to": "连续数学"}
},
{
"type": "SynonymousWith",
"direction": "undirected",
"description": "用于连接意思相近或相同的不同表述的概念。",
"example": {"from": "减法", "to": "差运算"}
},
{
"type": "HistoricallyDevelopedFrom",
"direction": "directed",
"description": "反映了概念的历史发展或演变。",
"example": {"from": "古典代数", "to": "现代代数"}
},
{
"type": "SubsetOf",
"direction": "directed",
"description": "表示一个概念是另一个概念的子集。",
"example": {"from": "有理数", "to": "实数"}
},
{
"type": "SpecialCaseOf",
"direction": "directed",
"description": "表示一个概念是另一个更一般概念的特殊情况。",
"example": {"from": "正方形", "to": "矩形"}
},
{
"type": "AnalogousTo",
"direction": "undirected",
"description": "表示两个概念在不同情境下具有类似的结构或性质。",
"example": {"from": "平面几何", "to": "立体几何"}
},
{
"type": "ComplementaryTo",
"direction": "undirected",
"description": "表示两个概念在一定程度上互为补充。",
"example": {"from": "微分", "to": "积分"}
}
]

```

# Description

This dataset is one of the foundational sub-projects of the **Root Cause Analysis and Exercises for Mathematics (RCAE)** system. It aims to efficiently identify the root causes of students' mathematical academic errors.


## Overview of the Overall Project

The **Root Cause Analysis and Exercises for Mathematics (RCAE)** system is an educational innovation tool leveraging advanced graph database technologies and powerful data analysis algorithms. By analyzing students' answer records, RCAE can quickly pinpoint knowledge points that students have not mastered proficiently, and generate personalized practice plans to help students improve their mathematical performance efficiently.

## Significance of This Dataset

This dataset is a sub-project of the **Root Cause Analysis and Exercises for Mathematics (RCAE)** system, containing a comprehensive knowledge graph of all primary school mathematics knowledge points published by Beijing Normal University Publishing House in China. Through this dataset, a comprehensive understanding and mastery of primary school mathematics knowledge points can be achieved, assisting the RCAE system in conducting more accurate root cause analysis and personalized practice recommendations.

## Advantages of This Dataset
1. **Fully MECE (Mutually Exclusive, Collectively Exhaustive)**: Knowledge points have been arranged to be non-missing, non-overlapping, non-repetitive, and mutually independent as much as possible.
2. **Rich Relationship Coverage**: Covers 12 types of relationships including prerequisite, inclusion, complementary relationships, etc., basically encompassing all relationships in the field of mathematics.
3. **Extensibility**: Supports various extensions such as counting the number of a certain type of relationship, judging the importance and complexity of nodes, etc.

## Future Development Plans
1. **Expanded Data Coverage**: Continue to expand to cover all grades of junior and senior high school, textbooks from People's Education Press, North American mathematics curricula, etc.
2. **Knowledge Point Explanations**: Provide vivid, engaging, and interesting explanations for each knowledge point to improve comprehensibility and reduce students' cognitive load.
3. **Question Design**: Design questions for each knowledge point with hierarchical difficulty levels based on Bloom's Taxonomy and children's cognitive rules.
4. **Root Cause Tracing**: Quickly identify the root causes of incorrect answers to prevent ineffective practice (a practice I strongly oppose).
5. **Teacher Interface**: Allow teachers to view various data pivot tables at any time, quickly grasping the academic performance of both groups and individual students.
6. **Integration with Neuroscience**: While learning may not always be enjoyable, efforts will be made to minimize harm to students' learning enthusiasm.

## Number of Nodes
742

## Number of Edges
2990

## Usage Instructions
1. **Download the Dataset**: Download the JSON-formatted knowledge point graph data from the GitHub repository.
2. **Load the Data**: Import the downloaded JSON data into a graph database (e.g., Neo4j).
3. **Build the Knowledge Graph**: Use graph database tools to construct the relationship graph between knowledge points.
4. **Use the API**: As follows.

## API
https://math.beike.ai/api/graph/get_nodes_edges
### Params:
grades (6th Grade Upper Semester Primary School, 6th Grade Lower Semester Primary School)
subject (Mathematics)

## Copyright Notice

This dataset and related code were created by [Zhang Yang] and licensed under the **[Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)](https://creativecommons.org/licenses/by-nc/4.0/deed.zh)** license.

### You are free to:
- **Share** — copy, distribute and transmit the dataset and related code in any medium or format.
- **Adapt** — remix, transform, and build upon the dataset and related code.

### Under the following terms:
- **Attribution** — You must give appropriate credit, provide a link to this license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- **NonCommercial** — You may not use the dataset and related code for commercial purposes.

### No additional restrictions:
- You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.

### Disclaimer:
- This dataset and related code are provided "as is", without warranty of any kind, express or implied. Users bear their own risks when using the dataset and related code. The author shall not be liable for any claims, damages or other liabilities arising from the use of the dataset and related code, whether in contract, tort or otherwise.

For more details, see the [Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) License](https://creativecommons.org/licenses/by-nc/4.0/deed.zh).

## Current Issues

Although the dataset has considerable usability, due to limited energy and limited expertise on my part, omissions are inevitable.
1. **Data Completeness**: The dataset may have missing knowledge points or incomplete descriptions, requiring continuous improvement.
2. **Relationship Accuracy**: The relationships between knowledge points need further verification and optimization to ensure their accuracy and logical consistency.
3. **System Compatibility**: Compatibility and performance differences between different graph databases may affect the construction and query efficiency of the knowledge graph.
4. **User Feedback**: More user feedback is needed to optimize the system's algorithms and data structures and improve overall performance.

## Needed Assistance
1. **Programming**: If you have programming skills and are passionate about AI+Education, please contact me.
2. **Frontline Teachers**: If you can practice and test this system in a real classroom setting, please contact me.
3. **Neuroscience**: If you are interested in education+cognitive science, please contact me.

## Contact the Author

If you have any questions or suggestions, please contact the author through the following methods:
- **WeChat**: 13510546101
- **Email**: [e-mail]
- **Twitter**: https://x.com/freethisslave

Everyone is welcome to provide valuable comments and suggestions to jointly improve the Root Cause Analysis and Exercises for Mathematics (RCAE) system!

## Relationship (Edge) Table:
json
[
{
"type": "Prerequisite",
"direction": "directed",
"description": "Describes that one concept is a prerequisite for understanding another concept.",
"example": {"from": "Addition", "to": "Multiplication"}
},
{
"type": "Includes",
"direction": "directed",
"description": "Indicates that one concept is part of a broader concept.",
"example": {"from": "Triangle", "to": "Geometric Figure"}
},
{
"type": "RelatedTo",
"direction": "undirected",
"description": "Indicates a correlation or association between two concepts.",
"example": {"from": "Probability", "to": "Statistics"}
},
{
"type": "AppliedIn",
"direction": "directed",
"description": "Refers to how one concept is applied in another field or instance.",
"example": {"from": "Geometry", "to": "Architectural Design"}
},
{
"type": "AdvancesTo",
"direction": "directed",
"description": "Indicates that one concept is an in-depth extension or advancement of another concept.",
"example": {"from": "Basic Algebra", "to": "Advanced Algebra"}
},
{
"type": "ContrastsWith",
"direction": "undirected",
"description": "Describes the contrast or difference between two concepts.",
"example": {"from": "Discrete Mathematics", "to": "Continuous Mathematics"}
},
{
"type": "SynonymousWith",
"direction": "undirected",
"description": "Used to connect concepts with similar or identical meanings expressed in different terms.",
"example": {"from": "Subtraction", "to": "Difference Calculation"}
},
{
"type": "HistoricallyDevelopedFrom",
"direction": "directed",
"description": "Reflects the historical development or evolution of a concept.",
"example": {"from": "Classical Algebra", "to": "Modern Algebra"}
},
{
"type": "SubsetOf",
"direction": "directed",
"description": "Indicates that one concept is a subset of another concept.",
"example": {"from": "Rational Number", "to": "Real Number"}
},
{
"type": "SpecialCaseOf",
"direction": "directed",
"description": "Indicates that one concept is a special case of a more general concept.",
"example": {"from": "Square", "to": "Rectangle"}
},
{
"type": "AnalogousTo",
"direction": "undirected",
"description": "Indicates that two concepts have similar structures or properties in different contexts.",
"example": {"from": "Plane Geometry", "to": "Solid Geometry"}
},
{
"type": "ComplementaryTo",
"direction": "undirected",
"description": "Indicates that two concepts are mutually complementary to a certain extent.",
"example": {"from": "Differentiation", "to": "Integration"}
}
]

原始信息汇总

数学根因分析与练习系统（RCAE）数据集概述

数据集介绍

本数据集是“数学根因分析与练习系统（RCAE）”的一个子项目，包含由中国北京师范大学出版社出版的小学数学全部知识点的详尽知识图谱。通过这个数据集，可以实现对小学数学知识点的全面了解和掌握，辅助RCAE系统进行更准确的根因分析和个性化练习推荐。

数据集优势

1. 充分MECE：已经尽可能的将知识点做到不缺失，不遗漏，不重复，相互独立。
2. 关系充分：从先决关系、包含关系、互补关系等12种关系。基本覆盖了数学领域的所有关系。
3. 拓展：比如统计某种关系的数量，判断节点的重要性和复杂性等。

数据集规模

• 节点数量：742
• 边数量：2990

使用方法

1. 下载数据集：从GitHub仓库下载JSON格式的知识点图数据。
2. 加载数据：将下载的JSON数据导入图数据库（如Neo4j）。
3. 构建知识图谱：使用图数据库工具构建知识点之间的关系图谱。
4. 使用API：如下。

API

• API链接：https://math.beike.ai/api/graph/get_nodes_edges
• 参数：
  • grades：小学六年级上册,小学六年级下册
  • subject：数学

版权声明

本数据集和相关代码由[张扬]创建，采用 Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) 许可证进行许可。

您可以自由地：

• 共享 — 在任何媒介以任何形式复制、分发和传播本数据集和相关代码。
• 演绎 — 修改、转换或以本数据集和相关代码为基础进行创作。

在以下条件下：

• 署名 — 您必须给出适当的署名，提供指向本声明的链接，并指明是否对作品进行了修改。您可以以任何合理方式进行，但不得以任何方式暗示许可人认可您或您的使用。
• 非商业性使用 — 您不得将本数据集和相关代码用于商业目的。

免责声明：

• 本数据集和相关代码按“原样”提供，不附带任何明示或暗示的担保。使用者需自行承担使用风险。作者不对因使用本数据集和相关代码而产生的任何索赔、损害或其他责任负责，无论是在合同诉讼、侵权诉讼或其他诉讼中。

关系(edge)表

json [ { "type": "Prerequisite", "direction": "directed", "description": "描述一个概念是理解另一个概念的先决条件。", "example": {"from": "加法", "to": "乘法"} }, { "type": "Includes", "direction": "directed", "description": "表明一个概念是另一个更广泛概念的一部分。", "example": {"from": "三角形", "to": "几何图形"} }, { "type": "RelatedTo", "direction": "undirected", "description": "表示两个概念之间的相关性或关联性。", "example": {"from": "概率", "to": "统计"} }, { "type": "AppliedIn", "direction": "directed", "description": "指一个概念如何在另一个领域或实例中被应用。", "example": {"from": "几何学", "to": "建筑设计"} }, { "type": "AdvancesTo", "direction": "directed", "description": "表明一个概念是另一个概念的深入或拓展。", "example": {"from": "基础代数", "to": "高等代数"} }, { "type": "ContrastsWith", "direction": "undirected", "description": "描述两个概念之间的对比或差异。", "example": {"from": "离散数学", "to": "连续数学"} }, { "type": "SynonymousWith", "direction": "undirected", "description": "用于连接意思相近或相同的不同表述的概念。", "example": {"from": "减法", "to": "差运算"} }, { "type": "HistoricallyDevelopedFrom", "direction": "directed", "description": "反映了概念的历史发展或演变。", "example": {"from": "古典代数", "to": "现代代数"} }, { "type": "SubsetOf", "direction": "directed", "description": "表示一个概念是另一个概念的子集。", "example": {"from": "有理数", "to": "实数"} }, { "type": "SpecialCaseOf", "direction": "directed", "description": "表示一个概念是另一个更一般概念的特殊情况。", "example": {"from": "正方形", "to": "矩形"} }, { "type": "AnalogousTo", "direction": "undirected", "description": "表示两个概念在不同情境下具有类似的结构或性质。", "example": {"from": "平面几何", "to": "立体几何"} }, { "type": "ComplementaryTo", "direction": "undirected", "description": "表示两个概念在一定程度上互为补充。", "example": {"from": "微分", "to": "积分"} } ]

搜集汇总

数据集介绍

构建方式

在数学教育领域，知识图谱的构建对于精准诊断学习障碍至关重要。本数据集以北京师范大学出版社的小学数学教材为蓝本，系统梳理了涵盖742个知识节点与2990条关联边的结构化知识网络。构建过程严格遵循MECE原则，确保知识点既不遗漏也不重叠，同时定义了包括先决关系、包含关系、互补关系在内的12种语义关系类型，通过人工标注与逻辑校验，形成了层次分明、关系完备的数学知识体系。

使用方法

使用者可通过下载JSON格式的数据文件，将其导入Neo4j等图数据库系统，即可构建可交互查询的知识图谱。基于该图谱，可开展知识路径追溯、节点重要性分析等操作，亦可通过配套API接口动态获取特定学段的知识子图。这一架构使得数据集能够无缝集成至智能教育系统，支撑个性化学习诊断与自适应练习推荐等高级应用场景。

背景与挑战

背景概述

在数学教育领域，精准诊断学生的学习障碍并实施个性化干预，一直是提升教学效能的核心议题。数字男孩（digitalboy）创建的mathGPT_graph_data数据集，作为数学根因分析与练习系统（RCAE）的基础子项目，于近年应运而生。该数据集依托北京师范大学出版社的小学数学教材，构建了一个包含742个节点与2990条边的知识图谱，系统性地刻画了知识点间的12种语义关系，如先决、包含与互补等。其核心研究目标在于通过图结构建模，实现对学生数学错误根源的自动化溯源，从而推动自适应学习系统的发展，为教育智能化提供了结构化的认知基础。

当前挑战

该数据集致力于解决数学教育中根因诊断这一复杂问题，其挑战在于如何从海量、异构的学生答题数据中，精准映射至知识图谱的特定节点与关系路径，并据此生成有效的个性化练习。构建过程中的挑战则更为具体：其一，确保知识点的MECE（相互独立、完全穷尽）原则，避免遗漏或冗余，这对小学数学知识体系的解构提出了极高要求；其二，定义并验证12类关系的逻辑准确性与教育适用性，需融合学科逻辑与教学经验；其三，图谱的扩展性与兼容性，如跨学段、跨版本教材的融合，以及不同图数据库系统的适配，均为持续性的工程难题。

常用场景

经典使用场景

在数学教育技术领域，知识图谱的构建为个性化学习提供了坚实基础。该数据集作为小学数学知识的结构化表达，其经典使用场景在于支撑智能教育系统进行学业诊断。系统通过分析学生在具体题目上的错误表现，利用图谱中知识点间的先决、包含等关系网络，追溯至薄弱的知识节点，从而实现精准的根因定位，为后续的干预措施提供明确方向。

解决学术问题

该数据集致力于解决教育数据挖掘中的关键学术问题，即如何从离散的学生答题记录中抽取出系统性的知识缺陷模式。传统方法往往局限于表面错误统计，而本数据集通过提供一套互斥且完备的知识点关系体系，使得研究者能够建模知识点之间的复杂依赖与推理路径。这为深入理解学习过程中的认知障碍形成机制，以及验证教育理论中的知识构建假设，提供了可计算、可验证的数据基础。

实际应用

在实际教学场景中，该数据集能够直接赋能自适应学习平台与教师辅助工具。平台可依据图谱关系，为不同学生动态生成遵循认知规律、覆盖知识薄弱点的个性化练习序列，避免无效的题海战术。教师则可通过系统提供的群体知识掌握度透视视图，快速把握班级整体学情与个体差异，从而调整教学重点，实现差异化辅导，提升课堂教学效率。

数据集最近研究

最新研究方向

在数学教育智能化领域，该数据集作为数学根因分析系统的核心知识图谱，正推动着个性化学习路径的前沿探索。当前研究聚焦于利用图神经网络与认知诊断模型深度融合，通过分析知识点间复杂的先决与互补关系，精准定位学生学业错误的深层根源。结合脑科学原理与布鲁姆目标分类，学者们致力于构建自适应练习生成系统，旨在减少无效刷题并保护学习热情，这一方向呼应了教育减负与因材施教的热点议题，为智能教育工具的可靠性与人性化设计提供了关键数据基础。