Bridging British Education Virtual Academy

1. Course Basic Information 1. 课程基本信息

Course Name: 0111 CS 课程名称： 0111 计算机科学

Topic: Databases (Normalization) and LeetCode Bitwise Problem Solving 主题： 数据库（范式）和 LeetCode 位运算问题解决

Date: Date not specified 日期： 日期未指定

Student: Henry 学生： Henry

Teaching Focus 教学重点

Reviewing database concepts (keys, relations, normalization 0NF-2NF/3NF) and practicing complex bit manipulation logic (Power of Two problem) using C++/Python concepts.

复习数据库概念（键、关系、范式 0NF-3NF）并使用 C++/Python 概念练习复杂的位操作逻辑（二的幂问题）。

Teaching Objectives 教学目标

Review and solidify understanding of database structure, primary keys, and relational concepts. 复习并巩固对数据库结构、主键和关系概念的理解。
Understand and apply database normalization concepts (0NF, 1NF, 2NF, 3NF). 理解并应用数据库范式概念（0NF, 1NF, 2NF, 3NF）。
Solve a complex LeetCode problem involving bitwise operations ('Power of Two') using logic derived from binary representation. 使用从二进制表示中得出的逻辑，解决一个涉及位运算的复杂 LeetCode 问题（二的幂）。

2. Course Content Overview 2. 课程内容概览

Main Teaching Activities and Time Allocation 主要教学活动和时间分配

Database Theory Review: Discussion on databases, primary keys (analogy to hash), composite keys, foreign keys, one-to-many relationships, and the importance of avoiding data redundancy.

数据库理论复习： 讨论数据库、主键（与哈希的类比）、复合键、外键、一对多关系以及避免数据冗余的重要性。

Database Normalization (0NF to 2NF/3NF): Analyzing a messy table (0NF), moving to 1NF (atomicity), and then splitting tables to achieve 2NF/3NF to remove repeating data (e.g., storing names separately from subjects).

数据库范式（0NF 到 2NF/3NF）： 分析一个混乱的表（0NF），过渡到 1NF（原子性），然后拆分表以实现 2NF/3NF，以消除重复数据（例如，将姓名与科目分开存储）。

LeetCode: Power of Two (Bitwise Operations): Guided solving of the 'Power of Two' problem, focusing on the binary representation property (only one '1' bit) and using bitwise operators (AND, NOT) to solve without loops, including handling edge cases (zero, negative numbers).

LeetCode：二的幂（位运算）： 引导解决“二的幂”问题，重点关注二进制表示特性（只有一个 '1' 位），并使用位运算符（AND, NOT）在不使用循环的情况下解决问题，包括处理边界情况（零、负数）。

Language Knowledge and Skills 语言知识与技能

Vocabulary:
Database, Primary Key, Composite Key, Foreign Key, Relation, Atomic, Normal Form (0NF, 1NF, 2NF, 3NF), Hashable, Collision, Bitwise Operations (AND, OR, NOT), Binary Representation.

词汇：
数据库, 主键, 复合键, 外键, 关系, 原子性, 范式 (0NF, 1NF, 2NF, 3NF), 可哈希, 冲突, 位运算 (与, 或, 非), 二进制表示。

Concepts:
Database integrity through keys; importance of atomicity in 1NF; redundancy removal in 2NF/3NF; property that powers of two have exactly one set bit in binary.

概念：
通过键保证数据库完整性；1NF 中原子性的重要性；2NF/3NF 中冗余的消除；二的幂在二进制中恰好有一个设置位的特性。

Skills Practiced:
Conceptual explanation, table modeling/restructuring, abstract logical deduction, complex bitwise problem solving, adapting logic across programming languages (Python vs C++).

练习技能：
概念解释、表格建模/重构、抽象逻辑推理、复杂的位运算问题解决、在编程语言之间（Python vs C++）适应逻辑。

Teaching Resources and Materials 教学资源与材料

On-screen whiteboard for drawing database tables and relationship diagrams. 用于绘制数据库表和关系图的屏幕白板。
LeetCode problem interface (Count Complete Tree Nodes, Power of Two). LeetCode 问题界面（计算完全二叉树节点数，二的幂）。

3. Student Performance Assessment (Henry) 3. 学生表现评估 (Henry)

Participation and Activeness 参与度和积极性

High engagement, especially in the database discussion, providing thoughtful answers regarding primary key alternatives (e.g., phone numbers) and normalization structure. 参与度高，尤其是在数据库讨论中，对主键替代方案（如电话号码）和范式结构提供了深思熟虑的回答。

Language Comprehension and Mastery 语言理解和掌握

Demonstrated strong understanding of database principles (keys, relationships) and grasped the core logic for the bitwise 'Power of Two' problem quickly. 表现出对数据库原理（键、关系）的深刻理解，并迅速掌握了位运算“二的幂”问题的核心逻辑。

Language Output Ability 语言输出能力

Oral: 口语：

Fluent and clear explanation when describing concepts like composite keys and the purpose of normalization. 在描述复合键和范式的目的等概念时，表达流利清晰。

Written: 书面：

Student successfully applied the derived bitwise logic (N & (N-1) == 0 and edge case checks) to solve the difficult LeetCode problem.

学生成功应用了推导出的位运算逻辑（N & (N-1) == 0 和边界条件检查）解决了困难的 LeetCode 问题。

Student's Strengths 学生的优势

Excellent grasp of abstract computing concepts, particularly logic puzzles involving bits and operations. 对抽象计算概念有出色的掌握，特别是涉及位和操作的逻辑谜题。
Strong ability to think critically about data constraints (e.g., why phone numbers make poor primary keys due to siblings). 具备强大的批判性思维能力来分析数据约束（例如，为什么电话号码因为有兄弟姐妹而成为不好的主键）。

Areas for Improvement 需要改进的方面

Requires more familiarity with specific C++ bitwise operator implementations/compiler behavior compared to Python, leading to slight hesitation on the final edge case. 与 Python 相比，需要更熟悉特定的 C++ 位运算符实现/编译器行为，导致在最终边界情况上略有犹豫。
Needs practice translating the conceptual knowledge of Normal Forms into practical structuring of complex datasets. 需要练习将范式的概念知识转化为复杂数据集的实际结构化。

4. Teaching Reflection 4. 教学反思

Effectiveness of Teaching Methods 教学方法的有效性

High effectiveness due to the rapid pivot between deep theory (Normalization) and practical application (LeetCode), keeping the student engaged. 由于在深入理论（范式）和实际应用（LeetCode）之间快速切换，保持了学生的参与度，因此教学效果很高。

Teaching Pace and Time Management 教学节奏和时间管理

The pace was adjusted well, starting slow for theory, speeding up for concept application, and allocating sufficient time for the difficult bitwise problem. 课程节奏管理得当，理论部分开始较慢，概念应用部分加快，并为困难的位运算问题分配了足够的时间。

Classroom Interaction and Atmosphere 课堂互动和氛围

Interactive, problem-solving focused, and supportive, with the teacher compensating effectively for the late start.

互动性强，以解决问题为中心，且支持性好，教师有效地弥补了迟到的时间。

Achievement of Teaching Objectives 教学目标的达成

All objectives were substantially met, with the student showing mastery in conceptual review and solid execution in the coding challenge. 所有目标都得到了实质性的实现，学生在概念复习中表现出掌握，在编码挑战中表现出扎实的执行力。

5. Subsequent Teaching Suggestions 5. 后续教学建议

Teaching Strengths 教学优势

Identified Strengths: 识别的优势：

Effective management of late start by offering compensatory time at the end of the session and next session. 通过在本次课结束和下一次课增加补偿时间，有效管理了迟到的问题。
Strong scaffolding provided during the bitwise problem, guiding the student to the solution using hints about binary representation without giving the answer immediately. 在位运算问题解决过程中提供了强大的脚手架支持，通过关于二进制表示的提示引导学生找到答案，而不是直接给出答案。

Effective Methods: 有效方法：

Using real-world examples (siblings sharing a phone) to illustrate abstract database risks (collision, redundancy). 使用现实生活中的例子（兄弟姐妹共享电话）来说明抽象的数据库风险（冲突、冗余）。
Connecting theory (Normalization) directly to practical issues (table size, access speed). 将理论（范式）直接与实际问题（表大小、访问速度）联系起来。

Positive Feedback: 正面反馈：

The student's ability to pivot from database theory to complex bit manipulation logic was highly impressive. 学生从数据库理论迅速转向复杂的位操作逻辑的能力令人印象深刻。

Next Teaching Focus 下一步教学重点

Continue with more challenging LeetCode problems (Medium difficulty) focusing on core algorithms or dynamic programming principles. 继续解决更具挑战性的 LeetCode 问题（中等难度），重点关注核心算法或动态规划原理。
Introduce 3NF/BCNF concepts in database normalization if time permits, or move to SQL introduction. 如果时间允许，引入数据库范式中的 3NF/BCNF 概念，或转向 SQL 介绍。

Specific Suggestions for Student's Needs 针对学生需求的具体建议

Database Design: 数据库设计：

When reviewing normalization, practice converting a specific, complex, multi-column relationship into separate 3NF tables to reinforce relational design. 在复习范式时，练习将特定、复杂的多列关系转换为单独的 3NF 表，以加强关系设计。

Programming Logic & Bitwise: 编程逻辑与位运算：

For C++ bitwise problems, spend time verifying how standard integer limits (like INT_MAX) affect results compared to Python's dynamic integers, especially concerning N-1 operations on negative numbers. 对于 C++ 位运算问题，花时间验证标准的整数限制（如 INT_MAX）与 Python 的动态整数相比如何影响结果，特别是关于负数的 N-1 操作。

Recommended Supplementary Learning Resources or Homework 推荐的补充学习资源或家庭作业

Review the derivation of the 'Power of Two' solution (N & (N-1) == 0) and attempt a similar bit manipulation problem from an easy/medium list on LeetCode. 复习“二的幂”解决方案的推导（N & (N-1) == 0），并尝试在 LeetCode 简单/中等列表中解决一个类似的位操作问题。
Look up examples of tables that would require moving into 3NF to identify transitive dependencies. 查找需要进入 3NF 才能识别传递依赖的表示例。